constant engine
The Constant Engine is a reproducible computational implementation of the Transform Dictionary. It combines a finite set of geometric and algebraic inputs according to two constructive rules—the hyperbolic partition equation and the binomial constructor—to produce and evaluate proposed closed-form expressions for all 288 constants of Nature. Each result is compared directly with the corresponding CODATA 2022 value. It therefore provides a direct computational test of the central claim of this project: that all 288 constants of Nature can be constructed as a coherent, mutually constrained system within a common geometric framework.
Download CodeDownload EvaluatorDownload 288 RecipesDownload Input ParametersDownload Latest OutputOpen Raw Code
Build Script
from __future__ import annotations
import csv
import math
import re
import yaml
import sys
import os
from decimal import Decimal, ROUND_FLOOR, getcontext
from pathlib import Path
from typing import Dict, Any, List, Tuple
from collections.abc import Mapping
import mpmath as mp
from evaluator import evaluate_constant, Quantity, parse_dimension
# ------------------------------------------------------------
# Precision
# ------------------------------------------------------------
mp.mp.dps = 180
PRINT_DIGITS = 15
CSV_DIGITS = 120
def require_effectively_real(
cid: str,
x: Any,
*,
abs_tol: float = 1e-15,
rel_tol: float = 1e-18,
) -> Any:
"""
Treat tiny imaginary parts as numerical residue and drop them.
Raise only when the imaginary part is meaningfully nonzero.
- abs_tol handles near-zero values
- rel_tol handles scaling with magnitude
"""
# mpmath complex
if isinstance(x, mp.mpc):
scale = max(mp.mpf("1.0"), abs(x.real))
thresh = max(mp.mpf(abs_tol), mp.mpf(rel_tol) * scale)
if abs(x.imag) <= thresh:
return x.real
raise ValueError(
f"{cid} produced a non-real value "
f"(imag={mp.nstr(x.imag, 20)}, thresh={mp.nstr(thresh, 20)}): {x!r}"
)
# python complex
if isinstance(x, complex):
scale = max(1.0, abs(x.real))
thresh = max(abs_tol, rel_tol * scale)
if abs(x.imag) <= thresh:
return x.real
raise ValueError(
f"{cid} produced a non-real value "
f"(imag={x.imag:.6g}, thresh={thresh:.6g}): {x!r}"
)
# real already
return x
def as_display_real(cid: str, x: Any) -> Any:
"""
Normalize values for display/reporting:
- If x is complex (mp or python), drop tiny imaginary residue using the same tolerances
- Otherwise return x unchanged
"""
if isinstance(x, (mp.mpc, complex)):
return require_effectively_real(cid, x, abs_tol=1e-12, rel_tol=1e-20)
return x
def expected_kind_of(recipe: Dict[str, Any]) -> str:
return (recipe.get("expected_kind", "measured") or "measured").strip().lower()
# ------------------------------------------------------------
# Paths
# ------------------------------------------------------------
HERE = Path(__file__).resolve().parent
ENGINE_ROOT = HERE.parent
SYMBOLS_CSV = ENGINE_ROOT / "symbols" / "symbols.csv"
GENERATED_SYMBOLS_CSV = ENGINE_ROOT / "symbols" / "generated_symbols.csv"
RECIPES_YAML = ENGINE_ROOT / "recipes" / "constants.yaml"
# ------------------------------------------------------------
# Terminal colors
# ------------------------------------------------------------
FORCE_COLOR = os.environ.get("FORCE_COLOR", "").lower() in {
"1",
"true",
"yes",
}
NO_COLOR = "NO_COLOR" in os.environ
USE_COLOR = (sys.stdout.isatty() or FORCE_COLOR) and not NO_COLOR
GREEN = "\033[92m" if USE_COLOR else ""
YELLOW = "\033[93m" if USE_COLOR else ""
ORANGE = "\033[38;5;214m" if USE_COLOR else ""
RED = "\033[91m" if USE_COLOR else ""
RESET = "\033[0m" if USE_COLOR else ""
SIGMA_LIMIT = 5.2
# ------------------------------------------------------------
# Formatting: ALWAYS scientific notation for display
# ------------------------------------------------------------
_SUPERS = str.maketrans("0123456789-", "⁰¹²³⁴⁵⁶⁷⁸⁹⁻")
def _to_float_for_display(x: Any) -> float:
# Only for display/reporting; compute path stays mp.
try:
if isinstance(x, mp.mpc):
return float(x.real)
if isinstance(x, mp.mpf):
return float(x)
except Exception:
pass
return float(x)
def sci_pretty(x: object, sig: int = 15) -> str:
"""
Pretty scientific notation:
mantissa × 10^exponent
Display-only. Compute precision is handled by mpmath everywhere else.
"""
# mpmath complex
if isinstance(x, mp.mpc):
if x.imag != 0:
a = mp.nstr(x.real, sig)
b = mp.nstr(abs(x.imag), sig)
sign = "+" if x.imag >= 0 else "-"
return f"({a}{sign}{b}j)"
x = x.real
# python complex
if isinstance(x, complex):
if abs(x.imag) > 1e-16:
return f"({x.real:.{sig}e}{'+' if x.imag >= 0 else '-'}{abs(x.imag):.{sig}e}j)"
x = x.real
try:
xf = _to_float_for_display(x) # display
except Exception:
return str(x)
if xf == 0.0:
return f"0 × 10^{0}"
sign = "-" if xf < 0 else ""
ax = abs(xf)
s = f"{ax:.{sig - 1}e}"
mant_s, exp_s = s.split("e")
exp10 = int(exp_s)
return f"{sign}{mant_s} × 10^{str(exp10).translate(_SUPERS)}"
def sci_precise(x: Any, sig: int = PRINT_DIGITS) -> str:
"""
Format every real value in normalized scientific notation:
mantissa × 10^exponent
This stays in mpmath precision and never converts through float.
"""
def format_real(value: Any) -> str:
if isinstance(value, mp.mpf):
v = value
else:
v = mp.mpf(str(value))
if not mp.isfinite(v):
return mp.nstr(v, n=sig)
if v == 0:
return f"0 × 10^{str(0).translate(_SUPERS)}"
exp10 = int(mp.floor(mp.log10(abs(v))))
mantissa = v / mp.power(10, exp10)
mantissa_str = mp.nstr(
mantissa,
n=sig,
strip_zeros=False,
)
# Rounding can occasionally turn 9.999... into 10.000...
# Renormalize in that case.
if abs(mp.mpf(mantissa_str)) >= 10:
exp10 += 1
mantissa /= 10
mantissa_str = mp.nstr(
mantissa,
n=sig,
strip_zeros=False,
)
exponent_str = str(exp10).translate(_SUPERS)
return f"{mantissa_str} × 10^{exponent_str}"
if isinstance(x, mp.mpc):
if x.imag == 0:
return format_real(x.real)
real = format_real(x.real)
imag = format_real(abs(x.imag))
sign = "+" if x.imag >= 0 else "-"
return f"({real} {sign} {imag}j)"
if isinstance(x, complex):
return sci_precise(
mp.mpc(
mp.mpf(str(x.real)),
mp.mpf(str(x.imag)),
),
sig=sig,
)
return format_real(x)
def sci_csv(x: Any, sig: int = 60) -> str:
"""
Scientific notation string for CSV.
Uses mpmath printing if value is mp.mpf/mp.mpc, so digits are not truncated.
"""
# mpmath complex
if isinstance(x, mp.mpc):
if x.imag == 0:
return mp.nstr(x.real, n=sig, strip_zeros=False)
a = mp.nstr(x.real, n=sig, strip_zeros=False)
b = mp.nstr(abs(x.imag), n=sig, strip_zeros=False)
sign = "+" if x.imag >= 0 else "-"
return f"({a}{sign}{b}j)"
# mpmath real
if isinstance(x, mp.mpf):
return mp.nstr(x, n=sig, strip_zeros=False)
# python complex
if isinstance(x, complex):
if x.imag == 0.0:
return f"{x.real:.{sig}e}"
sign = "+" if x.imag >= 0 else "-"
return f"({x.real:.{sig}e}{sign}{abs(x.imag):.{sig}e}j)"
# python real
return f"{float(x):.{sig}e}"
# ------------------------------------------------------------
# Parsing CODATA-style "measured" strings
# ------------------------------------------------------------
_CODATA_RE = re.compile(
r"""
^\s*
(?P<mant>[+-]?\d+(?:\.\d+)?)
(?:\((?P<unc>\d+)\))?
(?:
[eE](?P<exp>[+-]?\d+)
| [dD](?P<exp2>[+-]?\d+)
| \s*E(?P<exp3>[+-]?\d+)
)?
\s*$
""",
re.VERBOSE,
)
_SUBFACT_CALL_RE = re.compile(r"^\s*subfact\(\s*(\d+)\s*\)\s*$")
_BANG_SUBFACT_RE = re.compile(r"^\s*!\s*(\d+)\s*$")
_POSTFIX_FACTORIAL_RE = re.compile(r"^\s*(\d+)\s*!\s*$")
_ZETA_CALL_RE = re.compile(r"^\s*zeta\(\s*[+-]?\d+\s*\)\s*$")
_GAMMA_CALL_RE = re.compile(r"^\s*(?:gamma|Γ)\(\s*(.+?)\s*\)\s*$")
_EXPR_PAREN_RE = re.compile(r"^\s*\(.+\)\s*$")
_EXP_SYMBOL_RE = re.compile(r"^\s*([+-]?)\s*([^\s]+)\s*$")
def parse_measured_value(raw: Any) -> Tuple[float, Optional[float], str, Optional[float], Optional[int], Optional[int]]:
if raw is None:
return (float("nan"), None, "(missing)", None, None, None)
if isinstance(raw, (int, float)):
v = float(raw)
return (v, None, sci_pretty(v), None, None, 0)
s = str(raw).strip()
m = _CODATA_RE.match(s)
if not m:
try:
v = float(s)
return (v, None, sci_pretty(v), None, None, 0)
except Exception:
return (float("nan"), None, s, None, None, None)
mant_s = m.group("mant")
unc_s = m.group("unc")
exp_s = m.group("exp") or m.group("exp2") or m.group("exp3")
mant = float(mant_s)
exp = int(exp_s) if exp_s is not None else 0
value = mant * (10 ** exp)
sigma = None
unc_int = None
if unc_s is not None:
unc_int = int(unc_s)
decimals = len(mant_s.split(".", 1)[1]) if "." in mant_s else 0
sigma_mant = unc_int * (10 ** (-decimals))
sigma = sigma_mant * (10 ** exp)
pretty = f"{mant_s}({unc_s}) × 10^{str(exp).translate(_SUPERS)}"
else:
pretty = sci_pretty(value)
return (value, sigma, pretty, mant, unc_int, exp)
# ------------------------------------------------------------
# Digits matching for exact constants (display/reporting only)
# ------------------------------------------------------------
def digits_match_count(a: str, b: str) -> int:
a_digits = [ch for ch in a if ch.isdigit()]
b_digits = [ch for ch in b if ch.isdigit()]
n = min(len(a_digits), len(b_digits))
count = 0
for i in range(n):
if a_digits[i] == b_digits[i]:
count += 1
else:
break
return count
def computed_mantissa_digits_string(x: Any, ref_digits: str) -> str:
"""
Reporting-only: uses Decimal + float conversion to compare mantissa prefixes.
Does not affect computation of constants.
"""
if isinstance(x, (mp.mpf, mp.mpc)):
x = x.real if isinstance(x, mp.mpc) else x
x = float(x)
if isinstance(x, complex):
x = abs(x)
ref_len = sum(ch.isdigit() for ch in ref_digits)
if ref_len <= 0:
return ""
x = float(x)
if x == 0.0:
return "0" * ref_len
exp10 = int(math.floor(math.log10(abs(x))))
getcontext().prec = ref_len + 40
x_dec = Decimal(str(abs(x)))
mant_dec = x_dec / (Decimal(10) ** exp10)
scale = Decimal(10) ** (ref_len - 1)
digits_int = int((mant_dec * scale).to_integral_value(rounding=ROUND_FLOOR))
return str(digits_int).zfill(ref_len)[:ref_len]
# ------------------------------------------------------------
# Canonical factor list handling (must match evaluator.py)
# ------------------------------------------------------------
def _is_number(x: Any) -> bool:
return isinstance(x, (int, float)) and not isinstance(x, bool)
def _split_token_and_power_from_string(s: str) -> Tuple[str, Optional[str]]:
s = s.strip()
if not s:
return "", None
if _EXPR_PAREN_RE.match(s):
return s, None
depth = 0
split_at = -1
for i, ch in enumerate(s):
if ch == "(":
depth += 1
elif ch == ")" and depth > 0:
depth -= 1
elif ch == "^" and depth == 0:
split_at = i
if split_at == -1:
return s, None
tok = s[:split_at].strip()
pow_s = s[split_at + 1:].strip()
return tok, pow_s or None
def _extract_exponent_dependencies(power_str: str) -> List[str]:
"""
Returns the symbol dependencies used by an exponent.
Examples:
"-γ" -> ["γ"]
"γ" -> ["γ"]
"(-i)" -> ["i"]
"(1+γ)/2" -> ["γ"]
"1/3" -> []
"(2^0.5)" -> []
"""
s = (power_str or "").strip()
if not s:
return []
# numeric-only exponent expressions -> no symbol deps
if re.fullmatch(r"[\s0-9+\-*/^().]+", s) and any(ch.isdigit() for ch in s):
return []
try:
float(s)
return []
except ValueError:
pass
# Simple symbol exponent: optional leading sign, then one name token (no operators/parens)
m = _EXP_SYMBOL_RE.match(s)
if m:
sym = m.group(2)
if not any(ch in sym for ch in "()+*/^"):
return [sym]
# General exponent expression: extract all names inside
expr = s
if not (expr.startswith("(") and expr.endswith(")")):
expr = f"({expr})"
return _names_in_expression_token(expr)
def _iter_factor_items(factors):
if factors is None:
return
if isinstance(factors, Mapping):
for k, v in factors.items():
yield (k, v)
return
if isinstance(factors, list):
for item in factors:
if isinstance(item, (tuple, list)) and len(item) == 2:
yield (item[0], item[1])
continue
if isinstance(item, dict):
if "id" in item:
yield (item["id"], item.get("power", 1))
elif len(item) == 1:
(kk, vv), = item.items()
yield (kk, vv)
else:
raise TypeError(f"Bad factor dict item: {item!r}")
continue
if isinstance(item, str):
yield (item, 1)
continue
raise TypeError(f"Bad factor item type: {type(item).__name__}: {item!r}")
return
raise TypeError(f"Factors must be a dict or list. Got {type(factors).__name__}: {factors!r}")
# Unicode-safe: matches names like i, zhe_1, γ, etc.
_NAME_IN_EXPR_RE = re.compile(r"\b[^\W\d]\w*\b", re.UNICODE)
def _names_in_expression_token(expr: str) -> list[str]:
s = (expr or "").strip()
if s.startswith("(") and s.endswith(")"):
s = s[1:-1]
s = s.replace("m_+", "m_plus")
names = _NAME_IN_EXPR_RE.findall(s)
out: list[str] = [("m_+" if n == "m_plus" else n) for n in names]
blacklist = {"Im", "Re", "log", "ln"}
return [n for n in out if n not in blacklist]
# ------------------------------------------------------------
# Dependencies (tokens)
# ------------------------------------------------------------
def collect_dependencies(recipe: Dict[str, Any]) -> Tuple[List[str], List[str]]:
display_set: set[str] = set()
required_set: set[str] = set()
def add_factor_list(lst: Any):
for tok, pow_val in _iter_factor_items(lst):
if _is_number(tok):
continue
tok_s = str(tok).strip()
if not tok_s:
continue
if tok_s == "ten":
raise ValueError("Recipe contains forbidden token 'ten'. It is not allowed.")
if _EXPR_PAREN_RE.match(tok_s):
for nm in _names_in_expression_token(tok_s):
display_set.add(nm)
required_set.add(nm)
if pow_val is not None:
for sym in _extract_exponent_dependencies(str(pow_val).strip()):
display_set.add(sym)
required_set.add(sym)
continue
try:
float(tok_s)
continue
except ValueError:
pass
base_tok, tok_pow = _split_token_and_power_from_string(tok_s)
base_tok = base_tok.strip()
try:
float(base_tok)
continue
except ValueError:
pass
if _EXPR_PAREN_RE.match(base_tok):
for nm in _names_in_expression_token(base_tok):
display_set.add(nm)
required_set.add(nm)
else:
if (
_ZETA_CALL_RE.match(base_tok)
or _SUBFACT_CALL_RE.match(base_tok)
or _BANG_SUBFACT_RE.match(base_tok)
or _POSTFIX_FACTORIAL_RE.match(base_tok)
or _GAMMA_CALL_RE.match(base_tok)
):
# function tokens are display-only; they are not symbols loaded from CSV
display_set.add(base_tok)
else:
display_set.add(base_tok)
required_set.add(base_tok)
if tok_pow:
for sym in _extract_exponent_dependencies(tok_pow):
display_set.add(sym)
required_set.add(sym)
if pow_val is not None:
for sym in _extract_exponent_dependencies(str(pow_val).strip()):
display_set.add(sym)
required_set.add(sym)
eg = recipe["external_geometry"]
eb = recipe["external_boundary"]
ig = recipe["inversion_geometry"]
add_factor_list(eg.get("numerator"))
add_factor_list(eg.get("denominator"))
add_factor_list(eb.get("numerator"))
add_factor_list(eb.get("denominator"))
add_factor_list(ig.get("numerator"))
add_factor_list(ig.get("denominator"))
display_set.add("IB")
required_set.add("IB")
rt = recipe["root_transform"]["id"]
DERIVED_EXPAND = {"zhe_1_minus_zhe_2": ["zhe_1", "zhe_2"]}
if rt in DERIVED_EXPAND:
for t in DERIVED_EXPAND[rt]:
display_set.add(t)
required_set.add(t)
else:
rt_s = str(rt).strip()
if any(op in rt_s for op in "+-*/()^ "):
for nm in _names_in_expression_token(f"({rt_s})"):
display_set.add(nm)
required_set.add(nm)
else:
display_set.add(rt_s)
required_set.add(rt_s)
preferred = ["l_p", "t_p", "q_p", "T_p", "m_p", "G_Gi"]
display_ordered = [t for t in preferred if t in display_set]
remaining = sorted(t for t in display_set if t not in preferred and t != "IB")
display_ordered += remaining + ["IB"]
required_ordered = [t for t in preferred if t in required_set]
required_remaining = sorted(t for t in required_set if t not in preferred and t != "IB")
required_ordered += required_remaining + ["IB"]
return display_ordered, required_ordered
def _digits_only(s: str) -> str:
return "".join(ch for ch in (s or "") if ch.isdigit())
def expected_prefix_from_digits(expected_value: float, expected_digits: str) -> tuple[float, int, int]:
digs = _digits_only(expected_digits)
sig = len(digs)
if sig <= 0:
return (expected_value, int(math.floor(math.log10(abs(expected_value)))) if expected_value else 0, 0)
if expected_value == 0.0:
exp10 = 0
sign = 1.0
else:
exp10 = int(math.floor(math.log10(abs(expected_value))))
sign = -1.0 if expected_value < 0 else 1.0
mant_int = int(digs)
mant = mant_int / (10 ** (sig - 1))
expected_prefix = sign * mant * (10 ** exp10)
return (expected_prefix, exp10, sig)
def classify_by_last_digit_units(expected_prefix: float, computed: float, exp10: int, sig_digits: int) -> tuple[str, float, float]:
if sig_digits <= 0:
return ("fail", float("inf"), float("nan"))
step = 10 ** (exp10 - (sig_digits - 1))
err = abs(computed - expected_prefix)
k = err / step if step != 0 else float("inf")
if k < 1:
return ("full", k, step)
elif k < 10:
return ("almost", k, step)
else:
return ("fail", k, step)
# ------------------------------------------------------------
# Verification report per constant
# ------------------------------------------------------------
def verify_and_format(recipe: Dict[str, Any], computed: Quantity) -> List[str]:
lines: List[str] = []
dim = recipe.get("dimension", "-")
cid = recipe.get("constant_id", "?")
cv_disp = as_display_real(cid, computed.value)
lines.append(f"computed: {sci_precise(cv_disp, PRINT_DIGITS)} {dim}")
expected_kind = expected_kind_of(recipe)
expected_value = recipe.get("expected_value")
if expected_value is None:
lines.append("expected: (missing)")
return lines
if expected_kind == "exact":
label = recipe.get("expected_digits_label", "exact")
ref_digits = recipe.get("expected_digits")
try:
ev = float(expected_value)
lines.append(f"expected: {sci_pretty(ev)} {dim} ({label})")
except Exception:
ev = None
lines.append(f"expected: {expected_value} {dim} ({label})")
if ref_digits and ev is not None:
cv = as_display_real(cid, computed.value)
cv_f = float(cv) # reporting comparison
expected_prefix, exp10, sig = expected_prefix_from_digits(float(ev), ref_digits)
label2, _, _ = classify_by_last_digit_units(expected_prefix, cv_f, exp10, sig)
comp_digits = computed_mantissa_digits_string(cv_f, ref_digits)
match_n = digits_match_count(comp_digits, ref_digits)
if label2 == "full":
match_label = "full match"
elif label2 == "almost":
match_label = "almost-full match"
else:
match_label = "not a match"
missing_digits = max(0, sig - match_n)
if missing_digits <= 1:
match_color = GREEN
elif missing_digits == 2:
match_color = YELLOW
elif missing_digits == 3:
match_color = ORANGE
else:
match_color = ""
match_reset = RESET if match_color else ""
lines.append(
f"digits: {match_color}"
f"{match_label} ({match_n}/{sig})"
f"{match_reset}"
)
else:
if ev is not None:
cv_f = float(computed.value.real) if isinstance(computed.value, mp.mpc) else float(computed.value)
abs_err = abs(cv_f - ev)
lines.append(f"abs err: {sci_pretty(abs_err)}")
else:
lines.append("abs err: (unavailable)")
return lines
# measured
codata_label = recipe.get("expected_digits_label", "measured")
ev, sigma, ev_pretty, mant, _, exp = parse_measured_value(expected_value)
lines.append(f"expected: {ev_pretty} {dim} ({codata_label})")
cv = as_display_real(cid, computed.value)
# Preserve mpmath precision when calculating the displayed error.
cv_mp = cv if isinstance(cv, mp.mpf) else mp.mpf(str(cv))
if mant is not None and exp is not None:
ev_mp = mp.mpf(str(mant)) * mp.power(10, exp)
else:
ev_mp = mp.mpf(str(ev))
signed_err_mp = cv_mp - ev_mp
signed_err = float(signed_err_mp)
abs_err_mp = abs(signed_err_mp)
lines.append(
f"abs err: {sci_precise(abs_err_mp, PRINT_DIGITS)} {dim}"
)
if sigma is not None and sigma > 0:
z = signed_err / sigma
if abs(z) < 0.0005:
z = 0.0
lines.append(f"sigma: {z:+.2f}")
sigma_label = f"{SIGMA_LIMIT:g}"
lines.append(
f"within {sigma_label}σ: {GREEN}yes{RESET}"
if abs(z) <= SIGMA_LIMIT
else f"within {sigma_label}σ: {RED}no{RESET}"
)
else:
lines.append("sigma: (missing)")
lines.append("within 5σ: (missing)")
return lines
def constant_passes(recipe: Dict[str, Any], computed: Quantity) -> bool:
expected_kind = expected_kind_of(recipe)
expected_value = recipe.get("expected_value")
if expected_value is None:
return False
cv = computed.value
if isinstance(cv, (mp.mpc, complex)):
try:
cv = require_effectively_real(recipe.get("constant_id", "?"), cv)
except Exception:
return False
cv_f = float(cv) # summary classification
if expected_kind == "exact":
ref_digits = recipe.get("expected_digits")
if not ref_digits:
return False
try:
ev = float(expected_value)
except Exception:
return False
expected_prefix, exp10, sig = expected_prefix_from_digits(ev, ref_digits)
label2, _, _ = classify_by_last_digit_units(expected_prefix, cv_f, exp10, sig)
return label2 in {"full", "almost"}
ev, sigma, _, _, _, _ = parse_measured_value(expected_value)
if sigma is None or sigma <= 0 or math.isnan(ev):
return False
signed_err = cv_f - float(ev)
z = signed_err / float(sigma)
if abs(z) < 0.0005:
z = 0.0
return abs(z) <= SIGMA_LIMIT
# ------------------------------------------------------------
# CSV IO
# ------------------------------------------------------------
def _parse_csv_number_to_mp(value: str) -> Any:
"""
Parse:
- real: "1.23e-4"
- complex: "a+bj" or "a-bj" or "(a+bj)" or "(a-bj)" (a,b may be scientific notation)
- pure imaginary: "4j" or "-4j" (and parenthesized forms)
Returns: mp.mpf or mp.mpc
"""
v_str = (value or "").strip()
if not v_str:
raise ValueError("Empty numeric string")
s = v_str.replace("J", "j").strip()
# strip optional parentheses
if s.startswith("(") and s.endswith(")"):
s = s[1:-1].strip()
# complex / imaginary
if "j" in s:
if not s.endswith("j"):
raise ValueError(f"Bad complex literal (missing trailing j): {v_str!r}")
body = s[:-1].strip() # drop trailing 'j'
# Find separator between real and imag: last + or - not part of exponent
split_idx = None
for i in range(len(body) - 1, 0, -1):
if body[i] in "+-" and body[i - 1] not in "eE":
split_idx = i
break
# pure imaginary like "4j" or "-4j"
if split_idx is None:
a = mp.mpf("0")
b = mp.mpf(body) if body else mp.mpf("1") # "j" -> 1j (rare)
return mp.mpc(a, b)
a_s = body[:split_idx].strip()
b_s = body[split_idx:].strip()
a = mp.mpf(a_s) if a_s else mp.mpf("0")
b = mp.mpf(b_s) if b_s else mp.mpf("0")
return mp.mpc(a, b)
# real
return mp.mpf(s)
def _parse_csv_dimension(dim: str) -> Dict[str, int]:
"""
CSV convention:
- "-" means dimensionless
- "" also means dimensionless
"""
d = (dim or "").strip()
if d in {"", "-"}:
return {}
return parse_dimension(d)
def load_symbols(path: Path) -> Dict[str, Quantity]:
symbols: Dict[str, Quantity] = {}
if not path.exists():
return symbols
with path.open("r", encoding="utf-8") as f:
reader = csv.DictReader(f)
for row in reader:
token = (row.get("token") or "").strip()
value = (row.get("value") or "").strip()
dim = (row.get("dimension") or "").strip()
if token and value:
v = _parse_csv_number_to_mp(value)
symbols[token] = Quantity(v, _parse_csv_dimension(dim))
if token == "m_+":
symbols["m_plus"] = symbols[token]
# HARD COHERENCE GUARANTEE FOR OMEGAS
if "omega_2" in symbols and "phi_i" in symbols:
o2 = symbols["omega_2"]
ph = symbols["phi_i"]
if o2.units != {}:
raise ValueError(f"omega_2 must be dimensionless; got units={o2.units}")
if ph.units != {}:
raise ValueError(f"phi_i must be dimensionless; got units={ph.units}")
symbols["omega_1"] = Quantity(o2.value * ph.value, {})
return symbols
def load_recipes(path: Path) -> List[Dict[str, Any]]:
data = yaml.safe_load(path.read_text(encoding="utf-8"))
recipes = data.get("constants", [])
seen: Dict[int, str] = {}
for recipe in recipes:
if "recipe_number" not in recipe:
raise ValueError(
f"Recipe missing recipe_number: {recipe.get('constant_id', '?')}"
)
n = int(recipe["recipe_number"])
cid = str(recipe.get("constant_id", "?"))
if n in seen:
raise ValueError(
f"Duplicate recipe_number {n}: {seen[n]} and {cid}"
)
seen[n] = cid
expected = set(range(1, len(recipes) + 1))
actual = set(seen.keys())
if actual != expected:
missing = sorted(expected - actual)
extra = sorted(actual - expected)
raise ValueError(
f"Recipe numbers must be exactly 1..{len(recipes)}. "
f"Missing={missing}; extra={extra}"
)
return sorted(recipes, key=lambda r: int(r["recipe_number"]))
def reset_generated_symbols_file() -> None:
GENERATED_SYMBOLS_CSV.parent.mkdir(parents=True, exist_ok=True)
with GENERATED_SYMBOLS_CSV.open("w", encoding="utf-8", newline="") as f:
writer = csv.writer(f)
writer.writerow(["token", "value", "dimension"])
def append_generated_symbols(rows: List[Tuple[str, Quantity, str]]) -> None:
with GENERATED_SYMBOLS_CSV.open("a", encoding="utf-8", newline="") as f:
writer = csv.writer(f)
for token, q, dim in rows:
writer.writerow([token, sci_csv(q.value, sig=CSV_DIGITS), dim or "-"])
# ------------------------------------------------------------
# Build loop
# ------------------------------------------------------------
def main() -> None:
reset_generated_symbols_file()
base_symbols = load_symbols(SYMBOLS_CSV)
symbols: Dict[str, Quantity] = dict(base_symbols)
recipes = load_recipes(RECIPES_YAML)
recipe_by_id: Dict[str, Dict[str, Any]] = {r["constant_id"]: r for r in recipes}
unresolved = {r["constant_id"] for r in recipes}
pass_number = 0
total_built = 0
built_exact = 0
built_measured = 0
passed_exact = 0
failed_exact = 0
passed_measured = 0
failed_measured = 0
failed_exact_ids: List[str] = []
failed_measured_ids: List[str] = []
build_errors: Dict[str, str] = {} # <-- persist across passes
built_records: Dict[str, Tuple[int, Quantity, str]] = {}
while True:
pass_number += 1
built_this_pass: List[Tuple[str, Quantity, str]] = []
blocked: Dict[str, List[str]] = {}
print(f"\n=== Build pass {pass_number} ===")
for recipe in recipes:
cid = recipe["constant_id"]
if cid in symbols:
unresolved.discard(cid)
continue
_, deps_required = collect_dependencies(recipe)
missing = [t for t in deps_required if t not in symbols]
if missing:
blocked[cid] = missing
continue
try:
value_q = evaluate_constant(recipe, symbols, inversion_boundary_token="IB")
except Exception as e:
msg = f"{type(e).__name__}: {e}"
build_errors[cid] = msg
print(f"ERROR building {cid}: {msg}")
continue
dim = recipe.get("dimension", "-")
# Force away tiny imaginary numerical residue at the source
value_real = as_display_real(cid, value_q.value)
if value_real is not value_q.value:
value_q = Quantity(value_real, value_q.units)
built_this_pass.append((cid, value_q, dim))
built_records[cid] = (pass_number, value_q, dim)
symbols[cid] = value_q
unresolved.discard(cid)
total_built += 1
kind = expected_kind_of(recipe)
ok = constant_passes(recipe, value_q)
if kind == "exact":
built_exact += 1
if ok:
passed_exact += 1
else:
failed_exact += 1
failed_exact_ids.append(cid)
else:
built_measured += 1
if ok:
passed_measured += 1
else:
failed_measured += 1
failed_measured_ids.append(cid)
if not built_this_pass:
unresolved_exact = 0
unresolved_measured = 0
for cid in unresolved:
r = recipe_by_id.get(cid, {})
kind = expected_kind_of(r)
if kind == "exact":
unresolved_exact += 1
else:
unresolved_measured += 1
total_exact = built_exact + unresolved_exact
total_measured = built_measured + unresolved_measured
failed_exact_total = failed_exact + unresolved_exact
failed_measured_total = failed_measured + unresolved_measured
print(f"\n{total_built} constants built.")
print(f" {total_exact} exact, {GREEN}{passed_exact} passed{RESET}, {ORANGE}{failed_exact_total} failed{RESET}")
print(f" {total_measured} measured, {GREEN}{passed_measured} passed{RESET}, {ORANGE}{failed_measured_total} failed{RESET}")
print("\nNo further constants can be built.")
if unresolved:
print("\nUnresolved constants:")
for cid in sorted(unresolved):
if cid in build_errors:
print(f" {cid}: build error: {build_errors[cid]}")
continue
miss = blocked.get(cid, [])
if miss:
print(f" {cid}: missing {', '.join(miss)}")
else:
print(f" {cid}: missing (unknown)")
if failed_exact_ids or failed_measured_ids:
print("\nFailed constants:")
if failed_exact_ids:
print(" exact:")
for cid in failed_exact_ids:
r = recipe_by_id.get(cid, {})
name = r.get("display_name", cid)
print(f" {cid} — {name}")
if failed_measured_ids:
print(" measured:")
for cid in failed_measured_ids:
r = recipe_by_id.get(cid, {})
name = r.get("display_name", cid)
print(f" {cid} — {name}")
break
append_generated_symbols(built_this_pass)
print("\n=== Constants in official order ===")
for recipe in recipes:
cid = recipe["constant_id"]
if cid not in built_records:
continue
pass_built, value, dim = built_records[cid]
recipe_number = int(recipe.get("recipe_number", 0))
name = recipe.get("display_name", cid)
deps_display, _ = collect_dependencies(recipe)
print(f"\n{recipe_number:03}. {cid} — {name} [built on pass {pass_built}]")
print(f"deps: {', '.join(deps_display)}")
for line in verify_and_format(recipe, value):
print(line)
print("\nBuild complete.")
if __name__ == "__main__":
main()
Evaluator
from __future__ import annotations
import ast
import numbers
import operator as _op
import re
from dataclasses import dataclass
from typing import Any, Dict, Iterable, Tuple, Union
from collections.abc import Mapping
import mpmath as mp
# ============================================================
# Precision
# ============================================================
mp.mp.dps = 80 # match build_all.py; raise if you want more digits
# ============================================================
# Types
# ============================================================
Units = Dict[str, mp.mpf]
DIMENSIONLESS: Units = {}
FactorToken = Union[str, int, float] # we ACCEPT float inputs but immediately convert to mp
FactorItem = Union[str, int, float, Dict[str, Any]]
# ============================================================
# Quantity: value + units
# ============================================================
@dataclass(frozen=True)
class Quantity:
# value can be mp.mpf (real) or mp.mpc (complex), or python numeric in legacy cases
value: Any
units: Units # base unit -> exponent (mp.mpf)
# ============================================================
# Unit helpers (mp-safe)
# ============================================================
def _mp(x: Any) -> mp.mpf:
"""Convert to mp.mpf without going through float."""
if isinstance(x, mp.mpf):
return x
if isinstance(x, mp.mpc):
if x.imag != 0:
raise ValueError(f"Expected real mp.mpf, got complex {x!r}")
return x.real
if isinstance(x, complex):
if x.imag != 0:
raise ValueError(f"Expected real, got complex {x!r}")
return mp.mpf(str(x.real))
# int/float/Decimal/str
return mp.mpf(str(x))
def _clean_units(u: Units) -> Units:
"""Drop tiny exponents and normalize to mp.mpf."""
out: Units = {}
tol = mp.mpf("1e-40")
for k, v in u.items():
vv = v if isinstance(v, mp.mpf) else mp.mpf(str(v))
if abs(vv) > tol:
out[k] = vv
return out
def units_mul(a: Units, b: Units, sign: Any = mp.mpf("1")) -> Units:
out: Units = dict(a)
sgn = sign if isinstance(sign, mp.mpf) else mp.mpf(str(sign))
for k, v in b.items():
vv = v if isinstance(v, mp.mpf) else mp.mpf(str(v))
out[k] = out.get(k, mp.mpf("0")) + sgn * vv
return _clean_units(out)
def _as_mpc(x: Any) -> mp.mpc:
if isinstance(x, mp.mpc):
return x
if isinstance(x, mp.mpf):
return mp.mpc(x, mp.mpf("0"))
if isinstance(x, complex):
return mp.mpc(mp.mpf(str(x.real)), mp.mpf(str(x.imag)))
# int/float/Decimal/str
return mp.mpc(mp.mpf(str(x)), mp.mpf("0"))
def _is_effectively_integer(p: mp.mpf, tol: mp.mpf = mp.mpf("1e-30")) -> Tuple[bool, int]:
n = int(mp.nint(p))
if abs(p - mp.mpf(n)) <= tol:
return True, n
return False, 0
def units_pow(u: Units, p: Any) -> Units:
pr = _mp(p)
ok_int, n = _is_effectively_integer(pr)
if ok_int:
nn = mp.mpf(n)
return _clean_units({k: (v * nn) for k, v in u.items()})
return _clean_units({k: (v * pr) for k, v in u.items()})
# ============================================================
# Quantity arithmetic (mp-safe)
# ============================================================
def q_pow(a: Quantity, p: Any) -> Quantity:
"""
Raise a Quantity to a power.
Rules:
- Real exponent: units are exponentiated normally.
- Complex exponent: base must be dimensionless (units must be {}).
(Complex powers of dimensionful quantities are not supported.)
"""
# Convert exponent to mp.mpc
if isinstance(p, (int, float, mp.mpf, complex, mp.mpc)):
pr = _as_mpc(p)
elif isinstance(p, str):
pr = _as_mpc(eval_quantity_expr(p, {}).value)
else:
raise TypeError(f"Unsupported exponent type: {type(p)}")
# Units handling
if pr.imag != 0:
if a.units:
raise ValueError(
f"Complex exponent requires dimensionless base; got units={a.units}"
)
new_units = DIMENSIONLESS
else:
new_units = units_pow(a.units, pr.real)
# Integer exponent optimization (real-only)
if pr.imag == 0:
ok_int, n = _is_effectively_integer(pr.real)
if ok_int:
if n == 0:
return Quantity(mp.mpf("1"), DIMENSIONLESS)
base = _as_mpc(a.value)
if n > 0:
out = mp.mpc(1)
for _ in range(n):
out *= base
else:
out = mp.mpc(1)
for _ in range(-n):
out *= base
out = mp.mpc(1) / out
if out.imag == 0:
return Quantity(out.real, new_units)
return Quantity(out, new_units)
# General exponent (real non-integer OR complex)
vv = _as_mpc(a.value)
res = mp.power(vv, pr)
if res.imag == 0:
return Quantity(res.real, new_units)
return Quantity(res, new_units)
def q_mul(a: Quantity, b: Quantity) -> Quantity:
va = _as_mpc(a.value)
vb = _as_mpc(b.value)
out = va * vb
new_units = units_mul(a.units, b.units, mp.mpf("1"))
if out.imag == 0:
return Quantity(out.real, new_units)
return Quantity(out, new_units)
def q_div(a: Quantity, b: Quantity) -> Quantity:
va = _as_mpc(a.value)
vb = _as_mpc(b.value)
out = va / vb
new_units = units_mul(a.units, b.units, mp.mpf("-1"))
if out.imag == 0:
return Quantity(out.real, new_units)
return Quantity(out, new_units)
def q_add(a: Quantity, b: Quantity) -> Quantity:
if a.units != b.units:
raise ValueError(f"Unit mismatch in addition: {a.units} vs {b.units}")
va = _as_mpc(a.value)
vb = _as_mpc(b.value)
out = va + vb
if out.imag == 0:
return Quantity(out.real, dict(a.units))
return Quantity(out, dict(a.units))
def q_sub(a: Quantity, b: Quantity) -> Quantity:
return q_add(a, Quantity(-_as_mpc(b.value), dict(b.units)))
def _q_from_number(x: Any) -> Quantity:
return Quantity(mp.mpf(str(x)), {})
# ============================================================
# Dimension parser (for symbols CSV)
# ============================================================
def parse_dimension(dim: str) -> Units:
dim = (dim or "").strip()
if dim in ("", "-"):
return {}
# ------------------------------------------------------------
# Expand common derived unit labels into base-unit expressions
# ------------------------------------------------------------
UNIT_ALIASES: dict[str, str] = {
# mechanics
"Hz": "1/s",
"N": "m*kg/s^2",
"Pa": "kg/(m*s^2)",
"pascal": "kg/(m*s^2)",
"J": "m^2*kg/s^2",
"W": "m^2*kg/s^3",
# EM (base units: m, kg, s, C)
"V": "m^2*kg/(s^2*C)",
"ohm": "m^2*kg/(s*C^2)",
"Ω": "m^2*kg/(s*C^2)",
"S": "s*C^2/(m^2*kg)", # siemens
"F": "s^2*C^2/(m^2*kg)", # farad
"H": "m^2*kg/(C^2)", # henry
"T": "kg/(s^2*C)", # tesla
"Wb": "m^2*kg/(s^2*C)", # weber
}
s = dim.replace("·", "*").replace(" ", "")
# Expand aliases safely (whole-token replacements), iterate to stability.
for _ in range(8):
changed = False
for key, repl in UNIT_ALIASES.items():
# word boundary for identifier-like keys, raw escape otherwise (e.g. Ω)
if key.isidentifier():
pat = rf"\b{re.escape(key)}\b"
else:
pat = re.escape(key)
s2 = re.sub(pat, f"({repl})", s)
if s2 != s:
s = s2
changed = True
if not changed:
break
# ------------------------------------------------------------
# Proper parser with parentheses + */ and exponents
# Grammar:
# expr := term (('*'|'/') term)*
# term := factor ('^' power)?
# factor:= NAME | NUMBER | '(' expr ')'
# power supports: integer, decimal, or fraction like 3/2
# ------------------------------------------------------------
i = 0
n = len(s)
def peek() -> str:
return s[i] if i < n else ""
def consume(ch: str) -> None:
nonlocal i
if peek() != ch:
raise ValueError(f"Bad dimension syntax near {s[max(0,i-10):i+10]!r}: expected '{ch}'")
i += 1
def skip_ws() -> None:
nonlocal i
while i < n and s[i].isspace():
i += 1
def parse_name_or_number() -> tuple[str, bool]:
"""
Returns (token, is_number_literal)
token is:
- unit name like "kg"
- or number literal like "1"
"""
nonlocal i
skip_ws()
if i >= n:
raise ValueError("Unexpected end of dimension string")
# number literal (only "1" really matters in dimensions)
if s[i].isdigit() or s[i] == ".":
j = i
while j < n and (s[j].isdigit() or s[j] == "."):
j += 1
tok = s[i:j]
i = j
return tok, True
# name (allow underscores)
if s[i].isalpha() or s[i] == "_":
j = i
while j < n and (s[j].isalnum() or s[j] == "_"):
j += 1
tok = s[i:j]
i = j
return tok, False
raise ValueError(f"Unexpected character in dimension: {s[i]!r}")
def parse_power_value() -> mp.mpf:
nonlocal i
skip_ws()
# optional parentheses around the exponent
if peek() == "(":
consume("(")
p = parse_power_value()
skip_ws()
consume(")")
return p
# optional sign
sign = mp.mpf("1")
if peek() == "+":
consume("+")
elif peek() == "-":
consume("-")
sign = mp.mpf("-1")
# read a number (int/decimal)
j = i
while j < n and (s[j].isdigit() or s[j] == "."):
j += 1
if j == i:
raise ValueError(f"Missing exponent number near: {s[max(0, i - 10):i + 10]!r}")
a_str = s[i:j]
i = j
a = mp.mpf(a_str)
skip_ws()
# Treat "/" as an exponent fraction ONLY if the next non-space char is a digit or "."
# This prevents misreading C^2/(m^2*kg) as an exponent like 2/(...)
if peek() == "/":
k0 = i + 1
while k0 < n and s[k0].isspace():
k0 += 1
if k0 < n and (s[k0].isdigit() or s[k0] == "."):
consume("/")
skip_ws()
k = i
while k < n and (s[k].isdigit() or s[k] == "."):
k += 1
if k == i:
raise ValueError(f"Missing denominator in exponent fraction near: {s[max(0, i - 10):i + 10]!r}")
b_str = s[i:k]
i = k
b = mp.mpf(b_str)
return sign * (a / b)
return sign * a
def units_merge(a: Units, b: Units, scale: mp.mpf) -> Units:
out = dict(a)
for k, v in b.items():
out[k] = out.get(k, mp.mpf("0")) + scale * v
return _clean_units(out)
def parse_factor() -> Units:
nonlocal i
skip_ws()
if peek() == "(":
consume("(")
u = parse_expr()
skip_ws()
consume(")")
return u
tok, is_num = parse_name_or_number()
if is_num:
# numeric literals contribute no units (only "1" is meaningful)
return {}
return {tok: mp.mpf("1")}
def parse_term() -> Units:
u = parse_factor()
skip_ws()
if peek() == "^":
consume("^")
p = parse_power_value()
# multiply all exponents in u by p
return _clean_units({k: v * p for k, v in u.items()})
return _clean_units(u)
def parse_expr() -> Units:
u = parse_term()
while True:
skip_ws()
ch = peek()
if ch == "*":
consume("*")
u2 = parse_term()
u = units_merge(u, u2, mp.mpf("1"))
continue
if ch == "/":
consume("/")
u2 = parse_term()
u = units_merge(u, u2, mp.mpf("-1"))
continue
break
return _clean_units(u)
out = parse_expr()
skip_ws()
if i != n:
raise ValueError(f"Trailing junk in dimension string near: {s[i:]!r}")
return _clean_units(out)
# ============================================================
# Exponent parsing
# ============================================================
_EXP_SYMBOL_RE = re.compile(r"^\s*([+-]?)\s*([^\s]+)\s*$")
def _exponent_from_symbol_string(power_str: str, symbols: Dict[str, Quantity]) -> mp.mpf:
"""
Supports:
"-γ" -> -symbols["γ"].value
"γ" -> +symbols["γ"].value
Enforces:
- symbol must be dimensionless
- symbol must be real-valued
"""
s = power_str.strip()
m = _EXP_SYMBOL_RE.match(s)
if not m:
raise ValueError(f"Bad exponent string: {power_str!r}")
sign_s, sym = m.group(1), m.group(2)
sign = mp.mpf("-1") if sign_s == "-" else mp.mpf("1")
if sym not in symbols:
raise KeyError(f"Exponent symbol '{sym}' not found in symbols table.")
q = symbols[sym]
if q.units != DIMENSIONLESS:
raise ValueError(f"Exponent symbol '{sym}' must be dimensionless; got units={q.units}")
v = q.value
if isinstance(v, mp.mpc):
if v.imag != 0:
raise ValueError(f"Exponent symbol '{sym}' must be real; got value={v!r}")
v = v.real
elif isinstance(v, complex):
if v.imag != 0:
raise ValueError(f"Exponent symbol '{sym}' must be real; got value={v!r}")
v = v.real
return sign * _mp(v)
def _try_eval_numeric_exponent_expr(s: str) -> mp.mpf | None:
"""
If s is a purely-numeric expression like "(2^0.5)" or "2^(1/2)" or "1/3",
evaluate it to an mp.mpf. Returns None if it contains any names/symbols.
"""
ss = s.strip()
if ss.startswith("(") and ss.endswith(")"):
ss = ss[1:-1].strip()
# normalize to python power operator
ss = ss.replace("^", "**")
# If there are any letters/underscores, it's not a pure numeric exponent.
# parse any string expression, allowing unary minus on i
def exponent_to_complex(power: Any, symbols: Dict[str, Quantity] | None = None) -> mp.mpc:
"""
Exponent parser for factor powers. This MUST support expressions like:
-i, (-i), (-1*i), 1+2*i, (1/2), etc.
Rule:
- If it's a string and not plainly numeric, evaluate it with eval_quantity_expr.
- Exponent must be dimensionless.
"""
if power is None:
return mp.mpc(1, 0)
if isinstance(power, (list, tuple)) and len(power) == 2:
return _as_mpc(_mp(power[0]) * _mp(power[1]))
if isinstance(power, (int, float, mp.mpf, complex, mp.mpc)):
return _as_mpc(power)
if isinstance(power, str):
s = power.strip()
# numeric-only exponent expressions
v_num = _try_eval_numeric_exponent_expr(s)
if v_num is not None:
return mp.mpc(v_num, 0)
# plain numeric string
try:
return mp.mpc(mp.mpf(s), 0)
except Exception:
pass
# FORCE: expression evaluation (this is the path you want)
if symbols is None:
raise ValueError(f"String exponent {power!r} requires symbols lookup.")
q = eval_quantity_expr(s, symbols)
if q.units != DIMENSIONLESS:
raise ValueError(f"Exponent must be dimensionless; got units={q.units}")
return _as_mpc(q.value)
# last resort
return mp.mpc(_mp(power), 0)
# Safe AST eval for numeric-only expressions (+-*/** and parentheses)
node = ast.parse(ss, mode="eval")
def _walk(n) -> mp.mpf:
if isinstance(n, ast.Expression):
return _walk(n.body)
if isinstance(n, ast.Constant) and isinstance(n.value, (int, float)):
return mp.mpf(str(n.value))
if isinstance(n, ast.UnaryOp) and isinstance(n.op, (ast.UAdd, ast.USub)):
v = _walk(n.operand)
return v if isinstance(n.op, ast.UAdd) else -v
if isinstance(n, ast.BinOp) and isinstance(n.op, (ast.Add, ast.Sub, ast.Mult, ast.Div, ast.Pow)):
a = _walk(n.left)
b = _walk(n.right)
if isinstance(n.op, ast.Add): return a + b
if isinstance(n.op, ast.Sub): return a - b
if isinstance(n.op, ast.Mult): return a * b
if isinstance(n.op, ast.Div): return a / b
if isinstance(n.op, ast.Pow): return mp.power(a, b)
raise ValueError(f"Bad numeric exponent expression: {s!r}")
try:
return _walk(node)
except Exception:
return None
def exponent_to_mpf(power: Any, symbols: Dict[str, Quantity] | None = None) -> mp.mpf:
"""
Accepts:
- None -> 1
- number -> that number
- [a, b] -> a*b
- string numeric like "-4" or "0.5" or "(0.5)" -> numeric
- string like "-γ" or "γ" -> symbol lookup in `symbols`
"""
if power is None:
return mp.mpf("1")
if isinstance(power, (list, tuple)) and len(power) == 2:
return _mp(power[0]) * _mp(power[1])
if isinstance(power, str):
s = power.strip()
# NEW: allow purely-numeric exponent expressions like "(2^0.5)"
v_num = _try_eval_numeric_exponent_expr(s)
if v_num is not None:
return v_num
# existing behavior (simple numeric strings)
if s.startswith("(") and s.endswith(")"):
inner = s[1:-1].strip()
try:
return mp.mpf(inner)
except Exception:
pass
try:
return mp.mpf(s)
except Exception:
pass
# fallback: symbol exponent (γ, -γ, etc.)
if symbols is None:
raise ValueError(f"String exponent {power!r} requires symbols lookup.")
return _exponent_from_symbol_string(s, symbols)
return _mp(power)
def exponent_to_complex(power: Any, symbols: Dict[str, Quantity] | None = None) -> mp.mpc:
"""
Parse an exponent into mp.mpc.
Accepts:
- None -> 1
- numbers -> mp.mpc(number, 0)
- [a, b] -> a*b (both numeric)
- string numeric -> real
- string expression -> eval_quantity_expr (supports i, -i, (-1*i), 1+2*i, etc.)
- string symbol exponent like 'γ' or '-γ' -> dimensionless real symbol lookup
"""
if power is None:
return mp.mpc(1, 0)
# legacy [a,b] numeric pair
if isinstance(power, (list, tuple)) and len(power) == 2:
return _as_mpc(_mp(power[0]) * _mp(power[1]))
# numeric types
if isinstance(power, (int, float, mp.mpf, complex, mp.mpc)):
return _as_mpc(power)
if isinstance(power, str):
s = power.strip()
# Try numeric exponent expressions first (purely numeric)
v_num = _try_eval_numeric_exponent_expr(s)
if v_num is not None:
return mp.mpc(v_num, 0)
# Try plain numeric string
try:
return mp.mpc(mp.mpf(s), 0)
except Exception:
pass
# Try full expression (this is what enables (-1*i))
if symbols is None:
raise ValueError(f"String exponent {power!r} requires symbols lookup.")
q = eval_quantity_expr(s, symbols)
if q.units != DIMENSIONLESS:
raise ValueError(f"Exponent must be dimensionless; got units={q.units}")
return _as_mpc(q.value)
# fallback: treat as real numeric
return _as_mpc(_mp(power))
# ============================================================
# Subfactorial
# ============================================================
def _subfactorial_int(n: int) -> int:
if n < 0:
raise ValueError("subfactorial is only defined here for n >= 0")
if n == 0:
return 1
if n == 1:
return 0
a, b = 1, 0
for k in range(2, n + 1):
a, b = b, (k - 1) * (b + a)
return b
# ============================================================
# Expression token support
# ============================================================
_EXPR_TOKEN_RE = re.compile(r"^\s*\(.+\)\s*$")
_NUMERIC_EXPR_RE = re.compile(
r"""
^\s*
[+-]?
(?:\d+(?:\.\d*)?|\.\d+)
(?:\s*[-+*/]\s*(?:\d+(?:\.\d*)?|\.\d+))+
\s*$
""",
re.VERBOSE,
)
def _normalize_expr(s: str) -> str:
s = s.strip()
s = s.replace("^", "**")
# Insert explicit multiplication in safe implicit cases only.
s = re.sub(r"(\d)\s*([A-Za-z_])", r"\1*\2", s) # 2pi -> 2*pi
s = re.sub(r"\)\s*([A-Za-z_])", r")*\1", s) # )(x) -> )*x
s = re.sub(r"\)\s*(\d)", r")*\1", s) # )2 -> )*2
return s
_ALLOWED_BINOPS = {
ast.Add: _op.add,
ast.Sub: _op.sub,
ast.Mult: _op.mul,
ast.Div: _op.truediv,
ast.Pow: _op.pow,
}
_ALLOWED_UNARYOPS = {
ast.UAdd: _op.pos,
ast.USub: _op.neg,
}
def _names_in_expr(expr: str, symbols: Dict[str, Quantity]) -> set[str]:
"""
Extract symbol names referenced inside an exponent/expression string.
Example: "(-1*i)" -> {"i"}
"1+2*i" -> {"i"}
"zhe_r^2" -> {"zhe_r"} (the '^' will be normalized elsewhere)
"""
expr_n = _normalize_expr(expr)
placeholder_to_key: Dict[str, str] = {}
safe_expr = expr_n
bad_keys = [k for k in symbols.keys() if isinstance(k, str) and not k.isidentifier()]
bad_keys.sort(key=len, reverse=True)
for i, key in enumerate(bad_keys):
ph = f"SYM{i}"
placeholder_to_key[ph] = key
safe_expr = safe_expr.replace(key, ph)
node = ast.parse(safe_expr, mode="eval")
names: set[str] = set()
class V(ast.NodeVisitor):
def visit_Name(self, n: ast.Name):
real = placeholder_to_key.get(n.id, n.id)
names.add(real)
V().visit(node)
return names
def _resolve_name_as_quantity(name: str, symbols: Dict[str, Quantity]) -> Quantity:
if name not in symbols:
raise KeyError(f"Unknown name in expression token: '{name}'")
q = symbols[name]
if not isinstance(q, Quantity):
return _q_from_number(q)
return q
def eval_quantity_expr(expr: str, symbols: Dict[str, Quantity]) -> Quantity:
expr_n = _normalize_expr(expr)
placeholder_to_key: Dict[str, str] = {}
safe_expr = expr_n
bad_keys = [k for k in symbols.keys() if isinstance(k, str) and not k.isidentifier()]
bad_keys.sort(key=len, reverse=True)
for i, key in enumerate(bad_keys):
ph = f"SYM{i}"
placeholder_to_key[ph] = key
safe_expr = safe_expr.replace(key, ph)
node = ast.parse(safe_expr, mode="eval")
def _eval(n) -> Quantity:
if isinstance(n, ast.Expression):
return _eval(n.body)
if isinstance(n, ast.Constant):
if isinstance(n.value, (int, float)):
return Quantity(mp.mpf(str(n.value)), {})
raise TypeError(f"Bad constant in expression: {n.value!r}")
if isinstance(n, ast.Name):
real_name = placeholder_to_key.get(n.id, n.id)
return _resolve_name_as_quantity(real_name, symbols)
if isinstance(n, ast.Call):
# Support a small whitelist of safe 1-arg functions: Im, Re, log
if not isinstance(n.func, ast.Name):
raise TypeError(
"Only simple function calls like Im(x), Re(x), log(x) are allowed in expression tokens.")
fname = n.func.id
if fname not in {"Im", "Re", "log", "ln"}:
raise TypeError(f"Function '{fname}' is not allowed in expression tokens.")
if len(n.args) != 1 or n.keywords:
raise TypeError(f"Function '{fname}' must be called with exactly one positional argument.")
q = _eval(n.args[0])
# All these functions preserve units only if the argument is dimensionless (for log/ln)
z = _as_mpc(q.value)
if fname in {"Im", "Re"}:
v = mp.im(z) if fname == "Im" else mp.re(z)
return Quantity(v, dict(q.units))
# log/ln: require dimensionless
if q.units != DIMENSIONLESS:
raise ValueError(f"log argument must be dimensionless; got units={q.units}")
v = mp.log(z)
if isinstance(v, mp.mpc) and v.imag == 0:
v = v.real
return Quantity(v, {})
if isinstance(n, ast.UnaryOp) and type(n.op) in _ALLOWED_UNARYOPS:
q = _eval(n.operand)
opf = _ALLOWED_UNARYOPS[type(n.op)]
v = opf(_as_mpc(q.value))
if v.imag == 0:
return Quantity(v.real, dict(q.units))
return Quantity(v, dict(q.units))
if isinstance(n, ast.BinOp) and type(n.op) in _ALLOWED_BINOPS:
left = _eval(n.left)
right = _eval(n.right)
if type(n.op) is ast.Add:
return q_add(left, right)
if type(n.op) is ast.Sub:
return q_sub(left, right)
if type(n.op) is ast.Mult:
return q_mul(left, right)
if type(n.op) is ast.Div:
return q_div(left, right)
if type(n.op) is ast.Pow:
# exponent must be dimensionless (real OR complex allowed)
if right.units:
raise ValueError(f"Exponent must be dimensionless; got units={right.units}")
return q_pow(left, right.value)
raise TypeError(f"Unsupported expression syntax: {ast.dump(n)}")
return _eval(node)
# ============================================================
# Factor tokens: functions + compact "token^power" parsing
# ============================================================
_ZETA_CALL_RE = re.compile(r"^\s*zeta\(\s*([+-]?\d+)\s*\)\s*$")
_SUBFACT_CALL_RE = re.compile(r"^\s*subfact\(\s*(\d+)\s*\)\s*$")
_BANG_SUBFACT_RE = re.compile(r"^\s*!\s*(\d+)\s*$")
_POSTFIX_FACTORIAL_RE = re.compile(r"^\s*(\d+)\s*!\s*$")
_GAMMA_CALL_RE = re.compile(r"^\s*(?:gamma|Γ)\(\s*(.+?)\s*\)\s*$")
def _split_factor_string(s: str) -> Tuple[str, Any]:
s = s.strip()
if not s:
raise ValueError("Empty factor string is not allowed.")
depth = 0
split_at = -1
for i, ch in enumerate(s):
if ch == "(":
depth += 1
elif ch == ")" and depth > 0:
depth -= 1
elif ch == "^" and depth == 0:
split_at = i
if split_at != -1:
tok = s[:split_at].strip()
pow_s = s[split_at + 1:].strip()
if not tok:
raise ValueError(f"Bad factor token in {s!r}")
if not pow_s:
raise ValueError(f"Bad factor power in {s!r}")
return tok, pow_s
return s, mp.mpf("1")
def _parse_factor_string_literal_first(s: str, symbols: Dict[str, Quantity]) -> Tuple[str, Any]:
"""
Rule:
If s exists as an exact key in symbols, treat it as a literal token with power=1.
Otherwise, parse TOKEN^POWER at top level.
"""
ss = s.strip()
if not ss:
raise ValueError("Empty factor string is not allowed.")
if ss in symbols:
return ss, mp.mpf("1")
tok, pow_ = _split_factor_string(ss)
return tok, pow_
def iter_factors(factors: Any) -> Iterable[Tuple[FactorToken, Any]]:
"""
Supported:
- None / {} -> yields nothing
- dict -> {token: power, ...}
- list -> items:
* number literal -> factor with power 1
* string "TOKEN" or "TOKEN^POWER" -> parse later
* dict {"token": TOKEN, "power": POWER}
"""
if factors is None:
return iter(())
def _gen_from_list(lst: list) -> Iterable[Tuple[FactorToken, Any]]:
for item in lst:
if isinstance(item, numbers.Real) and not isinstance(item, bool):
yield item, mp.mpf("1")
continue
if isinstance(item, str):
s = item.strip()
if not s:
raise ValueError("Empty factor string is not allowed.")
yield s, None
continue
if isinstance(item, dict):
if "token" in item:
tok = item["token"]
elif "id" in item:
tok = item["id"]
else:
raise TypeError(f"Dict factor item missing 'token'/'id': {item!r}")
pow_ = item.get("power", mp.mpf("1"))
yield tok, pow_
continue
raise TypeError(f"Bad factor list item: {item!r}")
if isinstance(factors, Mapping):
def _gen_from_map(m: Mapping) -> Iterable[Tuple[FactorToken, Any]]:
for k, v in m.items():
yield k, v
return _gen_from_map(factors)
if isinstance(factors, list):
return _gen_from_list(factors)
raise TypeError(f"Factors must be a dict or list. Got {type(factors).__name__}: {factors!r}")
def _resolve_token_to_quantity(token: FactorToken, symbols: Dict[str, Quantity]) -> Quantity:
# numeric literal -> mp immediately
if isinstance(token, numbers.Real) and not isinstance(token, bool):
return Quantity(mp.mpf(str(token)), {})
tok = str(token).strip()
# numeric string tokens
try:
return Quantity(mp.mpf(tok), {})
except Exception:
pass
if tok == "ten":
raise ValueError("Token 'ten' is not allowed.")
# Expression token
if _EXPR_TOKEN_RE.match(tok) or _NUMERIC_EXPR_RE.match(tok):
return eval_quantity_expr(tok, symbols)
# Function tokens
m = _ZETA_CALL_RE.match(tok)
if m:
n = int(m.group(1))
z = mp.zeta(n)
if isinstance(z, mp.mpc) and z.imag == 0:
z = z.real
return Quantity(z, {})
m2 = _SUBFACT_CALL_RE.match(tok)
if m2:
n = int(m2.group(1))
return Quantity(mp.mpf(str(_subfactorial_int(n))), {})
m3 = _BANG_SUBFACT_RE.match(tok)
if m3:
n = int(m3.group(1))
return Quantity(mp.mpf(str(_subfactorial_int(n))), {})
mf = _POSTFIX_FACTORIAL_RE.match(tok)
if mf:
n = int(mf.group(1))
return Quantity(mp.factorial(n), {})
mg = _GAMMA_CALL_RE.match(tok)
if mg:
arg_s = mg.group(1).strip()
# Evaluate the argument as a dimensionless quantity.
# This lets you do gamma(5), gamma(zhe_2), gamma(1/2), gamma((1+zhe_1)/2), etc.
qarg = eval_quantity_expr(f"({arg_s})", symbols)
if qarg.units != DIMENSIONLESS:
raise ValueError(f"gamma argument must be dimensionless; got units={qarg.units}")
z = _as_mpc(qarg.value) # mp.gamma supports complex too
g = mp.gamma(z)
if isinstance(g, mp.mpc) and g.imag == 0:
g = g.real
return Quantity(g, {})
if tok not in symbols:
raise KeyError(f"Token '{tok}' not found in symbols table.")
q = symbols[tok]
if not isinstance(q, Quantity):
return Quantity(mp.mpf(str(q)), {})
return q
def factor_product(factors: Any, symbols: Dict[str, Quantity]) -> Quantity:
"""Multiply factors into a Quantity (handles complex exponents like i, -i)."""
prod = Quantity(mp.mpc(1, 0), {})
# Ensure imaginary unit 'i' exists
if "i" not in symbols:
symbols["i"] = Quantity(mp.mpc(0, 1), {})
for token, power in iter_factors(factors):
# --- numeric literal tokens ---
if isinstance(token, numbers.Real) and not isinstance(token, bool):
base = _resolve_token_to_quantity(token, symbols)
p = exponent_to_complex(mp.mpf("1") if power is None else power, symbols)
prod = q_mul(prod, q_pow(base, p))
continue
# --- string tokens ---
if isinstance(token, str):
tok_s, pow_raw = _parse_factor_string_literal_first(token, symbols)
base = _resolve_token_to_quantity(tok_s, symbols)
# Determine exponent
if power is not None:
# explicit power overrides anything from TOKEN^POWER
p_val = exponent_to_complex(power, symbols)
elif isinstance(pow_raw, str):
# inline exponent: always parse as an expression (can be complex: -i, (-1*i), 1+2*i, etc.)
p_expr = eval_quantity_expr(pow_raw, symbols)
if p_expr.units != DIMENSIONLESS:
raise ValueError(f"Exponent must be dimensionless; got units={p_expr.units}")
p_val = _as_mpc(p_expr.value)
else:
p_val = mp.mpc(1, 0)
prod = q_mul(prod, q_pow(base, p_val))
continue
# --- other token types (dict keys, etc.) ---
base = _resolve_token_to_quantity(token, symbols)
p_val = exponent_to_complex(power, symbols)
prod = q_mul(prod, q_pow(base, p_val))
return prod
def fraction(numerator: Any, denominator: Any, symbols: Dict[str, Quantity]) -> Quantity:
num = factor_product(numerator, symbols)
den = factor_product(denominator, symbols)
return q_div(num, den)
# ============================================================
# Root-transform expression evaluator
# ============================================================
def _quantity_from_number(x: Any) -> Quantity:
return Quantity(mp.mpf(str(x)), {})
def _to_dimensionless_real(q: Quantity) -> mp.mpf:
if q.units:
raise ValueError(f"Exponent must be dimensionless, got units={q.units}")
v = q.value
if isinstance(v, mp.mpc):
if v.imag != 0:
raise ValueError(f"Exponent must be real, got {v!r}")
return v.real
if isinstance(v, complex):
if v.imag != 0:
raise ValueError(f"Exponent must be real, got {v!r}")
return mp.mpf(str(v.real))
return _mp(v)
def eval_quantity_expression(expr: str, symbols: Dict[str, Quantity]) -> Quantity:
if not isinstance(expr, str) or not expr.strip():
raise ValueError("root_transform.id must be a non-empty string")
src = expr.strip().replace("^", "**")
node = ast.parse(src, mode="eval")
def walk(n: ast.AST) -> Quantity:
if isinstance(n, ast.Expression):
return walk(n.body)
if isinstance(n, ast.Constant) and isinstance(n.value, (int, float)):
return _quantity_from_number(n.value)
if isinstance(n, ast.Name):
name = n.id
if name not in symbols:
raise KeyError(f"Root expression name '{name}' not found in symbols table.")
return symbols[name]
if isinstance(n, ast.UnaryOp) and isinstance(n.op, (ast.UAdd, ast.USub)):
v = walk(n.operand)
if isinstance(n.op, ast.UAdd):
return v
return q_mul(_quantity_from_number(mp.mpf("-1")), v)
if isinstance(n, ast.BinOp):
a = walk(n.left)
b = walk(n.right)
if isinstance(n.op, ast.Add):
return q_add(a, b)
if isinstance(n.op, ast.Sub):
return q_sub(a, b)
if isinstance(n.op, ast.Mult):
return q_mul(a, b)
if isinstance(n.op, ast.Div):
return q_div(a, b)
if isinstance(n.op, ast.Pow):
exp = _to_dimensionless_real(b)
return q_pow(a, exp)
raise ValueError(f"Unsupported syntax in root_transform.id: {expr!r}")
return walk(node)
# ============================================================
# Main evaluator
# ============================================================
def evaluate_constant(recipe: dict, symbols: Dict[str, Quantity], inversion_boundary_token: str = "IB") -> Quantity:
"""
Evaluate:
Constant = EG * EB * (1 + IG * R * IB)
IG*R*IB must be dimensionless.
"""
EG = fraction(
recipe["external_geometry"]["numerator"],
recipe["external_geometry"]["denominator"],
symbols,
)
EB = fraction(
recipe["external_boundary"]["numerator"],
recipe["external_boundary"]["denominator"],
symbols,
)
IG = fraction(
recipe["inversion_geometry"]["numerator"],
recipe["inversion_geometry"]["denominator"],
symbols,
)
rt = recipe["root_transform"]
R_id = rt["id"]
R_power = exponent_to_mpf(rt.get("power", mp.mpf("1")), symbols)
if isinstance(R_id, str) and any(op in R_id for op in "+-*/()^ "):
R_base = eval_quantity_expression(R_id, symbols)
else:
if R_id not in symbols:
raise KeyError(f"Root token '{R_id}' not found in symbols table.")
R_base = symbols[R_id]
R = q_pow(R_base, R_power)
if inversion_boundary_token not in symbols:
raise KeyError(f"Inversion boundary token '{inversion_boundary_token}' not found in symbols table.")
IB = symbols[inversion_boundary_token]
term = q_mul(q_mul(IG, R), IB)
one = Quantity(mp.mpf("1"), DIMENSIONLESS)
if term.units != one.units:
raise ValueError(f"{recipe.get('constant_id')} has non-dimensionless IG*R*IB: units={term.units}")
inner = q_add(one, term)
# --- NEW: per-recipe combine mode ---
# Default is multiply: EG*EB*(1 + term)
# Optional add: EG + EB*(1 + term)
# Optional subtract: EG*EB - (1 + term)
combine = (recipe.get("combine", "*") or "*").strip().lower()
if combine in {"*", "mul", "multiply"}:
left = q_mul(EG, EB)
return q_mul(left, inner)
if combine in {"inv", "invert", "inversion", "reciprocal"}:
# EG * EB * (1 + term)^(-1)
left = q_mul(EG, EB)
inv_inner = q_div(one, inner) # dimensionless inverse
return q_mul(left, inv_inner)
if combine in {"+", "add", "plus"}:
return q_add(EG, q_mul(EB, inner))
if combine in {"-", "sub", "subtract"}:
left = q_mul(EG, EB)
# inner is dimensionless, so left must be dimensionless too
if left.units != DIMENSIONLESS:
raise ValueError(
f"{recipe.get('constant_id')} combine='-' requires EG*EB dimensionless; got units={left.units}"
)
return q_sub(left, inner)
raise ValueError(
f"{recipe.get('constant_id')} has invalid combine={recipe.get('combine')!r}; use '*', 'inv', '+', or '-'"
)
288 Constant Recipes
# constants.yaml
# Each constant is a recipe that will be evaluated by:
# (EG * EB) * (1 + (IG * R * IB))
constants:
- { recipe_number: 1, constant_id: Delta_nu_Cs, display_name: "hyperfine transition frequency of Cs-133", column: "1", island: "1", dimension: "Hz",
external_geometry: { numerator: [ "E_1" ], denominator: [ "2","pi" ] }, external_boundary: { numerator: [ "t_p" ], denominator: [ "l_p^2","m_p" ] },
inversion_geometry: { numerator: [ "-1","zeta(2)^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: exact, expected_value: 9.192631770e9, expected_digits: "9192631770", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 2, constant_id: eV⋮Hz, display_name: "electron volt-hertz relationship", column: "1", island: "1", dimension: "Hz",
external_geometry: { numerator: [ "eV" ], denominator: [ "2","pi" ] }, external_boundary: { numerator: [ "t_p" ], denominator: [ "l_p^2","m_p" ] },
inversion_geometry: { numerator: [ "-1","zeta(2)^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: exact, expected_value: 2.417989242e14, expected_digits: "2417989242", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 3, constant_id: J⋮Hz, display_name: "joule-hertz relationship", column: "1", island: "1", dimension: "Hz",
external_geometry: { numerator: [ "joule" ], denominator: [ "2","pi" ] }, external_boundary: { numerator: [ "t_p" ], denominator: [ "l_p^2","m_p" ] },
inversion_geometry: { numerator: [ "-1","zeta(2)^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: exact, expected_value: 1.509190179e33, expected_digits: "1509190179", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 4, constant_id: Hz⋮J, display_name: "hertz-joule relationship", column: "1", island: "1", dimension: "J",
external_geometry: { numerator: [ "2","pi" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2", "m_p" ], denominator: [ "second", "t_p" ] },
inversion_geometry: { numerator: [ "zeta(2)^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: exact, expected_value: 6.62607015e-34, expected_digits: "662607015", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 5, constant_id: Hz⋮eV, display_name: "hertz-electron volt relationship", column: "1", island: "1", dimension: "eV",
external_geometry: { numerator: [ "2","pi" ], denominator: [ "eV" ] }, external_boundary: { numerator: [ "l_p^2", "m_p" ], denominator: [ "second", "t_p" ] },
inversion_geometry: { numerator: [ "zeta(2)^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: exact, expected_value: 4.135667696e-15, expected_digits: "4135667696", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 6, constant_id: ℏ̇, display_name: "natural unit of action in eV s", column: "1", island: "1", dimension: "eV s",
external_geometry: { numerator: [ ], denominator: [ "eV" ] }, external_boundary: { numerator: [ "l_p^2", "m_p" ], denominator: [ "t_p" ] },
inversion_geometry: { numerator: [ "zeta(2)^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: exact, expected_value: 6.582119569e-16, expected_digits: "6582119569", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 7, constant_id: ℏ, display_name: "reduced Planck constant", column: "1", island: "1", dimension: "J s",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2", "m_p" ], denominator: [ "t_p" ] },
inversion_geometry: { numerator: [ "zeta(2)^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: exact, expected_value: 1.054571817e-34, expected_digits: "1054571817", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 8, constant_id: h, display_name: "Planck constant", column: "1", island: "1", dimension: "J s",
external_geometry: { numerator: [ "2", "pi" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2", "m_p" ], denominator: [ "t_p" ] },
inversion_geometry: { numerator: [ "zeta(2)^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: exact, expected_value: 6.62607015e-34, expected_digits: "662607015", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 9, constant_id: q_c, display_name: "quantum of circulation", column: "1", island: "1", dimension: "m^2/s",
external_geometry: { numerator: [ "pi" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2","m_p" ], denominator: [ "t_p","m_e" ] },
inversion_geometry: { numerator: [ "zeta(2)^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: measured, expected_value: 3.6369475467(11)e-4, expected_digits: "36369475467", expected_digits_label: "SI measured" }
- { recipe_number: 10, constant_id: 2q_c, display_name: "quantum of circulation times 2", column: "1", island: "1", dimension: "m^2/s",
external_geometry: { numerator: [ "2","pi" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2","m_p" ], denominator: [ "t_p","m_e" ] },
inversion_geometry: { numerator: [ "zeta(2)^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: measured, expected_value: 7.2738950934(22)e-4, expected_digits: "72738950934", expected_digits_label: "SI measured" }
- { recipe_number: 11, constant_id: μ_B/e, display_name: "Bohr magneton in eV/T", column: "1", island: "1", dimension: "eV/T",
external_geometry: { numerator: [ ], denominator: [ "2" ] }, external_boundary: { numerator: [ "coulomb","l_p^2","m_p" ], denominator: [ "t_p","m_e" ] },
inversion_geometry: { numerator: [ "zeta(2)^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: measured, expected_value: 5.7883817982(18)e-5, expected_digits: "57883817982", expected_digits_label: "SI measured" }
- { recipe_number: 12, constant_id: μ_N/e, display_name: "nuclear magneton in eV/T", column: "1", island: "1", dimension: "eV/T",
external_geometry: { numerator: [ ], denominator: [ "2" ] }, external_boundary: { numerator: [ "coulomb","l_p^2","m_p" ], denominator: [ "t_p","m_+" ] },
inversion_geometry: { numerator: [ "zeta(2)^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: measured, expected_value: 3.15245125417(98)e-8, expected_digits: "315245125417", expected_digits_label: "SI measured" }
- { recipe_number: 13, constant_id: G_0^-1, display_name: "inverse of conductance quantum", column: "1", island: "1", dimension: "Ohm",
external_geometry: { numerator: [ "pi" ], denominator: [ "zhe_1","zhe_1" ] }, external_boundary: { numerator: [ "l_p^2","m_p" ], denominator: [ "t_p","q_p^2" ] },
inversion_geometry: { numerator: [ "zeta(3)^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: exact, expected_value: 1.290640372e4, expected_digits: "1290640372", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 14, constant_id: G_0, display_name: "conductance quantum", column: "1", island: "1", dimension: "S",
external_geometry: { numerator: [ "zhe_1","zhe_1" ], denominator: [ "pi" ] }, external_boundary: { numerator: [ "t_p","q_p^2" ], denominator: [ "l_p^2","m_p" ] },
inversion_geometry: { numerator: [ "-1","zeta(3)^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: exact, expected_value: 7.748091729e-5, expected_digits: "7748091729", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 15, constant_id: eV, display_name: "electron volt", column: "1", island: "2", dimension: "J",
external_geometry: { numerator: [ "zhe_1", "joule" ], denominator: [ ] }, external_boundary: { numerator: [ "q_p" ], denominator: [ "coulomb" ] },
inversion_geometry: { numerator: [ "e^-γ" ], denominator: [ "6" ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: exact, expected_value: 1.602176634e-19, expected_digits: "1602176634", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 16, constant_id: J⋮eV, display_name: "joule-electron volt relationship", column: "1", island: "2", dimension: "eV",
external_geometry: { numerator: [ ], denominator: [ "zhe_1" ] }, external_boundary: { numerator: [ "coulomb" ], denominator: [ "q_p" ] },
inversion_geometry: { numerator: [ "-1","e^-γ" ], denominator: [ "6" ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: exact, expected_value: 6.241509074e18, expected_digits: "6241509074", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 17, constant_id: -e/m_e, display_name: "electron charge to mass quotient", column: "1", island: "2", dimension: "C/kg",
external_geometry: { numerator: [ "-1","zhe_1" ], denominator: [ ] }, external_boundary: { numerator: [ "q_p" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ "e^-γ" ], denominator: [ "6" ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: measured, expected_value: -1.75882000838(55)e11, expected_digits: "175882000838", expected_digits_label: "SI measured" }
- { recipe_number: 18, constant_id: e/m_+, display_name: "proton charge to mass quotient", column: "1", island: "2", dimension: "C/kg",
external_geometry: { numerator: [ "zhe_1" ], denominator: [ ] }, external_boundary: { numerator: [ "q_p" ], denominator: [ "m_+" ] },
inversion_geometry: { numerator: [ "e^-γ" ], denominator: [ "6" ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: measured, expected_value: 9.5788331430(29)e7, expected_digits: "95788331430", expected_digits_label: "SI measured" }
- { recipe_number: 19, constant_id: μ_B/h, display_name: "Bohr magneton in Hz/T", column: "1", island: "2", dimension: "Hz/T",
external_geometry: { numerator: [ "zhe_1" ], denominator: [ "4","pi" ] }, external_boundary: { numerator: [ "q_p" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ "e^-γ" ], denominator: [ "6" ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: measured, expected_value: 1.39962449171(44)e10, expected_digits: "139962449171", expected_digits_label: "SI measured" }
- { recipe_number: 20, constant_id: μ_N/h, display_name: "nuclear magneton in MHz/T", column: "1", island: "2", dimension: "MHz/T",
external_geometry: { numerator: [ "zhe_1" ], denominator: [ "4", "pi", "MHz" ] }, external_boundary: { numerator: [ "q_p" ], denominator: [ "second", "m_+" ] },
inversion_geometry: { numerator: [ "e^-γ" ], denominator: [ "6" ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: measured, expected_value: 7.6225932118(24), expected_digits: "76225932118", expected_digits_label: "SI measured" }
- { recipe_number: 21, constant_id: a, display_name: "lattice parameter of silicon", column: "1", island: "3", dimension: "m",
external_geometry: { numerator: [ "4", "pi" ], denominator: [ "32", "s", "zhe_1^4" ] }, external_boundary: { numerator: [ "l_p", "m_p" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ "35", "4^5", "pi^5" ], denominator: [ "8^5" ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: measured, expected_value: 5.431020511(89)e-10, expected_digits: "5431020511", expected_digits_label: "SI measured" }
- { recipe_number: 22, constant_id: d_220, display_name: "lattice spacing of ideal Si (220)", column: "1", island: "3", dimension: "m",
external_geometry: { numerator: [ "4", "pi" ], denominator: [ "8^0.5", "32", "s", "zhe_1^4" ] }, external_boundary: { numerator: [ "l_p", "m_p" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ "35", "4^5", "pi^5" ], denominator: [ "8^5" ] }, root_transform: { id: "zhe_theta^2" },
expected_kind: measured, expected_value: 1.920155716(32)e-10, expected_digits: "1920155716", expected_digits_label: "SI measured" }
- { recipe_number: 23, constant_id: A_90, display_name: "conventional value of ampere-90", column: "1", island: "4", dimension: "A",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "ampere" ], denominator: [ ] },
inversion_geometry: { numerator: [ "4", "pi" ], denominator: [ "S*", "35" ] }, root_transform: { id: "zhe_theta^3" },
expected_kind: exact, expected_value: 1.00000008887, expected_digits: "100000008887", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 24, constant_id: C_90, display_name: "conventional value of coulomb-90", column: "1", island: "4", dimension: "C",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "coulomb" ], denominator: [ ] },
inversion_geometry: { numerator: [ "4", "pi" ], denominator: [ "S*", "35" ] }, root_transform: { id: "zhe_theta^3" },
expected_kind: exact, expected_value: 1.00000008887, expected_digits: "100000008887", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 25, constant_id: μ_B/hc, display_name: "Bohr magneton in inverse meter per tesla", column: "1", island: "5", dimension: "1/m*T",
external_geometry: { numerator: [ "zhe_1" ], denominator: [ "4", "pi" ] }, external_boundary: { numerator: [ "t_p", "q_p" ], denominator: [ "l_p", "m_e" ] },
inversion_geometry: { numerator: [ "S*", "K" ], denominator: [ "6" ] }, root_transform: { id: "zhe_theta^3" },
expected_kind: measured, expected_value: 4.6686447719(15)e1, expected_digits: "46686447719", expected_digits_label: "SI measured" }
- { recipe_number: 26, constant_id: μ_N/hc, display_name: "nuclear magneton in inverse meter per tesla", column: "1", island: "5", dimension: "1/m*T",
external_geometry: { numerator: [ "zhe_1" ], denominator: [ "4", "pi" ] }, external_boundary: { numerator: [ "t_p", "q_p" ], denominator: [ "l_p", "m_+" ] },
inversion_geometry: { numerator: [ "S*", "K" ], denominator: [ "6" ] }, root_transform: { id: "zhe_theta^3" },
expected_kind: measured, expected_value: 2.54262341009(79)e-2, expected_digits: "254262341009", expected_digits_label: "SI measured" }
- { recipe_number: 27, constant_id: R_∞, display_name: "Rydberg constant", column: "1", island: "6", dimension: "1/m",
external_geometry: { numerator: [ "zhe_1^4" ], denominator: [ "4","pi" ] }, external_boundary: { numerator: [ "m_e" ], denominator: [ "l_p","m_p" ] },
inversion_geometry: { numerator: [ "6^2" ], denominator: [ "-8", "V_fe^2" ] }, root_transform: { id: "zhe_theta^3" },
expected_kind: measured, expected_value: 1.0973731568157(12)e7, expected_digits: "10973731568157", expected_digits_label: "SI measured" }
- { recipe_number: 28, constant_id: E_h⋮1/m, display_name: "hartree-inverse meter relationship", column: "1", island: "6", dimension: "1/m",
external_geometry: { numerator: [ "zhe_1^4" ], denominator: [ "2","pi" ] }, external_boundary: { numerator: [ "m_e" ], denominator: [ "l_p","m_p" ] },
inversion_geometry: { numerator: [ "6^2" ], denominator: [ "-8","V_fe^2" ] }, root_transform: { id: "zhe_theta^3" },
expected_kind: measured, expected_value: 2.1947463136314(24)e7, expected_digits: "21947463136314", expected_digits_label: "SI measured" }
- { recipe_number: 29, constant_id: 1/m⋮E_h, display_name: "inverse meter-hartree relationship", column: "1", island: "6", dimension: "E_h",
external_geometry: { numerator: [ "2","pi" ], denominator: [ "zhe_1^4" ] }, external_boundary: { numerator: [ "l_p", "m_p" ], denominator: [ "meter","m_e" ] },
inversion_geometry: { numerator: [ "6^2" ], denominator: [ "8","V_fe^2" ] }, root_transform: { id: "zhe_theta^3" },
expected_kind: measured, expected_value: 4.5563352529132(50)e-8, expected_digits: "45563352529132", expected_digits_label: "SI measured" }
- { recipe_number: 30, constant_id: A_time, display_name: "atomic unit of time", column: "1", island: "7", dimension: "s",
external_geometry: { numerator: [ ], denominator: [ "zhe_1^4" ] }, external_boundary: { numerator: [ "t_p", "m_p" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ "5^0.5", "C_d" ], denominator: [ "C_U" ] }, root_transform: { id: "zhe_theta^4" },
expected_kind: measured, expected_value: 2.4188843265864(26)e-17, expected_digits: "24188843265864", expected_digits_label: "SI measured" }
- { recipe_number: 31, constant_id: Hz⋮E_h, display_name: "hertz-hartree relationship", column: "1", island: "7", dimension: "E_h",
external_geometry: { numerator: [ "2","pi" ], denominator: [ "zhe_1^4" ] }, external_boundary: { numerator: [ "t_p", "m_p" ], denominator: [ "second", "m_e" ] },
inversion_geometry: { numerator: [ "5^0.5", "C_d" ], denominator: [ "C_U" ] }, root_transform: { id: "zhe_theta^4" },
expected_kind: measured, expected_value: 1.5198298460574(17)e-16, expected_digits: "15198298460574", expected_digits_label: "SI measured" }
- { recipe_number: 32, constant_id: E_h⋮Hz, display_name: "hartree-hertz relationship", column: "1", island: "7", dimension: "Hz",
external_geometry: { numerator: [ "zhe_1^4" ], denominator: [ "2","pi" ] }, external_boundary: { numerator: [ "m_e" ], denominator: [ "t_p","m_p" ] },
inversion_geometry: { numerator: [ "-1", "5^0.5", "C_d" ], denominator: [ "C_U" ] }, root_transform: { id: "zhe_theta^4" },
expected_kind: measured, expected_value: 6.5796839204999(72)e15, expected_digits: "65796839204999", expected_digits_label: "SI measured" }
- { recipe_number: 33, constant_id: R_∞_c ̇, display_name: "Rydberg constant times c in Hz", column: "1", island: "7", dimension: "Hz",
external_geometry: { numerator: [ "zhe_1^4" ], denominator: [ "4","pi" ] }, external_boundary: { numerator: [ "m_e" ], denominator: [ "t_p","m_p" ] },
inversion_geometry: { numerator: [ "-1", "5^0.5", "C_d" ], denominator: [ "C_U" ] }, root_transform: { id: "zhe_theta^4" },
expected_kind: measured, expected_value: 3.2898419602500(36)e15, expected_digits: "32898419602500", expected_digits_label: "SI measured" }
- { recipe_number: 34, constant_id: κ, display_name: "Coulomb's constant", column: "1", island: "8", dimension: "m/F",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^3","m_p" ], denominator: [ "t_p^2","q_p^2" ] },
inversion_geometry: { numerator: [ "C_d" ], denominator: [ "6" ] }, root_transform: { id: "zhe_theta^4" },
expected_kind: measured, expected_value: 8.9875517923(14)e9, expected_digits: "89875517923", expected_digits_label: "SI measured" }
- { recipe_number: 35, constant_id: A_perm, display_name: "atomic unit of permittivity", column: "1", island: "8", dimension: "F/m",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "t_p^2","q_p^2" ], denominator: [ "l_p^3","m_p" ] },
inversion_geometry: { numerator: [ "C_d" ], denominator: [ "-6" ] }, root_transform: { id: "zhe_theta^4" },
expected_kind: measured, expected_value: 1.11265005620(17)e-10, expected_digits: "111265005620", expected_digits_label: "SI measured" }
- { recipe_number: 36, constant_id: ε_0, display_name: "vacuum electric permittivity", column: "1", island: "8", dimension: "F/m",
external_geometry: { numerator: [ ], denominator: [ "4","pi" ] }, external_boundary: { numerator: [ "t_p^2","q_p^2" ], denominator: [ "l_p^3","m_p" ] },
inversion_geometry: { numerator: [ "C_d" ], denominator: [ "-6" ] }, root_transform: { id: "zhe_theta^4" },
expected_kind: measured, expected_value: 8.8541878188(14)e-12, expected_digits: "88541878188", expected_digits_label: "SI measured" }
- { recipe_number: 37, constant_id: μ_n/μ_+, display_name: "neutron-proton magnetic moment ratio", column: "2", island: "1", dimension: "-",
external_geometry: { numerator: [ "-1", "S" ], denominator: [ "C_CFP" ] }, external_boundary: { numerator: [ "m_+" ], denominator: [ "m_n" ] },
inversion_geometry: { numerator: [ "!5", "2", "pi" ], denominator: [ "8","K" ] }, root_transform: { id: "zhe_r^2" },
expected_kind: measured, expected_value: -6.8497935(16)e-1, expected_digits: "68497935", expected_digits_label: "SI measured" }
- { recipe_number: 38, constant_id: μ_+/μ_n, display_name: "proton-neutron magnetic moment ratio", column: "2", island: "1", combine: inversion, dimension: "-",
external_geometry: { numerator: [ "-1", "C_CFP" ], denominator: [ "S" ] }, external_boundary: { numerator: [ "m_n" ], denominator: [ "m_+" ] },
inversion_geometry: { numerator: [ "!5", "2", "pi" ], denominator: [ "8","K" ] }, root_transform: { id: "zhe_r^2" },
expected_kind: measured, expected_value: -1.45989802(34), expected_digits: "145989802", expected_digits_label: "SI measured" }
- { recipe_number: 39, constant_id: μ_e/μ_n, display_name: "electron-neutron magnetic moment ratio", column: "2", island: "1", dimension: "-",
external_geometry: { numerator: [ "C_CFP" ], denominator: [ "P_up" ] }, external_boundary: { numerator: [ "m_n" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ "18","4", "K" ], denominator: [ "2", "pi" ] }, root_transform: { id: "zhe_r^2" },
expected_kind: measured, expected_value: 9.6092048(23)e2, expected_digits: "96092048", expected_digits_label: "SI measured" }
- { recipe_number: 40, constant_id: μ_n/μ_e, display_name: "neutron-electron magnetic moment ratio", column: "2", island: "1", combine: inversion, dimension: "-",
external_geometry: { numerator: [ "P_up" ], denominator: [ "C_CFP" ] }, external_boundary: { numerator: [ "m_e" ], denominator: [ "m_n" ] },
inversion_geometry: { numerator: [ "18","4", "K" ], denominator: [ "2", "pi" ] }, root_transform: { id: "zhe_r^2" },
expected_kind: measured, expected_value: 1.04066884(24)e-3, expected_digits: "104066884", expected_digits_label: "SI measured" }
- { recipe_number: 41, constant_id: A_mdm, display_name: "atomic unit of magnetic dipole moment", column: "2", island: "2", dimension: "J/T",
external_geometry: { numerator: [ "zhe_1" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2","q_p","m_p" ], denominator: [ "t_p","m_e" ] },
inversion_geometry: { numerator: [ "omega_2","2","pi" ], denominator: [ "35" ] }, root_transform: { id: "zhe_r^2" },
expected_kind: measured, expected_value: 1.85480201315(58)e-23, expected_digits: "185480201315", expected_digits_label: "SI measured" }
- { recipe_number: 42, constant_id: μ_B, display_name: "Bohr magneton", column: "2", island: "2", dimension: "J/T",
external_geometry: { numerator: [ "zhe_1" ], denominator: [ "2" ] }, external_boundary: { numerator: [ "l_p^2","q_p","m_p" ], denominator: [ "t_p","m_e" ] },
inversion_geometry: { numerator: [ "omega_2","2","pi" ], denominator: [ "35" ] }, root_transform: { id: "zhe_r^2" },
expected_kind: measured, expected_value: 9.2740100657(29)e-24, expected_digits: "92740100657", expected_digits_label: "SI measured" }
- { recipe_number: 43, constant_id: μ_N, display_name: "nuclear magneton", column: "2", island: "2", dimension: "J/T",
external_geometry: { numerator: [ "zhe_1" ], denominator: [ "2" ] }, external_boundary: { numerator: [ "l_p^2","q_p","m_p" ], denominator: [ "t_p","m_+" ] },
inversion_geometry: { numerator: [ "omega_2","2","pi" ], denominator: [ "35" ] }, root_transform: { id: "zhe_r^2" },
expected_kind: measured, expected_value: 5.0507837393(16)e-27, expected_digits: "50507837393", expected_digits_label: "SI measured" }
- { recipe_number: 44, constant_id: μ_tri, display_name: "triton magnetic moment", column: "2", island: "2", dimension: "J/T",
external_geometry: { numerator: [ "zhe_1^2","zhe_2^2","(D_Do+pi)" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2","q_p","m_p" ], denominator: [ "t_p","m_tri" ] },
inversion_geometry: { numerator: [ "-1", "omega_2", "2", "pi" ], denominator: [ "18" ] }, root_transform: { id: "zhe_r^2" },
expected_kind: measured, expected_value: 1.5046095178(30)e-26, expected_digits: "15046095178", expected_digits_label: "SI measured" }
- { recipe_number: 45, constant_id: μ_tri/μ_+, display_name: "triton to proton magnetic moment ratio", column: "2", island: "2", dimension: "-",
external_geometry: { numerator: [ "S","(D_Do+pi)" ], denominator: [ ] }, external_boundary: { numerator: [ "m_+" ], denominator: [ "m_tri" ] },
inversion_geometry: { numerator: [ "4", "32" ], denominator: [ "L_LL", "4", "pi" ] }, root_transform: { id: "zhe_r^2" },
expected_kind: measured, expected_value: 1.0666399189(21), expected_digits: "10666399189", expected_digits_label: "SI measured" }
- { recipe_number: 46, constant_id: μ_tri/μ_N, display_name: "triton magnetic moment to nuclear magneton ratio", column: "2", island: "2", dimension: "-",
external_geometry: { numerator: [ "zhe_1","zhe_2^2","(2D_Do + 2pi)" ], denominator: [ ] }, external_boundary: { numerator: [ "m_+" ], denominator: [ "m_tri" ] },
inversion_geometry: { numerator: [ "-18", "4", "pi" ], denominator: [ "8", "35" ] }, root_transform: { id: "zhe_r^2" },
expected_kind: measured, expected_value: 2.9789624650(59), expected_digits: "29789624650", expected_digits_label: "SI measured" }
- { recipe_number: 47, constant_id: μ_tri/μ_B, display_name: "triton magnetic moment to Bohr magneton ratio", column: "2", island: "2", dimension: "-",
external_geometry: { numerator: [ "zhe_1","zhe_2^2","(2D_Do + 2pi)" ], denominator: [ ] }, external_boundary: { numerator: [ "m_e" ], denominator: [ "m_tri" ] },
inversion_geometry: { numerator: [ "-18", "4", "pi" ], denominator: [ "8", "35" ] }, root_transform: { id: "zhe_r^2" },
expected_kind: measured, expected_value: 1.6223936648(32)e-3, expected_digits: "16223936648", expected_digits_label: "SI measured" }
- { recipe_number: 48, constant_id: g_tri, display_name: "triton g factor", column: "2", island: "2", dimension: "-",
external_geometry: { numerator: [ "zhe_1","zhe_2^2","(4D_Do + 4pi)" ], denominator: [ ] }, external_boundary: { numerator: [ "m_+" ], denominator: [ "m_tri" ] },
inversion_geometry: { numerator: [ "-18", "4", "pi" ], denominator: [ "8", "35" ] }, root_transform: { id: "zhe_r^2" },
expected_kind: measured, expected_value: 5.957924930(12), expected_digits: "5957924930", expected_digits_label: "SI measured" }
- { recipe_number: 49, constant_id: μ_e/μ_μ, display_name: "electron-muon magnetic moment ratio", column: "2", island: "3", dimension: "-",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "m_μ" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ "-4", "pi" ], denominator: [ "18" ] }, root_transform: { id: "zhe_r^3" },
expected_kind: measured, expected_value: 2.067669881(46)e2, expected_digits: "2067669881", expected_digits_label: "SI measured" }
- { recipe_number: 50, constant_id: G, display_name: "Newtonian constant of gravitation", column: "2", island: "3", dimension: "m^3/(s^2*kg)",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^3" ], denominator: [ "t_p^2","m_p" ] },
inversion_geometry: { numerator: [ "-4","pi" ], denominator: [ "18" ] }, root_transform: { id: "zhe_r^3" },
expected_kind: measured, expected_value: 6.67430(15)e-11, expected_digits: "667430", expected_digits_label: "SI measured" }
- { recipe_number: 51, constant_id: G/ℏc, display_name: "Newtonian constant of gravitation over h-bar c", column: "2", island: "3", dimension: "c^4/GeV^2",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "GeV^2","t_p^4" ], denominator: [ "l_p^4","m_p^2" ] },
inversion_geometry: { numerator: [ "-4","pi" ], denominator: [ "18" ] }, root_transform: { id: "zhe_r^3" },
expected_kind: measured, expected_value: 6.70883(15)e-39, expected_digits: "670883", expected_digits_label: "SI measured" }
- { recipe_number: 52, constant_id: m_n, display_name: "neutron mass", column: "2", island: "3", dimension: "kg",
external_geometry: { numerator: [ "φ^2", "2^2", "pi^2" ], denominator: [ "2^2", "s^2" ] }, external_boundary: { numerator: [ "GeV", "t_p^2" ], denominator: [ "l_p^2" ] },
inversion_geometry: { numerator: [ "s" ], denominator: [ "-2", "pi" ] }, root_transform: { id: "zhe_r^3" },
expected_kind: measured, expected_value: 1.67492750056(85)e-27, expected_digits: "167492750056", expected_digits_label: "SI measured" }
- { recipe_number: 53, constant_id: m_+, display_name: "proton mass", column: "2", island: "3", dimension: "kg",
external_geometry: { numerator: [ "2^2", "pi^2" ], denominator: [ "s^2", "omega_2" ] }, external_boundary: { numerator: [ "GeV", "t_p^2" ], denominator: [ "l_p^2" ] },
inversion_geometry: { numerator: [ "2^0.5", "-18" ], denominator: [ "e^(γ/3)", "2", "s" ] }, root_transform: { id: "zhe_r^3" },
expected_kind: measured, expected_value: 1.67262192595(52)e-27, expected_digits: "167262192595", expected_digits_label: "SI measured" }
- { recipe_number: 54, constant_id: μ_de/μ_e, display_name: "deuteron-electron magnetic moment ratio", column: "2", island: "4", dimension: "-",
external_geometry: { numerator: [ "-1","P_up","2^0.5","s^0.5" ], denominator: [ "6^0.5","pi^0.5" ] }, external_boundary: { numerator: [ "m_e" ], denominator: [ "m_de" ] },
inversion_geometry: { numerator: [ "-18","L_1^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_r^3" },
expected_kind: measured, expected_value: -4.664345550(12)e-4, expected_digits: "4664345550", expected_digits_label: "SI measured" }
- { recipe_number: 55, constant_id: μ_e/μ_de, display_name: "electron-deuteron magnetic moment ratio", column: "2", island: "4", combine: inversion, dimension: "-",
external_geometry: { numerator: [ "6^0.5","pi^0.5" ], denominator: [ "-1","P_up","2^0.5","s^0.5" ] }, external_boundary: { numerator: [ "m_de" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ "-18","L_1^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_r^3" },
expected_kind: measured, expected_value: -2.1439234921(56)e3, expected_digits: "21439234921", expected_digits_label: "SI measured" }
- { recipe_number: 56, constant_id: m_μ, display_name: "muon mass", column: "2", island: "4", dimension: "kg",
external_geometry: { numerator: [ "2","pi","4^0.5", "pi^0.5" ], denominator: [ "35","6^0.5","s^0.5" ] }, external_boundary: { numerator: [ "A_mass" ], denominator: [ ] },
inversion_geometry: { numerator: [ "-18","K_-6" ], denominator: [ ] }, root_transform: { id: "zhe_r^3" },
expected_kind: measured, expected_value: 1.883531627(42)e-28, expected_digits: "1883531627", expected_digits_label: "SI measured" }
- { recipe_number: 57, constant_id: m_de, display_name: "deuteron mass", column: "2", island: "4", dimension: "kg",
external_geometry: { numerator: [ "4", "pi", "6^0.5", "pi^0.5" ], denominator: [ "35^0.5", "4^0.5", "s^0.5" ] }, external_boundary: { numerator: [ "A_mass" ], denominator: [ ] },
inversion_geometry: { numerator: [ "K_-6^3", "7", "pi" ], denominator: [ "9", "s" ] }, root_transform: { id: "zhe_r^3" },
expected_kind: measured, expected_value: 3.3435837768(10)e-27, expected_digits: "33435837768", expected_digits_label: "SI measured" }
- { recipe_number: 58, constant_id: μ_de/μ_+, display_name: "deuteron-proton magnetic moment ratio", column: "2", island: "4", dimension: "-",
external_geometry: { numerator: [ "S", "2^0.5", "s^0.5" ], denominator: [ "6^0.5", "pi^0.5" ] }, external_boundary: { numerator: [ "m_+" ], denominator: [ "m_de" ] },
inversion_geometry: { numerator: [ "!5", "-4", "pi" ], denominator: [ "φ", "35" ] }, root_transform: { id: "zhe_r^3" },
expected_kind: measured, expected_value: 3.0701220930(79)e-1, expected_digits: "30701220930", expected_digits_label: "SI measured" }
- { recipe_number: 59, constant_id: μ_de/μ_n, display_name: "deuteron-neutron magnetic moment ratio", column: "2", island: "4", dimension: "-",
external_geometry: { numerator: [ "-1","C_CFP","2^0.5","s^0.5" ], denominator: [ "6^0.5","pi^0.5" ] }, external_boundary: { numerator: [ "m_n" ], denominator: [ "m_de" ] },
inversion_geometry: { numerator: [ "-35", "Im(omega_1)", "4", "pi" ], denominator: [ "32" ] }, root_transform: { id: "zhe_r^3" },
expected_kind: measured, expected_value: -4.4820652(11)e-1, expected_digits: "44820652", expected_digits_label: "SI measured" }
- { recipe_number: 60, constant_id: μ_de, display_name: "deuteron magnetic moment", column: "2", island: "4", dimension: "J/T",
external_geometry: { numerator: [ "zhe_1^2","zhe_2^2","2^0.5","s^0.5" ], denominator: [ "6^0.5","pi^0.5" ] }, external_boundary: { numerator: [ "l_p^2","q_p","m_p" ], denominator: [ "t_p","m_de" ] },
inversion_geometry: { numerator: [ "-8","32" ], denominator: [ "omega_2","4","pi" ] }, root_transform: { id: "zhe_r^3" },
expected_kind: measured, expected_value: 4.330735087(11)e-27, expected_digits: "4330735087", expected_digits_label: "SI measured" }
- { recipe_number: 61, constant_id: μ_he'/μ_B, display_name: "shielded helion magnetic moment to Bohr magneton ratio", column: "2", island: "5", dimension: "-",
external_geometry: { numerator: [ "-1" ], denominator: [ "2","4^0.5","pi^0.5", "4^0.5", "s^0.5" ] }, external_boundary: { numerator: [ "m_μ" ], denominator: [ "m_he" ] },
inversion_geometry: { numerator: [ "2", "pi" ], denominator: [ "7^0.5", "3", "K" ] }, root_transform: { id: "zhe_r^4" },
expected_kind: measured, expected_value: -1.15867149457(94)e-3, expected_digits: "115867149457", expected_digits_label: "SI measured" }
- { recipe_number: 62, constant_id: μ_he'/μ_N, display_name: "shielded helion magnetic moment to nuclear magneton ratio", column: "2", island: "5", dimension: "-",
external_geometry: { numerator: [ "-1" ], denominator: [ "2","4^0.5","pi^0.5", "4^0.5", "s^0.5" ] }, external_boundary: { numerator: [ "m_+", "m_μ" ], denominator: [ "m_e", "m_he" ] },
inversion_geometry: { numerator: [ "2", "pi" ], denominator: [ "7^0.5", "3", "K" ] }, root_transform: { id: "zhe_r^4" },
expected_kind: measured, expected_value: -2.1274977624(17), expected_digits: "21274977624", expected_digits_label: "SI measured" }
- { recipe_number: 63, constant_id: g_he, display_name: "helion g factor", column: "2", island: "5", dimension: "-",
external_geometry: { numerator: [ "-1" ], denominator: [ "4^0.5","pi^0.5", "4^0.5", "s^0.5" ] }, external_boundary: { numerator: [ "m_+", "m_μ" ], denominator: [ "m_e", "m_he" ] },
inversion_geometry: { numerator: [ "18","2", "K" ], denominator: [ "14" ] }, root_transform: { id: "zhe_r^4" },
expected_kind: measured, expected_value: -4.2552506995(34), expected_digits: "42552506995", expected_digits_label: "SI measured" }
- { recipe_number: 64, constant_id: μ_he/μ_N, display_name: "helion magnetic moment to nuclear magneton ratio", column: "2", island: "5", dimension: "-",
external_geometry: { numerator: [ ], denominator: [ "-2", "4^0.5","pi^0.5", "4^0.5", "s^0.5" ] }, external_boundary: { numerator: [ "m_+", "m_μ" ], denominator: [ "m_e", "m_he" ] },
inversion_geometry: { numerator: [ "18","2", "K" ], denominator: [ "14" ] }, root_transform: { id: "zhe_r^4" },
expected_kind: measured, expected_value: -2.1276253498(17), expected_digits: "21276253498", expected_digits_label: "SI measured" }
- { recipe_number: 65, constant_id: μ_he/μ_B, display_name: "helion magnetic moment to Bohr magneton ratio", column: "2", island: "5", dimension: "-",
external_geometry: { numerator: [ ], denominator: [ "-2", "4^0.5","pi^0.5", "4^0.5", "s^0.5" ] }, external_boundary: { numerator: [ "m_μ" ], denominator: [ "m_he" ] },
inversion_geometry: { numerator: [ "18","2", "K" ], denominator: [ "14" ] }, root_transform: { id: "zhe_r^4" },
expected_kind: measured, expected_value: -1.15874098083(94)e-3, expected_digits: "115874098083", expected_digits_label: "SI measured" }
- { recipe_number: 66, constant_id: μ_0, display_name: "vacuum magnetic permeability", column: "2", island: "6", dimension: "N/A^2",
external_geometry: { numerator: [ "4","pi" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p","m_p" ], denominator: [ "q_p^2" ] },
inversion_geometry: { numerator: [ "G_Ga", "14" ], denominator: [ "28", "4", "s" ] }, root_transform: { id: "zhe_r^4" },
expected_kind: measured, expected_value: 1.25663706127(20)e-6, expected_digits: "125663706127", expected_digits_label: "SI measured" }
- { recipe_number: 67, constant_id: m_e, display_name: "electron mass", column: "2", island: "6", dimension: "kg",
external_geometry: { numerator: [ "2","V_fe" ], denominator: [ ] }, external_boundary: { numerator: [ "m_p^4" ], denominator: [ "kilogram^3" ] },
inversion_geometry: { numerator: [ "14" ], denominator: [ "4", "s" ] }, root_transform: { id: "zhe_r^4" },
expected_kind: measured, expected_value: 9.1093837139(28)e-31, expected_digits: "91093837139", expected_digits_label: "SI measured" }
- { recipe_number: 68, constant_id: m_τ, display_name: "tau mass", column: "2", island: "6", dimension: "kg",
external_geometry: { numerator: [ "35^0.5", "L_LL^0.5", "4^0.5", "s^0.5" ], denominator: [ "(zhe_1^6)^0.5", "2^0.5", "pi^0.5" ] }, external_boundary: { numerator: [ "m_p^4" ], denominator: [ "kilogram^3" ] },
inversion_geometry: { numerator: [ "14" ], denominator: [ "4", "s" ] }, root_transform: { id: "zhe_r^4" },
expected_kind: measured, expected_value: 3.16754(21)e-27, expected_digits: "316754", expected_digits_label: "SI measured" }
- { recipe_number: 69, constant_id: m_tri, display_name: "triton mass", column: "2", island: "6", dimension: "kg",
external_geometry: { numerator: [ "zhe_1^-5","4^0.5","s^0.5" ], denominator: [ "18","2^0.5","pi^0.5" ] }, external_boundary: { numerator: [ "m_p^4" ], denominator: [ "kilogram^3" ] },
inversion_geometry: { numerator: [ "G_Ga^0.5", "18" ], denominator: [ "14^0.5", "2", "K" ] }, root_transform: { id: "zhe_r^4" },
expected_kind: measured, expected_value: 5.0073567512(16)e-27, expected_digits: "50073567512", expected_digits_label: "SI measured" }
- { recipe_number: 70, constant_id: K_cd, display_name: "luminous efficacy", column: "2", island: "6", dimension: "lm/W",
external_geometry: { numerator: [ "zhe_1^-7","4^0.5","s^0.5" ], denominator: [ "f_1","2^0.5","pi^0.5" ] }, external_boundary: { numerator: [ "t_p^2" ], denominator: [ "l_p^2","A_mass" ] },
inversion_geometry: { numerator: [ "G_Ga^0.5", "18" ], denominator: [ "14^0.5", "2", "K" ] }, root_transform: { id: "zhe_r^4" },
expected_kind: exact, expected_value: 6.83e2, expected_digits: "683", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 71, constant_id: m_he, display_name: "helion mass", column: "2", island: "6", dimension: "kg",
external_geometry: { numerator: [ "36", "9^0.5", "s^0.5" ], denominator: [ "e^pi", "4^0.5", "pi^0.5" ] }, external_boundary: { numerator: [ "A_mass" ], denominator: [ ] },
inversion_geometry: { numerator: [ "x_infinity" ], denominator: [ "14^0.5", "-2", "s" ] }, root_transform: { id: "zhe_r^4" },
expected_kind: measured, expected_value: 5.0064127862(16)e-27, expected_digits: "50064127862", expected_digits_label: "SI measured" }
- { recipe_number: 72, constant_id: m_α, display_name: "alpha particle mass", column: "2", island: "6", dimension: "kg",
external_geometry: { numerator: [ "12", "4^0.5", "s^0.5" ], denominator: [ "omega_2^4", "2^0.5", "pi^0.5" ] }, external_boundary: { numerator: [ "A_mass" ], denominator: [ ] },
inversion_geometry: { numerator: [ "32^0.5", "-2", "V_fe" ], denominator: [ "14^0.5", "x_infinity^2" ] }, root_transform: { id: "zhe_r^4" },
expected_kind: measured, expected_value: 6.6446573450(21)e-27, expected_digits: "66446573450", expected_digits_label: "SI measured" }
- { recipe_number: 73, constant_id: E_p ̇, display_name: "Planck mass energy equivalent in GeV", column: "3", island: "1", dimension: "GeV",
external_geometry: { numerator: [ ], denominator: [ "GeV" ] }, external_boundary: { numerator: [ "l_p^2", "m_p" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Re(ipt)" ], denominator: [ "2" ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 1.220890(14)e19, expected_digits: "1220890", expected_digits_label: "SI measured" }
- { recipe_number: 74, constant_id: R_K, display_name: "von Klitzing constant", column: "3", island: "1", dimension: "Ohm",
external_geometry: { numerator: [ "2", "pi" ], denominator: [ "zhe_1^2" ] }, external_boundary: { numerator: [ "l_p^2", "m_p" ], denominator: [ "t_p", "q_p^2" ] },
inversion_geometry: { numerator: [ "Re(ipt)" ], denominator: [ "2" ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: exact, expected_value: 2.581280745e4, expected_digits: "2581280745", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 75, constant_id: Z_0, display_name: "characteristic impedance of vacuum", column: "3", island: "1", dimension: "Ohm",
external_geometry: { numerator: [ "4", "pi" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2", "m_p" ], denominator: [ "t_p", "q_p^2" ] },
inversion_geometry: { numerator: [ "Re(ipt)" ], denominator: [ "2" ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 3.76730313412(59)e2, expected_digits: "376730313412", expected_digits_label: "SI measured" }
- { recipe_number: 76, constant_id: Z_p, display_name: "Planck electric impedance", column: "3", island: "1", dimension: "Ohm",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2", "m_p" ], denominator: [ "t_p", "q_p^2" ] },
inversion_geometry: { numerator: [ "Re(ipt)" ], denominator: [ "2" ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 2.99792458(45)E1, expected_digits: "299792458", expected_digits_label: "SI measured" }
- { recipe_number: 77, constant_id: Hz⋮1/m, display_name: "hertz-inverse meter relationship", column: "3", island: "2", dimension: "cycles/m",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "t_p" ], denominator: [ "second", "l_p" ] },
inversion_geometry: { numerator: [ "Im(ipt)" ], denominator: [ "2" ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: exact, expected_value: 3.335640951e-9, expected_digits: "3335640951", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 78, constant_id: A_vel, display_name: "atomic unit of velocity", column: "3", island: "2", dimension: "m/s",
external_geometry: { numerator: [ "zhe_1^2" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p" ], denominator: [ "t_p" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ "2" ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 2.18769126216(34)e6, expected_digits: "218769126216", expected_digits_label: "SI measured" }
- { recipe_number: 79, constant_id: A_mom, display_name: "atomic unit of momentum", column: "3", island: "2", dimension: "m*kg/s",
external_geometry: { numerator: [ "zhe_1^2" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p", "m_e" ], denominator: [ "t_p" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ "2" ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 1.99285191545(31)e-24, expected_digits: "199285191545", expected_digits_label: "SI measured" }
- { recipe_number: 80, constant_id: N_mom, display_name: "natural unit of momentum", column: "3", island: "2", dimension: "m*kg/s",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p", "m_e" ], denominator: [ "t_p" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ "2" ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 2.73092453446(85)e-22, expected_digits: "273092453446", expected_digits_label: "SI measured" }
- { recipe_number: 81, constant_id: N_mom ̇, display_name: "natural unit of momentum in MeV/c", column: "3", island: "3", dimension: "MeV/c",
external_geometry: { numerator: [ "second" ], denominator: [ "MeV" ] }, external_boundary: { numerator: [ "l_p^2", "m_e" ], denominator: [ "meter", "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 5.1099895069(16)e-1, expected_digits: "51099895069", expected_digits_label: "SI measured" }
- { recipe_number: 82, constant_id: E_A_mass ̇, display_name: "atomic mass constant energy equivalent in MeV", column: "3", island: "3", dimension: "MeV",
external_geometry: { numerator: [ ], denominator: [ "MeV" ] }, external_boundary: { numerator: [ "A_mass", "l_p^2" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 9.3149410372(29)e2, expected_digits: "93149410372", expected_digits_label: "SI measured" }
- { recipe_number: 83, constant_id: E_e ̇, display_name: "natural unit of energy in MeV", column: "3", island: "3", dimension: "MeV",
external_geometry: { numerator: [ ], denominator: [ "MeV" ] }, external_boundary: { numerator: [ "l_p^2", "m_e" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 5.1099895069(16)E-1, expected_digits: "51099895069", expected_digits_label: "SI measured" }
- { recipe_number: 84, constant_id: E_μ ̇, display_name: "muon mass energy equivalent in MeV", column: "3", island: "3", dimension: "MeV",
external_geometry: { numerator: [ ], denominator: [ "MeV" ] }, external_boundary: { numerator: [ "l_p^2", "m_μ" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 1.056583755(23)e2, expected_digits: "1056583755", expected_digits_label: "SI measured" }
- { recipe_number: 85, constant_id: E_+ ̇, display_name: "proton mass energy equivalent in MeV", column: "3", island: "3", dimension: "MeV",
external_geometry: { numerator: [ ], denominator: [ "MeV" ] }, external_boundary: { numerator: [ "l_p^2", "m_+" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 9.3827208943(29)e2, expected_digits: "93827208943", expected_digits_label: "SI measured" }
- { recipe_number: 86, constant_id: E_n ̇, display_name: "neutron mass energy equivalent in MeV", column: "3", island: "3", dimension: "MeV",
external_geometry: { numerator: [ ], denominator: [ "MeV" ] }, external_boundary: { numerator: [ "l_p^2", "m_n" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 9.3956542194(48)e2, expected_digits: "93956542194", expected_digits_label: "SI measured" }
- { recipe_number: 87, constant_id: E_∆ ̇, display_name: "neutron-proton mass difference energy equivalent in MeV", column: "3", island: "3", dimension: "MeV",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "(m_n - m_+)", "l_p^2" ], denominator: [ "MeV", "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 1.29333251(38), expected_digits: "129333251", expected_digits_label: "SI measured" }
- { recipe_number: 88, constant_id: E_τ ̇, display_name: "tau energy equivalent", column: "3", island: "3", dimension: "MeV",
external_geometry: { numerator: [ ], denominator: [ "MeV" ] }, external_boundary: { numerator: [ "l_p^2", "m_τ" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 1.77686(12)e3, expected_digits: "177686", expected_digits_label: "SI measured" }
- { recipe_number: 89, constant_id: E_de ̇, display_name: "deuteron mass energy equivalent in MeV", column: "3", island: "3", dimension: "MeV",
external_geometry: { numerator: [ ], denominator: [ "MeV" ] }, external_boundary: { numerator: [ "l_p^2", "m_de" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 1.87561294500(58)e3, expected_digits: "187561294500", expected_digits_label: "SI measured" }
- { recipe_number: 90, constant_id: E_he ̇, display_name: "helion mass energy equivalent in MeV", column: "3", island: "3", dimension: "MeV",
external_geometry: { numerator: [ ], denominator: [ "MeV" ] }, external_boundary: { numerator: [ "l_p^2", "m_he" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 2.80839161112(88)e3, expected_digits: "280839161112", expected_digits_label: "SI measured" }
- { recipe_number: 91, constant_id: E_tri ̇, display_name: "triton mass energy equivalent in MeV", column: "3", island: "3", dimension: "MeV",
external_geometry: { numerator: [ ], denominator: [ "MeV" ] }, external_boundary: { numerator: [ "l_p^2", "m_tri" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 2.80892113668(88)e3, expected_digits: "280892113668", expected_digits_label: "SI measured" }
- { recipe_number: 92, constant_id: E_α ̇, display_name: "alpha particle mass energy equivalent in MeV", column: "3", island: "3", dimension: "MeV",
external_geometry: { numerator: [ ], denominator: [ "MeV" ] }, external_boundary: { numerator: [ "l_p^2", "m_α" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 3.7273794118(12)e3, expected_digits: "37273794118", expected_digits_label: "SI measured" }
- { recipe_number: 93, constant_id: kg⋮eV, display_name: "kilogram-electron volt relationship", column: "3", island: "3", dimension: "eV",
external_geometry: { numerator: [ ], denominator: [ "eV" ] }, external_boundary: { numerator: [ "kilogram", "l_p^2" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: exact, expected_value: 5.609588603E35, expected_digits: "5609588603", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 94, constant_id: eV⋮kg, display_name: "electron volt-kilogram relationship", column: "3", island: "3", dimension: "kg",
external_geometry: { numerator: [ "eV" ], denominator: [ ] }, external_boundary: { numerator: [ "t_p^2" ], denominator: [ "l_p^2" ] },
inversion_geometry: { numerator: [ "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: exact, expected_value: 1.782661921E-36, expected_digits: "1782661921", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 95, constant_id: J⋮kg, display_name: "joule-kilogram relationship", column: "3", island: "3", dimension: "kg",
external_geometry: { numerator: [ "joule" ], denominator: [ ] }, external_boundary: { numerator: [ "t_p^2" ], denominator: [ "l_p^2" ] },
inversion_geometry: { numerator: [ "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: exact, expected_value: 1.112650056e-17, expected_digits: "1112650056", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 96, constant_id: J⋮A_mass, display_name: "joule-atomic mass unit relationship", column: "3", island: "3", dimension: "u",
external_geometry: { numerator: [ "joule" ], denominator: [ ] }, external_boundary: { numerator: [ "t_p^2" ], denominator: [ "A_mass", "l_p^2" ] },
inversion_geometry: { numerator: [ "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 6.7005352471(21)e9, expected_digits: "67005352471", expected_digits_label: "SI measured" }
- { recipe_number: 97, constant_id: kg⋮J, display_name: "kilogram-joule relationship", column: "3", island: "3", dimension: "J",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "kilogram", "l_p^2" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: exact, expected_value: 8.987551787E16, expected_digits: "8987551787", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 98, constant_id: A_mass⋮J, display_name: "atomic mass unit-joule relationship", column: "3", island: "3", dimension: "J",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "A_mass", "l_p^2" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 1.49241808768(46)e-10, expected_digits: "149241808768", expected_digits_label: "SI measured" }
- { recipe_number: 99, constant_id: E_e, display_name: "electron mass energy equivalent", column: "3", island: "3", dimension: "J",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2", "m_e" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 8.1871057880(26)e-14, expected_digits: "81871057880", expected_digits_label: "SI measured" }
- { recipe_number: 100, constant_id: E_μ, display_name: "muon mass energy equivalent", column: "3", island: "3", dimension: "J",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2", "m_μ" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 1.692833804(38)e-11, expected_digits: "1692833804", expected_digits_label: "SI measured" }
- { recipe_number: 101, constant_id: E_+, display_name: "proton mass energy equivalent", column: "3", island: "3", dimension: "J",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2", "m_+" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 1.50327761802(47)e-10, expected_digits: "150327761802", expected_digits_label: "SI measured" }
- { recipe_number: 102, constant_id: E_n, display_name: "neutron mass energy equivalent", column: "3", island: "3", dimension: "J",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2", "m_n" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 1.50534976514(76)e-10, expected_digits: "150534976514", expected_digits_label: "SI measured" }
- { recipe_number: 103, constant_id: E_∆, display_name: "neutron-proton mass difference energy equivalent", column: "3", island: "3", dimension: "J",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "(m_n - m_+)", "l_p^2" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 2.07214712(60)e-13, expected_digits: "207214712", expected_digits_label: "SI measured" }
- { recipe_number: 104, constant_id: E_τ, display_name: "tau mass energy equivalent", column: "3", island: "3", dimension: "J",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2", "m_τ" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 2.84684(19)e-10, expected_digits: "284684", expected_digits_label: "SI measured" }
- { recipe_number: 105, constant_id: E_de, display_name: "deuteron mass energy equivalent", column: "3", island: "3", dimension: "J",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2", "m_de" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 3.00506323491(94)e-10, expected_digits: "300506323491", expected_digits_label: "SI measured" }
- { recipe_number: 106, constant_id: E_he, display_name: "helion mass energy equivalent", column: "3", island: "3", dimension: "J",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2", "m_he" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 4.4995394185(14)e-10, expected_digits: "44995394185", expected_digits_label: "SI measured" }
- { recipe_number: 107, constant_id: E_tri, display_name: "triton mass energy equivalent", column: "3", island: "3", dimension: "J",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2", "m_tri" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 4.5003878119(14)e-10, expected_digits: "45003878119", expected_digits_label: "SI measured" }
- { recipe_number: 108, constant_id: E_α, display_name: "alpha particle mass energy equivalent", column: "3", island: "3", dimension: "J",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2", "m_α" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "-1", "Im(ipt)" ], denominator: [ ] }, root_transform: { id: "zhe_3*zhe_4" },
expected_kind: measured, expected_value: 5.9719201997(19)e-10, expected_digits: "59719201997", expected_digits_label: "SI measured" }
- { recipe_number: 109, constant_id: g_de, display_name: "deuteron g factor", column: "4", island: "1", dimension: "-",
external_geometry: { numerator: [ "2", "pi" ], denominator: [ "8", "K" ] }, external_boundary: { numerator: [ ], denominator: [ ] },
inversion_geometry: { numerator: [ "-8", "2", "pi" ], denominator: [ "W_We" ] }, root_transform: { id: "zhe_1 * zhe_3 * zhe_4" },
expected_kind: measured, expected_value: 8.574382335(22)e-1, expected_digits: "8574382335", expected_digits_label: "SI measured" }
- { recipe_number: 110, constant_id: μ_de/μ_N, display_name: "deuteron magnetic moment to nuclear magneton ratio", column: "4", island: "1", dimension: "-",
external_geometry: { numerator: [ "2", "pi" ], denominator: [ "8", "K" ] }, external_boundary: { numerator: [ ], denominator: [ ] },
inversion_geometry: { numerator: [ "-8", "2", "pi" ], denominator: [ "W_We" ] }, root_transform: { id: "zhe_1 * zhe_3 * zhe_4" },
expected_kind: measured, expected_value: 8.574382335(22)e-1, expected_digits: "8574382335", expected_digits_label: "SI measured" }
- { recipe_number: 111, constant_id: μ_de/μ_B, display_name: "deuteron magnetic moment to Bohr magneton ratio", column: "4", island: "1", dimension: "-",
external_geometry: { numerator: [ "2", "pi" ], denominator: [ "8", "K" ] }, external_boundary: { numerator: [ "m_e" ], denominator: [ "m_+" ] },
inversion_geometry: { numerator: [ "-8", "2", "pi" ], denominator: [ "W_We" ] }, root_transform: { id: "zhe_1 * zhe_3 * zhe_4" },
expected_kind: measured, expected_value: 4.669754568(12)e-4, expected_digits: "4669754568", expected_digits_label: "SI measured" }
- { recipe_number: 112, constant_id: μ_μ, display_name: "muon magnetic moment", column: "4", island: "2", dimension: "J/T",
external_geometry: { numerator: [ "-1", "zhe_1^2","zhe_2^2" ], denominator: [ "P_up" ] }, external_boundary: { numerator: [ "l_p^2","q_p","m_p" ], denominator: [ "t_p","m_μ" ] },
inversion_geometry: { numerator: [ "35", "G_Gi" ], denominator: [ "(L_Li)^2", "12" ] }, root_transform: { id: "zhe_1^2 * zhe_3^2 * zhe_4^2" },
expected_kind: measured, expected_value: -4.49044830(10)e-26, expected_digits: "449044830", expected_digits_label: "SI measured" }
- { recipe_number: 113, constant_id: a_e, display_name: "electron magnetic moment anomaly", column: "4", island: "2", dimension: "-", combine: "-",
external_geometry: { numerator: [ "2", "zhe_1", "zhe_2^2" ], denominator: [ "P_up" ] }, external_boundary: { numerator: [ ], denominator: [ ] },
inversion_geometry: { numerator: [ "-35","2^0.5" ], denominator: [ "L_Li", "V_fe" ] }, root_transform: { id: "zhe_1^2 * zhe_3^2 * zhe_4^2" },
expected_kind: measured, expected_value: 1.15965218046(18)e-3, expected_digits: "115965218046", expected_digits_label: "SI measured" }
- { recipe_number: 114, constant_id: a_μ, display_name: "muon magnetic moment anomaly", column: "4", island: "2", dimension: "-", combine: "-",
external_geometry: { numerator: [ "2", "zhe_1", "zhe_2^2" ], denominator: [ "P_up" ] }, external_boundary: { numerator: [ ], denominator: [ ] },
inversion_geometry: { numerator: [ "-2", "!5", "K" ], denominator: [ "(L_Li)^0.5" ] }, root_transform: { id: "zhe_1^2 * zhe_3^2 * zhe_4^2" },
expected_kind: measured, expected_value: 1.16592062(41)e-3, expected_digits: "116592062", expected_digits_label: "SI measured" }
- { recipe_number: 115, constant_id: g_μ, display_name: "muon g factor", column: "4", island: "3", dimension: "-",
external_geometry: { numerator: [ "-4", "zhe_1","zhe_2^2" ], denominator: [ "P_up" ] }, external_boundary: { numerator: [ ], denominator: [ ] },
inversion_geometry: { numerator: [ "zeta(2)^(1/3)", "35" ], denominator: [ "C_d" ] }, root_transform: { id: "zhe_1^3 * zhe_3^3 * zhe_4^3" },
expected_kind: measured, expected_value: -2.00233184123(82), expected_digits: "200233184123", expected_digits_label: "SI measured" }
- { recipe_number: 116, constant_id: μ_μ/μ_B, display_name: "muon magnetic moment to Bohr magneton ratio", column: "4", island: "3", dimension: "-",
external_geometry: { numerator: [ "-2", "zhe_1","zhe_2^2" ], denominator: [ "P_up" ] }, external_boundary: { numerator: [ "m_e" ], denominator: [ "m_μ" ] },
inversion_geometry: { numerator: [ "zeta(2)^(1/3)", "35" ], denominator: [ "C_d" ] }, root_transform: { id: "zhe_1^3 * zhe_3^3 * zhe_4^3" },
expected_kind: measured, expected_value: -4.84197048(11)e-3, expected_digits: "484197048", expected_digits_label: "SI measured" }
- { recipe_number: 117, constant_id: μ_μ/μ_N, display_name: "muon magnetic moment to nuclear magneton ratio", column: "4", island: "3", dimension: "-",
external_geometry: { numerator: [ "-2", "zhe_1","zhe_2^2" ], denominator: [ "P_up" ] }, external_boundary: { numerator: [ "m_+" ], denominator: [ "m_μ" ] },
inversion_geometry: { numerator: [ "zeta(2)^(1/3)", "35" ], denominator: [ "C_d" ] }, root_transform: { id: "zhe_1^3 * zhe_3^3 * zhe_4^3" },
expected_kind: measured, expected_value: -8.89059704(20), expected_digits: "889059704", expected_digits_label: "SI measured" }
- { recipe_number: 118, constant_id: R, display_name: "molar gas constant", column: "4", island: "4", dimension: "J/mol*K",
external_geometry: { numerator: [ "6", "zhe_1^2" ], denominator: [ "e^γ" ] }, external_boundary: { numerator: [ "l_p^2", "coulomb", "kilogram" ], denominator: [ "t_p^2", "q_p", "T_p" ] },
inversion_geometry: { numerator: [ "-8" ], denominator: [ "C_d" ] }, root_transform: { id: "zhe_1^4*zhe_3^4*zhe_4^4" },
expected_kind: exact, expected_value: 8.314462618, expected_digits: "8314462618", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 119, constant_id: V_m_0, display_name: "molar volume of ideal gas (273.15 K, 100 kPa)", column: "4", island: "4", dimension: "m^3/mol",
external_geometry: { numerator: [ "6", "zhe_1^2" ], denominator: [ "e^γ" ] }, external_boundary: { numerator: [ "T_0", "l_p^2", "coulomb", "kilogram" ], denominator: [ "p_0", "t_p^2", "q_p", "T_p" ] },
inversion_geometry: { numerator: [ "-8" ], denominator: [ "C_d" ] }, root_transform: { id: "zhe_1^4*zhe_3^4*zhe_4^4" },
expected_kind: exact, expected_value: 2.271095464e-2, expected_digits: "2271095464", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 120, constant_id: V_m_1, display_name: "molar volume of ideal gas (273.15 K, 101.325 kPa)", column: "4", island: "4", dimension: "m^3/mol",
external_geometry: { numerator: [ "6", "zhe_1^2" ], denominator: [ "e^γ" ] }, external_boundary: { numerator: [ "T_0", "l_p^2", "coulomb", "kilogram" ], denominator: [ "p_1", "t_p^2", "q_p", "T_p" ] },
inversion_geometry: { numerator: [ "-8" ], denominator: [ "C_d" ] }, root_transform: { id: "zhe_1^4*zhe_3^4*zhe_4^4" },
expected_kind: exact, expected_value: 2.241396954e-2, expected_digits: "2241396954", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 121, constant_id: g_e, display_name: "electron g factor", column: "4", island: "5", dimension: "-",
external_geometry: { numerator: [ "-4","zhe_1","zhe_2","zhe_2" ], denominator: [ "P_up" ] }, external_boundary: { numerator: [ ], denominator: [ ] },
inversion_geometry: { numerator: [ "C_CFP^2","32" ], denominator: [ "D_d" ] }, root_transform: { id: "zhe_1^6 * zhe_3^6 * zhe_4^6" },
expected_kind: measured, expected_value: -2.00231930436092(36), expected_digits: "200231930436092", expected_digits_label: "SI measured" }
- { recipe_number: 122, constant_id: μ_e/μ_B, display_name: "electron magnetic moment to Bohr magneton ratio", column: "4", island: "5", dimension: "-",
external_geometry: { numerator: [ "-2","zhe_1","zhe_2","zhe_2" ], denominator: [ "P_up" ] }, external_boundary: { numerator: [ ], denominator: [ ] },
inversion_geometry: { numerator: [ "C_CFP^2","32" ], denominator: [ "D_d" ] }, root_transform: { id: "zhe_1^6 * zhe_3^6 * zhe_4^6" },
expected_kind: measured, expected_value: -1.00115965218046(18), expected_digits: "100115965218046", expected_digits_label: "SI measured" }
- { recipe_number: 123, constant_id: μ_e/μ_N, display_name: "electron magnetic moment to nuclear magneton ratio", column: "4", island: "5", dimension: "-",
external_geometry: { numerator: [ "-2","zhe_1","zhe_2","zhe_2" ], denominator: [ "P_up" ] }, external_boundary: { numerator: [ "m_+" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ "C_CFP^2","32" ], denominator: [ "D_d" ] }, root_transform: { id: "zhe_1^6 * zhe_3^6 * zhe_4^6" },
expected_kind: measured, expected_value: -1.838281971877(32)e3, expected_digits: "1838281971877", expected_digits_label: "SI measured" }
- { recipe_number: 124, constant_id: μ_e, display_name: "electron magnetic moment", column: "4", island: "6", dimension: "J/T",
external_geometry: { numerator: [ "-1","zhe_1^2","zhe_2^2" ], denominator: [ "P_up" ] }, external_boundary: { numerator: [ "l_p^2","q_p","m_p" ], denominator: [ "t_p","m_e" ] },
inversion_geometry: { numerator: [ "7^0.5","8", "s" ], denominator: [ "4", "pi" ] }, root_transform: { id: "zhe_1^8 * zhe_3^8 * zhe_4^8" },
expected_kind: measured, expected_value: -9.2847646917(29)e-24, expected_digits: "92847646917", expected_digits_label: "SI measured" }
- { recipe_number: 125, constant_id: γ_e, display_name: "electron gyromagnetic ratio", column: "4", island: "6", dimension: "1/s*T",
external_geometry: { numerator: [ "2", "zhe_1^2", "zhe_2^2" ], denominator: [ "P_up" ] }, external_boundary: { numerator: [ "q_p" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ "7", "3", "s" ], denominator: [ "4", "pi" ] }, root_transform: { id: "zhe_1^8 * zhe_3^8 * zhe_4^8" },
expected_kind: measured, expected_value: 1.76085962784(55)e11, expected_digits: "176085962784", expected_digits_label: "SI measured" }
- { recipe_number: 126, constant_id: γ_e ̇, display_name: "electron gyromagnetic ratio in MHz/T", column: "4", island: "6", dimension: "MHz/T",
external_geometry: { numerator: [ "zhe_1^2", "zhe_2^2" ], denominator: [ "pi", "P_up", "MHz" ] }, external_boundary: { numerator: [ "q_p" ], denominator: [ "second", "m_e" ] },
inversion_geometry: { numerator: [ "7", "3", "s" ], denominator: [ "4", "pi" ] }, root_transform: { id: "zhe_1^8*zhe_3^8*zhe_4^8" },
expected_kind: measured, expected_value: 2.80249513861(87)e4, expected_digits: "280249513861", expected_digits_label: "SI measured" }
- { recipe_number: 127, constant_id: γ_+' ̇, display_name: "shielded proton gyromagnetic ratio in MHz/T", column: "4", island: "7", dimension: "MHz/T",
external_geometry: { numerator: [ "zhe_1^2", "zhe_2^2" ], denominator: [ "pi", "S", "MHz" ] }, external_boundary: { numerator: [ "q_p" ], denominator: [ "second", "m_+" ] },
inversion_geometry: { numerator: [ "35^0.5", "-7" ], denominator: [ "s" ] }, root_transform: { id: "zhe_2*zhe_3*zhe_4" },
expected_kind: measured, expected_value: 4.257638543(17)e1, expected_digits: "4257638543", expected_digits_label: "SI measured" }
- { recipe_number: 128, constant_id: γ_+', display_name: "shielded proton gyromagnetic ratio", column: "4", island: "7", dimension: "1/s*T",
external_geometry: { numerator: [ "2", "zhe_1^2", "zhe_2^2" ], denominator: [ "S" ] }, external_boundary: { numerator: [ "q_p" ], denominator: [ "m_+" ] },
inversion_geometry: { numerator: [ "35^0.5", "-7" ], denominator: [ "s" ] }, root_transform: { id: "zhe_2*zhe_3*zhe_4" },
expected_kind: measured, expected_value: 2.675153194(11)e8, expected_digits: "2675153194", expected_digits_label: "SI measured" }
- { recipe_number: 129, constant_id: μ_+', display_name: "shielded proton magnetic moment", column: "4", island: "7", dimension: "J/T",
external_geometry: { numerator: [ "zhe_1^2","zhe_2^2" ], denominator: [ "S" ] }, external_boundary: { numerator: [ "l_p^2","q_p","m_p" ], denominator: [ "t_p","m_+" ] },
inversion_geometry: { numerator: [ "3^0.5", "35^0.5", "7" ], denominator: [ "M", "s" ] }, root_transform: { id: "zhe_2 * zhe_3 * zhe_4" },
expected_kind: measured, expected_value: 1.4105705830(58)e-26, expected_digits: "14105705830", expected_digits_label: "SI measured" }
- { recipe_number: 130, constant_id: μ_+/μ_B, display_name: "proton magnetic moment to Bohr magneton ratio", column: "4", island: "8", dimension: "-",
external_geometry: { numerator: [ "2", "zhe_1", "zhe_2^2" ], denominator: [ "S" ] }, external_boundary: { numerator: [ "m_e" ], denominator: [ "m_+" ] },
inversion_geometry: { numerator: [ "-6", "2^2", "pi^2" ], denominator: [ "8^2", "K^2" ] }, root_transform: { id: "zhe_2*zhe_3*zhe_4" },
expected_kind: measured, expected_value: 1.52103220230(45)e-3, expected_digits: "152103220230", expected_digits_label: "SI measured" }
- { recipe_number: 131, constant_id: μ_+/μ_N, display_name: "proton magnetic moment to nuclear magneton ratio", column: "4", island: "8", dimension: "-",
external_geometry: { numerator: [ "2", "zhe_1", "zhe_2^2" ], denominator: [ "S" ] }, external_boundary: { numerator: [ ], denominator: [ ] },
inversion_geometry: { numerator: [ "-6", "2^2", "pi^2" ], denominator: [ "8^2", "K^2" ] }, root_transform: { id: "zhe_2*zhe_3*zhe_4" },
expected_kind: measured, expected_value: 2.79284734463(82), expected_digits: "279284734463", expected_digits_label: "SI measured" }
- { recipe_number: 132, constant_id: g_+, display_name: "proton g factor", column: "4", island: "8", dimension: "-",
external_geometry: { numerator: [ "4", "zhe_1", "zhe_2^2" ], denominator: [ "S" ] }, external_boundary: { numerator: [ ], denominator: [ ] },
inversion_geometry: { numerator: [ "-6", "2^2", "pi^2" ], denominator: [ "8^2", "K^2" ] }, root_transform: { id: "zhe_2*zhe_3*zhe_4" },
expected_kind: measured, expected_value: 5.5856946893(16), expected_digits: "55856946893", expected_digits_label: "SI measured" }
- { recipe_number: 133, constant_id: μ_n/μ_+', display_name: "neutron to shielded proton magnetic moment ratio", column: "4", island: "9", dimension: "-",
external_geometry: { numerator: [ "-1", "S" ], denominator: [ "C_CFP" ] }, external_boundary: { numerator: [ "m_+" ], denominator: [ "m_n" ] },
inversion_geometry: { numerator: [ "5^0.5", "4", "pi" ], denominator: [ "V_fe" ] }, root_transform: { id: "zhe_2 * zhe_3 * zhe_4" },
expected_kind: measured, expected_value: -6.8499694(16)e-1, expected_digits: "68499694", expected_digits_label: "SI measured" }
- { recipe_number: 134, constant_id: μ_e/μ_+, display_name: "electron-proton magnetic moment ratio", column: "4", island: "9", dimension: "-",
external_geometry: { numerator: [ "-1", "S" ], denominator: [ "P_up" ] }, external_boundary: { numerator: [ "m_+" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ "7^0.5", "4", "x_infinity" ], denominator: [ "2", "K" ] }, root_transform: { id: "zhe_2 * zhe_3 * zhe_4" },
expected_kind: measured, expected_value: -6.5821068789(19)e2, expected_digits: "65821068789", expected_digits_label: "SI measured" }
- { recipe_number: 135, constant_id: μ_e/μ_+', display_name: "electron to shielded proton magnetic moment ratio", column: "4", island: "10", dimension: "-",
external_geometry: { numerator: [ "-1", "S" ], denominator: [ "P_up" ] }, external_boundary: { numerator: [ "m_+" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ "5^0.5", "2", "K" ], denominator: [ "18" ] }, root_transform: { id: "zhe_2^2 * zhe_3^2 * zhe_4^2" },
expected_kind: measured, expected_value: -6.582275856(27)e2, expected_digits: "6582275856", expected_digits_label: "SI measured" }
- { recipe_number: 136, constant_id: μ_μ/μ_+, display_name: "muon-proton magnetic moment ratio", column: "4", island: "10", dimension: "-",
external_geometry: { numerator: [ "-1", "S" ], denominator: [ "P_up" ] }, external_boundary: { numerator: [ "m_+" ], denominator: [ "m_μ" ] },
inversion_geometry: { numerator: [ "35^0.5", "4", "K" ], denominator: [ "2", "pi", "18" ] }, root_transform: { id: "zhe_2^2 * zhe_3^2 * zhe_4^2" },
expected_kind: measured, expected_value: -3.183345146(71), expected_digits: "3183345146", expected_digits_label: "SI measured" }
- { recipe_number: 137, constant_id: μ_+'/μ_N, display_name: "shielded proton magnetic moment to nuclear magneton ratio", column: "4", island: "11", dimension: "-",
external_geometry: { numerator: [ "2", "zhe_1", "zhe_2^2" ], denominator: [ "S" ] }, external_boundary: { numerator: [ ], denominator: [ ] },
inversion_geometry: { numerator: [ "-2", "pi" ], denominator: [ "e^(6*γ)", "2", "K" ] }, root_transform: { id: "zhe_2^2 * zhe_3^2 * zhe_4^2" },
expected_kind: measured, expected_value: 2.792775648(11), expected_digits: "2792775648", expected_digits_label: "SI measured" }
- { recipe_number: 138, constant_id: μ_+'/μ_B, display_name: "shielded proton magnetic moment to Bohr magneton ratio", column: "4", island: "11", dimension: "-",
external_geometry: { numerator: [ "2", "zhe_1", "zhe_2^2" ], denominator: [ "S" ] }, external_boundary: { numerator: [ "m_e" ], denominator: [ "m_+" ] },
inversion_geometry: { numerator: [ "-2", "pi" ], denominator: [ "e^(6*γ)", "2", "K" ] }, root_transform: { id: "zhe_2^2 * zhe_3^2 * zhe_4^2" },
expected_kind: measured, expected_value: 1.5209931551(62)e-3, expected_digits: "15209931551", expected_digits_label: "SI measured" }
- { recipe_number: 139, constant_id: γ_+, display_name: "proton gyromagnetic ratio", column: "4", island: "12", dimension: "1/s*T",
external_geometry: { numerator: [ "2", "zhe_1^2","zhe_2^2" ], denominator: [ "S" ] }, external_boundary: { numerator: [ "q_p" ], denominator: [ "m_+" ] },
inversion_geometry: { numerator: [ "2", "pi" ], denominator: [ "-5", "4", "s" ] }, root_transform: { id: "zhe_2^2*zhe_3^2*zhe_4^2" },
expected_kind: measured, expected_value: 2.6752218708(11)e8, expected_digits: "26752218708", expected_digits_label: "SI measured" }
- { recipe_number: 140, constant_id: γ_+ ̇, display_name: "proton gyromagnetic ratio in MHz/T", column: "4", island: "12", dimension: "MHz/T",
external_geometry: { numerator: [ "zhe_1^2", "zhe_2^2", "second" ], denominator: [ "pi", "S", "MHz" ] }, external_boundary: { numerator: [ "q_p" ], denominator: [ "m_+" ] },
inversion_geometry: { numerator: [ "2", "pi" ], denominator: [ "-5", "4", "s" ] }, root_transform: { id: "zhe_2^2*zhe_3^2*zhe_4^2" },
expected_kind: measured, expected_value: 4.2577478461(18)e1, expected_digits: "42577478461", expected_digits_label: "SI measured" }
- { recipe_number: 141, constant_id: μ_+, display_name: "proton magnetic moment", column: "4", island: "12", dimension: "J/T",
external_geometry: { numerator: [ "zhe_1^2","zhe_2^2" ], denominator: [ "S" ] }, external_boundary: { numerator: [ "l_p^2","q_p","m_p" ], denominator: [ "t_p","m_+" ] },
inversion_geometry: { numerator: [ "-2", "pi" ], denominator: [ "3", "G_Gi", "35" ] }, root_transform: { id: "zhe_2^2 * zhe_3^2 * zhe_4^2" },
expected_kind: measured, expected_value: 1.41060679545(60)e-26, expected_digits: "141060679545", expected_digits_label: "SI measured" }
- { recipe_number: 142, constant_id: F, display_name: "Faraday constant", column: "4", island: "13", dimension: "C/mol",
external_geometry: { numerator: [ "6", "zhe_1^3" ], denominator: [ "e^γ" ] }, external_boundary: { numerator: [ "coulomb", "kilogram" ], denominator: [ "m_p" ] },
inversion_geometry: { numerator: [ "-2", "K" ], denominator: [ "35" ] }, root_transform: { id: "zhe_2^2 * zhe_3^2 * zhe_4^2" },
expected_kind: exact, expected_value: 9.648533212e4, expected_digits: "9648533212", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 143, constant_id: M_p, display_name: "molar Planck constant", column: "4", island: "13", dimension: "J/(Hz*mol)",
external_geometry: { numerator: [ "6", "2", "pi", "zhe_1^2" ], denominator: [ "e^γ" ] }, external_boundary: { numerator: [ "l_p^2", "coulomb", "kilogram" ], denominator: [ "t_p", "q_p" ] },
inversion_geometry: { numerator: [ "-5", "2", "K" ], denominator: [ "32^0.5", "6", "s" ] }, root_transform: { id: "zhe_2^2 * zhe_3^2 * zhe_4^2" },
expected_kind: exact, expected_value: 3.990312712e-10, expected_digits: "3990312712", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 144, constant_id: V_m(Si), display_name: "molar volume of silicon", column: "4", island: "13", dimension: "m^3/mol",
external_geometry: { numerator: [ "6", "2^3", "pi^3" ], denominator: [ "e^γ", "32^3", "s^3", "zhe_1^10" ] }, external_boundary: { numerator: [ "coulomb", "kilogram", "l_p^3", "m_p^2" ], denominator: [ "q_p", "m_e^3" ] },
inversion_geometry: { numerator: [ "2^0.5", "2", "pi" ], denominator: [ "7", "2", "K" ] }, root_transform: { id: "zhe_2^2 * zhe_3^2 * zhe_4^2" },
expected_kind: measured, expected_value: 1.205883199(60)e-5, expected_digits: "1205883199", expected_digits_label: "SI measured" }
- { recipe_number: 145, constant_id: c, display_name: "speed of light", column: "5", island: "1", dimension: "m/s",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p" ], denominator: [ "t_p" ] },
inversion_geometry: { numerator: [ "G_Gi^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: exact, expected_value: 2.99792458e8, expected_digits: "299792458", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 146, constant_id: 1/m⋮Hz, display_name: "inverse meter-hertz relationship", column: "5", island: "1", dimension: "Hz",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p" ], denominator: [ "meter", "t_p" ] },
inversion_geometry: { numerator: [ "G_Gi^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: exact, expected_value: 2.99792458e8, expected_digits: "299792458", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 147, constant_id: r_e, display_name: "classical electron radius", column: "5", island: "2", dimension: "m",
external_geometry: { numerator: [ "zhe_1^2" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p", "m_p" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ "-1", "6^0.5", "C_R1^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 2.8179403205(13)e-15, expected_digits: "28179403205", expected_digits_label: "SI measured" }
- { recipe_number: 148, constant_id: a_0, display_name: "atomic unit of length", column: "5", island: "2", dimension: "m",
external_geometry: { numerator: [ ], denominator: [ "zhe_1^2" ] }, external_boundary: { numerator: [ "l_p", "m_p" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ "-1", "6^0.5", "C_R1^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 5.29177210544(82)e-11, expected_digits: "529177210544", expected_digits_label: "SI measured" }
- { recipe_number: 149, constant_id: σ_e, display_name: "Thomson cross section", column: "5", island: "2", dimension: "m^2",
external_geometry: { numerator: [ "32^0.5", "2", "pi", "zhe_1^4" ], denominator: [ "18^0.5" ] }, external_boundary: { numerator: [ "l_p^2", "m_p^2" ], denominator: [ "m_e^2" ] },
inversion_geometry: { numerator: [ "-2", "6^0.5", "C_R1^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 6.6524587051(62)e-29, expected_digits: "66524587051", expected_digits_label: "SI measured" }
- { recipe_number: 150, constant_id: G_F/(ℏc)^3, display_name: "Fermi coupling constant", column: "5", island: "2", dimension: "1/GeV^2",
external_geometry: { numerator: [ "32^0.5", "2^2", "pi^2" ], denominator: [ "18^0.5" ] }, external_boundary: { numerator: [ "joule^2", "t_p^4" ], denominator: [ "GeV^2", "l_p^4", "m_p", "kilogram" ] },
inversion_geometry: { numerator: [ "28", "6^0.5", "C_R1^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 1.1663787(06)e-5, expected_digits: "11663787", expected_digits_label: "SI measured" }
- { recipe_number: 151, constant_id: A_mass, display_name: "atomic mass constant", column: "5", island: "3", dimension: "kg",
external_geometry: { numerator: [ "18^0.5", "P_up^0.5" ], denominator: [ "32^0.5", "(zhe_1^6)^0.5" ] }, external_boundary: { numerator: [ "m_e" ], denominator: [ ] },
inversion_geometry: { numerator: [ ], denominator: [ "L" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 1.66053906892(52)e-27, expected_digits: "166053906892", expected_digits_label: "SI measured" }
- { recipe_number: 152, constant_id: kg⋮A_mass, display_name: "kilogram-atomic mass unit relationship", column: "5", island: "3", dimension: "u",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^6)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ "kilogram" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ ], denominator: [ "-1", "L" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 6.0221407537(19)e26, expected_digits: "60221407537", expected_digits_label: "SI measured" }
- { recipe_number: 153, constant_id: A_r(e), display_name: "electron relative atomic mass", column: "5", island: "3", dimension: "-",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^6)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ ], denominator: [ ] },
inversion_geometry: { numerator: [ ], denominator: [ "-1", "L" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 5.485799090441(97)e-4, expected_digits: "5485799090441", expected_digits_label: "SI measured" }
- { recipe_number: 154, constant_id: A_r(+), display_name: "proton relative atomic mass", column: "5", island: "3", dimension: "-",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^6)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ "m_+" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ ], denominator: [ "-1", "L" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 1.0072764665789(83), expected_digits: "10072764665789", expected_digits_label: "SI measured" }
- { recipe_number: 155, constant_id: A_r(n), display_name: "neutron relative atomic mass", column: "5", island: "3", dimension: "-",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^6)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ "m_n" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ ], denominator: [ "-1", "L" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 1.00866491606(40), expected_digits: "100866491606", expected_digits_label: "SI measured" }
- { recipe_number: 156, constant_id: A_r(de), display_name: "deuteron relative atomic mass", column: "5", island: "3", dimension: "-",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^6)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ "m_de" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ ], denominator: [ "-1", "L" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 2.013553212544(15), expected_digits: "2013553212544", expected_digits_label: "SI measured" }
- { recipe_number: 157, constant_id: A_r(he), display_name: "helion relative atomic mass", column: "5", island: "3", dimension: "-",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^6)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ "m_he" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ ], denominator: [ "-1", "L" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 3.014932246932(74), expected_digits: "3014932246932", expected_digits_label: "SI measured" }
- { recipe_number: 158, constant_id: A_r(tri), display_name: "triton relative atomic mass", column: "5", island: "3", dimension: "-",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^6)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ "m_tri" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ ], denominator: [ "-1", "L" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 3.01550071597(10), expected_digits: "301550071597", expected_digits_label: "SI measured" }
- { recipe_number: 159, constant_id: A_r(α), display_name: "alpha particle relative atomic mass", column: "5", island: "3", dimension: "-",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^6)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ "m_α" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ ], denominator: [ "-1", "L" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 4.001506179129(62), expected_digits: "4001506179129", expected_digits_label: "SI measured" }
- { recipe_number: 160, constant_id: m_e/A_mass, display_name: "electron mass in u", column: "5", island: "3", dimension: "u",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^6)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ ], denominator: [ ] },
inversion_geometry: { numerator: [ ], denominator: [ "-1", "L" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 5.485799090441(97)e-4, expected_digits: "5485799090441", expected_digits_label: "SI measured" }
- { recipe_number: 161, constant_id: m_∆/A_mass, display_name: "neutron-proton mass difference in u", column: "5", island: "3", dimension: "u",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^6)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ "(m_n - m_+)" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ ], denominator: [ "-1", "L" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 1.38844948(40)e-3, expected_digits: "138844948", expected_digits_label: "SI measured" }
- { recipe_number: 162, constant_id: m_μ/A_mass, display_name: "muon mass in u", column: "5", island: "3", dimension: "u",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^6)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ "m_μ" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ ], denominator: [ "-1", "L" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 1.134289257(25)e-1, expected_digits: "1134289257", expected_digits_label: "SI measured" }
- { recipe_number: 163, constant_id: m_+/A_mass, display_name: "proton mass in u", column: "5", island: "3", dimension: "u",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^6)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ "m_+" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ ], denominator: [ "-1", "L" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 1.0072764665789(83), expected_digits: "10072764665789", expected_digits_label: "SI measured" }
- { recipe_number: 164, constant_id: m_n/A_mass, display_name: "neutron mass in u", column: "5", island: "3", dimension: "u",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^6)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ "m_n" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ ], denominator: [ "-1", "L" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 1.00866491606(40), expected_digits: "100866491606", expected_digits_label: "SI measured" }
- { recipe_number: 165, constant_id: m_τ/A_mass, display_name: "tau mass in u", column: "5", island: "3", dimension: "u",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^6)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ "m_τ" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ ], denominator: [ "-1", "L" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 1.90754(13), expected_digits: "190754", expected_digits_label: "SI measured" }
- { recipe_number: 166, constant_id: m_de/A_mass, display_name: "deuteron mass in u", column: "5", island: "3", dimension: "u",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^6)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ "m_de" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ ], denominator: [ "-1", "L" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 2.013553212544(15), expected_digits: "2013553212544", expected_digits_label: "SI measured" }
- { recipe_number: 167, constant_id: m_he/A_mass, display_name: "helion mass in u", column: "5", island: "3", dimension: "u",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^6)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ "m_he" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ ], denominator: [ "-1", "L" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 3.014932246932(74), expected_digits: "3014932246932", expected_digits_label: "SI measured" }
- { recipe_number: 168, constant_id: m_tri/A_mass, display_name: "triton mass in u", column: "5", island: "3", dimension: "u",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^6)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ "m_tri" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ ], denominator: [ "-1", "L" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 3.01550071597(10), expected_digits: "301550071597", expected_digits_label: "SI measured" }
- { recipe_number: 169, constant_id: m_α/A_mass, display_name: "alpha particle mass in u", column: "5", island: "3", dimension: "u",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^6)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ "m_α" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ ], denominator: [ "-1", "L" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 4.001506179129(62), expected_digits: "4001506179129", expected_digits_label: "SI measured" }
- { recipe_number: 170, constant_id: eV⋮A_mass, display_name: "electron volt-atomic mass unit relationship", column: "5", island: "4", dimension: "u",
external_geometry: { numerator: [ "joule^2", "32^0.5", "(zhe_1^8)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ "t_p^2", "q_p" ], denominator: [ "l_p^2", "coulomb", "m_e" ] },
inversion_geometry: { numerator: [ "-1", "α_F" ], denominator: [ ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 1.07354410083(33)e-9, expected_digits: "107354410083", expected_digits_label: "SI measured" }
- { recipe_number: 171, constant_id: A_mass⋮eV, display_name: "atomic mass unit-electron volt relationship", column: "5", island: "4", dimension: "eV",
external_geometry: { numerator: [ "18^0.5", "P_up^0.5" ], denominator: [ "32^0.5", "(zhe_1^8)^0.5" ] }, external_boundary: { numerator: [ "l_p^2", "coulomb", "m_e" ], denominator: [ "t_p^2", "q_p" ] },
inversion_geometry: { numerator: [ "α_F" ], denominator: [ ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: measured, expected_value: 9.3149410372(29)e8, expected_digits: "93149410372", expected_digits_label: "SI measured" }
- { recipe_number: 172, constant_id: ℏc ̇, display_name: "reduced Planck constant times c in MeV fm", column: "5", island: "5", dimension: "MeV fm",
external_geometry: { numerator: [ ], denominator: [ "MeV" ] }, external_boundary: { numerator: [ "l_p^3", "m_p" ], denominator: [ "t_p^2", "fm" ] },
inversion_geometry: { numerator: [ "-2" ], denominator: [ "δ_F" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: exact, expected_value: 1.973269804e2, expected_digits: "1973269804", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 173, constant_id: 1/m⋮eV, display_name: "inverse meter-electron volt relationship", column: "5", island: "5", dimension: "eV",
external_geometry: { numerator: [ "2", "pi" ], denominator: [ "eV" ] }, external_boundary: { numerator: [ "l_p^3", "m_p" ], denominator: [ "t_p^2", "meter" ] },
inversion_geometry: { numerator: [ "-2" ], denominator: [ "δ_F" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: exact, expected_value: 1.239841984E-6, expected_digits: "1239841984", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 174, constant_id: eV⋮1/m, display_name: "electron volt-inverse meter relationship", column: "5", island: "5", dimension: "cycles/m",
external_geometry: { numerator: [ "eV" ], denominator: [ "2", "pi" ] }, external_boundary: { numerator: [ "t_p^2" ], denominator: [ "l_p^3", "m_p" ] },
inversion_geometry: { numerator: [ "2" ], denominator: [ "δ_F" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: exact, expected_value: 8.065543937e5, expected_digits: "8065543937", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 175, constant_id: 1/m⋮J, display_name: "inverse meter-joule relationship", column: "5", island: "5", dimension: "J",
external_geometry: { numerator: [ "2", "pi" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^3", "m_p" ], denominator: [ "t_p^2", "meter" ] },
inversion_geometry: { numerator: [ "-2" ], denominator: [ "δ_F" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: exact, expected_value: 1.986445857E-25, expected_digits: "1986445857", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 176, constant_id: J⋮1/m, display_name: "joule-inverse meter relationship", column: "5", island: "5", dimension: "cycles/m",
external_geometry: { numerator: [ "joule" ], denominator: [ "2", "pi" ] }, external_boundary: { numerator: [ "t_p^2" ], denominator: [ "l_p^3", "m_p" ] },
inversion_geometry: { numerator: [ "2" ], denominator: [ "δ_F" ] }, root_transform: { id: "zhe_1 - zhe_2" },
expected_kind: exact, expected_value: 5.034116567e24, expected_digits: "5034116567", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 177, constant_id: A_e_pot, display_name: "atomic unit of electric potential", column: "5", island: "6", dimension: "V",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^12)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ "l_p^2", "A_mass" ], denominator: [ "t_p^2", "q_p" ] },
inversion_geometry: { numerator: [ "-35", "4" ], denominator: [ "18", "δ_F" ] }, root_transform: { id: "zhe_1 + zhe_2" },
expected_kind: measured, expected_value: 2.7211386245981(30)e1, expected_digits: "27211386245981", expected_digits_label: "SI measured" }
- { recipe_number: 178, constant_id: R_∞hc ̇, display_name: "Rydberg constant times hc in eV", column: "5", island: "6", dimension: "eV",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^12)^0.5" ], denominator: [ "2", "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ "coulomb", "l_p^2", "A_mass" ], denominator: [ "t_p^2", "q_p" ] },
inversion_geometry: { numerator: [ "-35", "4" ], denominator: [ "18", "δ_F" ] }, root_transform: { id: "zhe_1 + zhe_2" },
expected_kind: measured, expected_value: 1.3605693122990(15)e1, expected_digits: "13605693122990", expected_digits_label: "SI measured" }
- { recipe_number: 179, constant_id: E_h⋮eV, display_name: "hartree-electron volt relationship", column: "5", island: "6", dimension: "eV",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^12)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ "coulomb", "l_p^2", "A_mass" ], denominator: [ "t_p^2", "q_p" ] },
inversion_geometry: { numerator: [ "-35", "4" ], denominator: [ "18", "δ_F" ] }, root_transform: { id: "zhe_1 + zhe_2" },
expected_kind: measured, expected_value: 2.7211386245981(30)e1, expected_digits: "27211386245981", expected_digits_label: "SI measured" }
- { recipe_number: 180, constant_id: eV⋮E_h, display_name: "electron volt-hartree relationship", column: "5", island: "6", dimension: "E_h",
external_geometry: { numerator: [ "18^0.5", "P_up^0.5" ], denominator: [ "32^0.5", "(zhe_1^12)^0.5" ] }, external_boundary: { numerator: [ "t_p^2", "q_p" ], denominator: [ "coulomb", "l_p^2", "A_mass" ] },
inversion_geometry: { numerator: [ "35", "4" ], denominator: [ "18", "δ_F" ] }, root_transform: { id: "zhe_1 + zhe_2" },
expected_kind: measured, expected_value: 3.6749322175665(40)e-2, expected_digits: "36749322175665", expected_digits_label: "SI measured" }
- { recipe_number: 181, constant_id: F_90, display_name: "conventional value of farad-90", column: "6", island: "1", dimension: "F",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "farad" ], denominator: [ ] },
inversion_geometry: { numerator: [ "C_d" ], denominator: [ "6" ] }, root_transform: { id: "zhe_1 + zhe_3 + zhe_4" },
expected_kind: exact, expected_value: 0.99999998220, expected_digits: "99999998220", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 182, constant_id: H_90, display_name: "conventional value of henry-90", column: "6", island: "1", dimension: "H",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "henry" ], denominator: [ ] },
inversion_geometry: { numerator: [ "C_d" ], denominator: [ "-6" ] }, root_transform: { id: "zhe_1 + zhe_3 + zhe_4" },
expected_kind: exact, expected_value: 1.00000001779, expected_digits: "100000001779", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 183, constant_id: Ω_90, display_name: "conventional value of ohm-90", column: "6", island: "1", dimension: "Ω",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "ohm" ], denominator: [ ] },
inversion_geometry: { numerator: [ "C_d" ], denominator: [ "-6" ] }, root_transform: { id: "zhe_1 + zhe_3 + zhe_4" },
expected_kind: exact, expected_value: 1.00000001779, expected_digits: "100000001779", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 184, constant_id: m_∆, display_name: "neutron-proton mass difference", column: "6", island: "1", dimension: "kg",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "(m_n - m_+)" ], denominator: [ ] },
inversion_geometry: { numerator: [ "-35", "C_d" ], denominator: [ "6" ] }, root_transform: { id: "zhe_1 + zhe_3 + zhe_4" },
expected_kind: measured, expected_value: 2.30557461(67)e-30, expected_digits: "230557461", expected_digits_label: "SI measured" }
- { recipe_number: 185, constant_id: σ_he, display_name: "helion shielding shift", column: "6", island: "2", dimension: "-", combine: "-",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ ], denominator: [ ] },
inversion_geometry: { numerator: [ "-1", "7^0.5", "(s^4)^0.5" ], denominator: [ "((P*)^8)^0.5", "(2^3)^0.5", "(pi^3)^0.5" ] }, root_transform: { id: "zhe_1 - zhe_3 - zhe_4" },
expected_kind: measured, expected_value: 5.9967029(23)e-5, expected_digits: "59967029", expected_digits_label: "SI measured" }
- { recipe_number: 186, constant_id: σ_tp, display_name: "shielding difference of t and p in HT", column: "6", island: "2", dimension: "-", combine: "-",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ ], denominator: [ ] },
inversion_geometry: { numerator: [ "(s^4)^0.5" ], denominator: [ "-7", "(2^4)^0.5", "(2^3)^0.5", "(pi^3)^0.5" ] }, root_transform: { id: "zhe_1 - zhe_3 - zhe_4" },
expected_kind: measured, expected_value: 2.39450(20)e-8, expected_digits: "239450", expected_digits_label: "SI measured" }
- { recipe_number: 187, constant_id: σ_dp, display_name: "shielding difference of d and p in HD", column: "6", island: "2", dimension: "-", combine: "-",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ ], denominator: [ ] },
inversion_geometry: { numerator: [ "5^0.5", "(s^4)^0.5" ], denominator: [ "-3", "(2^4)^0.5", "(2^5)^0.5", "(pi^5)^0.5" ] }, root_transform: { id: "zhe_1 - zhe_3 - zhe_4" },
expected_kind: measured, expected_value: 1.98770(10)e-8, expected_digits: "198770", expected_digits_label: "SI measured" }
- { recipe_number: 188, constant_id: σ_+', display_name: "proton magnetic shielding correction", column: "6", island: "2", dimension: "-", combine: "-",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ ], denominator: [ ] },
inversion_geometry: { numerator: [ "-35", "(s^8)^0.5" ], denominator: [ "(4^2)^0.5", "(2^5)^0.5", "(pi^5)^0.5" ] }, root_transform: { id: "zhe_1 - zhe_3 - zhe_4" },
expected_kind: measured, expected_value: 2.56715(41)e-5, expected_digits: "256715", expected_digits_label: "SI measured" }
- { recipe_number: 189, constant_id: A_ep, display_name: "atomic unit of electric polarizability", column: "6", island: "3", dimension: "m^2*C^2/J",
external_geometry: { numerator: [ ], denominator: [ "zhe_1^6" ] }, external_boundary: { numerator: [ "t_p^2", "q_p^2", "m_p^2" ], denominator: [ "m_e^3" ] },
inversion_geometry: { numerator: [ "-18", "s^(9/2)" ], denominator: [ "(2^11)^0.5", "2^(5/2)", "pi^(5/2)" ] }, root_transform: { id: "zhe_1 + zhe_3 + zhe_4" },
expected_kind: measured, expected_value: 1.64877727212(51)e-41, expected_digits: "164877727212", expected_digits_label: "SI measured" }
- { recipe_number: 190, constant_id: A_ef, display_name: "atomic unit of electric field", column: "6", island: "3", dimension: "V/m",
external_geometry: { numerator: [ "zhe_1^5" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p", "m_e^2" ], denominator: [ "t_p^2", "q_p", "m_p" ] },
inversion_geometry: { numerator: [ "18", "(s^8)^0.5" ], denominator: [ "24^0.5", "(2^7)^0.5", "(pi^7)^0.5" ] }, root_transform: { id: "zhe_1 + zhe_3 + zhe_4" },
expected_kind: measured, expected_value: 5.14220675112(80)e11, expected_digits: "514220675112", expected_digits_label: "SI measured" }
- { recipe_number: 191, constant_id: A_force, display_name: "atomic unit of force", column: "6", island: "3", dimension: "N",
external_geometry: { numerator: [ "zhe_1^6" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p", "m_e^2" ], denominator: [ "t_p^2", "m_p" ] },
inversion_geometry: { numerator: [ "18", "((s^8)^0.5)" ], denominator: [ "4^(0.5)", "((2^8)^0.5)", "((pi^8)^0.5)" ] }, root_transform: { id: "zhe_1 + zhe_3 + zhe_4" },
expected_kind: measured, expected_value: 8.2387235038(13)e-8, expected_digits: "82387235038", expected_digits_label: "SI measured" }
- { recipe_number: 192, constant_id: A_cd, display_name: "atomic unit of charge density", column: "6", island: "3", dimension: "C/m^3",
external_geometry: { numerator: [ "zhe_1^7" ], denominator: [ ] }, external_boundary: { numerator: [ "q_p", "m_e^3" ], denominator: [ "l_p^3", "m_p^3" ] },
inversion_geometry: { numerator: [ "18", "((s^9)^0.5)" ], denominator: [ "8^(0.5)", "((2^8)^0.5)", "((pi^8)^0.5)" ] }, root_transform: { id: "zhe_1 + zhe_3 + zhe_4" },
expected_kind: measured, expected_value: 1.08120238677(51)e12, expected_digits: "108120238677", expected_digits_label: "SI measured" }
- { recipe_number: 193, constant_id: μ_n, display_name: "neutron magnetic moment", column: "6", island: "4", dimension: "J/T",
external_geometry: { numerator: [ "-1", "zhe_1^2", "zhe_2^2" ], denominator: [ "C_CFP" ] }, external_boundary: { numerator: [ "l_p^2", "q_p", "m_p" ], denominator: [ "t_p", "m_n" ] },
inversion_geometry: { numerator: [ "18", "2", "pi" ], denominator: [ ] }, root_transform: { id: "zhe_1 - zhe_3 - zhe_4" },
expected_kind: measured, expected_value: -9.6623653(23)e-27, expected_digits: "96623653", expected_digits_label: "SI measured" }
- { recipe_number: 194, constant_id: γ_n ̇, display_name: "neutron gyromagnetic ratio in MHz/T", column: "6", island: "4", dimension: "MHz/T",
external_geometry: { numerator: [ "zhe_1^2", "zhe_2^2" ], denominator: [ "pi", "C_CFP" ] }, external_boundary: { numerator: [ "q_p" ], denominator: [ "MHz", "second", "m_n" ] },
inversion_geometry: { numerator: [ "18", "2", "pi" ], denominator: [ ] }, root_transform: { id: "zhe_1 - zhe_3 - zhe_4" },
expected_kind: measured, expected_value: 2.91646935(69)e1, expected_digits: "291646935", expected_digits_label: "SI measured" }
- { recipe_number: 195, constant_id: γ_n, display_name: "neutron gyromagnetic ratio", column: "6", island: "4", dimension: "1/(s*T)",
external_geometry: { numerator: [ "2", "zhe_1^2", "zhe_2^2" ], denominator: [ "C_CFP" ] }, external_boundary: { numerator: [ "q_p" ], denominator: [ "m_n" ] },
inversion_geometry: { numerator: [ "18", "2", "pi" ], denominator: [ ] }, root_transform: { id: "zhe_1 - zhe_3 - zhe_4" },
expected_kind: measured, expected_value: 1.83247174(43)e8, expected_digits: "183247174", expected_digits_label: "SI measured" }
- { recipe_number: 196, constant_id: μ_n/μ_B, display_name: "neutron magnetic moment to Bohr magneton ratio", column: "6", island: "4", dimension: "-",
external_geometry: { numerator: [ "-2", "zhe_1", "zhe_2^2" ], denominator: [ "C_CFP" ] }, external_boundary: { numerator: [ "m_e" ], denominator: [ "m_n" ] },
inversion_geometry: { numerator: [ "18", "2", "pi" ], denominator: [ ] }, root_transform: { id: "zhe_1 - zhe_3 - zhe_4" },
expected_kind: measured, expected_value: -1.04187565(25)e-3, expected_digits: "104187565", expected_digits_label: "SI measured" }
- { recipe_number: 197, constant_id: μ_n/μ_N, display_name: "neutron magnetic moment to nuclear magneton ratio", column: "6", island: "4", dimension: "-",
external_geometry: { numerator: [ "-2", "zhe_1", "zhe_2^2" ], denominator: [ "C_CFP" ] }, external_boundary: { numerator: [ "m_+" ], denominator: [ "m_n" ] },
inversion_geometry: { numerator: [ "18", "2", "pi" ], denominator: [ ] }, root_transform: { id: "zhe_1 - zhe_3 - zhe_4" },
expected_kind: measured, expected_value: -1.91304276(45), expected_digits: "191304276", expected_digits_label: "SI measured" }
- { recipe_number: 198, constant_id: g_n, display_name: "neutron g factor", column: "6", island: "4", dimension: "-",
external_geometry: { numerator: [ "-4", "zhe_1", "zhe_2^2" ], denominator: [ "C_CFP" ] }, external_boundary: { numerator: [ "m_+" ], denominator: [ "m_n" ] },
inversion_geometry: { numerator: [ "18", "2", "pi" ], denominator: [ ] }, root_transform: { id: "zhe_1 - zhe_3 - zhe_4" },
expected_kind: measured, expected_value: -3.82608552(90), expected_digits: "382608552", expected_digits_label: "SI measured" }
- { recipe_number: 199, constant_id: Hz⋮kg, display_name: "hertz-kilogram relationship", column: "6", island: "5", dimension: "kg",
external_geometry: { numerator: [ "2", "pi" ], denominator: [ ] }, external_boundary: { numerator: [ "t_p", "m_p" ], denominator: [ "second" ] },
inversion_geometry: { numerator: [ "2" ], denominator: [ "C_CFP" ] }, root_transform: { id: "zhe_2 - zhe_3 - zhe_4" },
expected_kind: exact, expected_value: 7.372497323e-51, expected_digits: "7372497323", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 200, constant_id: Hz⋮A_mass, display_name: "hertz-atomic mass unit relationship", column: "6", island: "5", dimension: "u",
external_geometry: { numerator: [ "2", "pi" ], denominator: [ ] }, external_boundary: { numerator: [ "t_p", "m_p" ], denominator: [ "second", "A_mass" ] },
inversion_geometry: { numerator: [ "2" ], denominator: [ "C_CFP" ] }, root_transform: { id: "zhe_2 - zhe_3 - zhe_4" },
expected_kind: measured, expected_value: 4.4398216590(14)e-24, expected_digits: "44398216590", expected_digits_label: "SI measured" }
- { recipe_number: 201, constant_id: N_time, display_name: "natural unit of time", column: "6", island: "5", dimension: "s",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "t_p", "m_p" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ "2" ], denominator: [ "C_CFP" ] }, root_transform: { id: "zhe_2 - zhe_3 - zhe_4" },
expected_kind: measured, expected_value: 1.28808866644(40)e-21, expected_digits: "128808866644", expected_digits_label: "SI measured" }
- { recipe_number: 202, constant_id: A_mass⋮Hz, display_name: "atomic mass unit-hertz relationship", column: "6", island: "5", dimension: "Hz",
external_geometry: { numerator: [ ], denominator: [ "2", "pi" ] }, external_boundary: { numerator: [ "A_mass" ], denominator: [ "t_p", "m_p" ] },
inversion_geometry: { numerator: [ "-2" ], denominator: [ "C_CFP" ] }, root_transform: { id: "zhe_2 - zhe_3 - zhe_4" },
expected_kind: measured, expected_value: 2.25234272185(70)e23, expected_digits: "225234272185", expected_digits_label: "SI measured" }
- { recipe_number: 203, constant_id: kg⋮Hz, display_name: "kilogram-hertz relationship", column: "6", island: "5", dimension: "Hz",
external_geometry: { numerator: [ ], denominator: [ "2", "pi" ] }, external_boundary: { numerator: [ "kilogram" ], denominator: [ "t_p", "m_p" ] },
inversion_geometry: { numerator: [ "-2" ], denominator: [ "C_CFP" ] }, root_transform: { id: "zhe_2 - zhe_3 - zhe_4" },
expected_kind: exact, expected_value: 1.356392489E50, expected_digits: "1356392489", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 204, constant_id: k_B, display_name: "Boltzmann constant", column: "6", island: "6", dimension: "J/K",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2", "m_p" ], denominator: [ "t_p^2", "T_p" ] },
inversion_geometry: { numerator: [ "s", "2", "pi" ], denominator: [ "2^0.5", "4", "K" ] }, root_transform: { id: "zhe_2 - zhe_3 - zhe_4" },
expected_kind: exact, expected_value: 1.380649e-23, expected_digits: "1380649", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 205, constant_id: k_B ⃛, display_name: "Boltzmann constant in eV/K", column: "6", island: "6", dimension: "eV/K",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2", "m_p" ], denominator: [ "eV", "t_p^2", "T_p" ] },
inversion_geometry: { numerator: [ "s", "2", "pi" ], denominator: [ "2^0.5", "4", "K" ] }, root_transform: { id: "zhe_2 - zhe_3 - zhe_4" },
expected_kind: exact, expected_value: 8.617333262e-5, expected_digits: "8617333262", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 206, constant_id: K⋮eV, display_name: "kelvin-electron volt relationship", column: "6", island: "6", dimension: "eV",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2", "m_p", "kelvin" ], denominator: [ "eV", "t_p^2", "T_p" ] },
inversion_geometry: { numerator: [ "s", "2", "pi" ], denominator: [ "2^0.5", "4", "K" ] }, root_transform: { id: "zhe_2 - zhe_3 - zhe_4" },
expected_kind: exact, expected_value: 8.617333262e-5, expected_digits: "8617333262", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 207, constant_id: K⋮J, display_name: "kelvin-joule relationship", column: "6", island: "6", dimension: "J",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "kelvin", "l_p^2", "m_p" ], denominator: [ "t_p^2", "T_p" ] },
inversion_geometry: { numerator: [ "s", "2", "pi" ], denominator: [ "2^0.5", "4", "K" ] }, root_transform: { id: "zhe_2 - zhe_3 - zhe_4" },
expected_kind: exact, expected_value: 1.380649e-23, expected_digits: "1380649", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 208, constant_id: eV⋮K, display_name: "electron volt-kelvin relationship", column: "6", island: "6", dimension: "K",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "eV", "t_p^2", "T_p" ], denominator: [ "l_p^2", "m_p" ] },
inversion_geometry: { numerator: [ "s", "-2", "pi" ], denominator: [ "2^0.5", "4", "K" ] }, root_transform: { id: "zhe_2 - zhe_3 - zhe_4" },
expected_kind: exact, expected_value: 1.160451812e4, expected_digits: "1160451812", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 209, constant_id: J⋮K, display_name: "joule-kelvin relationship", column: "6", island: "6", dimension: "K",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "joule", "t_p^2", "T_p" ], denominator: [ "l_p^2", "m_p" ] },
inversion_geometry: { numerator: [ "s", "-2", "pi" ], denominator: [ "2^0.5", "4", "K" ] }, root_transform: { id: "zhe_2 - zhe_3 - zhe_4" },
expected_kind: exact, expected_value: 7.242970516e22, expected_digits: "7242970516", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 210, constant_id: n_0, display_name: "Loschmidt constant (273.15 K, 100 kPa)", column: "6", island: "6", dimension: "1/m^3",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "p_0", "t_p^2", "T_p" ], denominator: [ "T_0", "l_p^2", "m_p" ] },
inversion_geometry: { numerator: [ "s", "-2", "pi" ], denominator: [ "2^0.5", "4", "K" ] }, root_transform: { id: "zhe_2 - zhe_3 - zhe_4" },
expected_kind: exact, expected_value: 2.651645804e25, expected_digits: "2651645804", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 211, constant_id: n_1, display_name: "Loschmidt constant (273.15 K, 101.325 kPa)", column: "6", island: "6", dimension: "1/m^3",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "p_1", "t_p^2", "T_p" ], denominator: [ "T_0", "l_p^2", "m_p" ] },
inversion_geometry: { numerator: [ "s", "-2", "pi" ], denominator: [ "2^0.5", "4", "K" ] }, root_transform: { id: "zhe_2 - zhe_3 - zhe_4" },
expected_kind: exact, expected_value: 2.686780111e25, expected_digits: "2686780111", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 212, constant_id: μ_B/k_B, display_name: "Bohr magneton in K/T", column: "6", island: "7", dimension: "K/T",
external_geometry: { numerator: [ "zhe_1" ], denominator: [ "2" ] }, external_boundary: { numerator: [ "t_p", "q_p", "T_p" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ "-1", "32^0.5" ], denominator: [ "G_Gi^0.5" ] }, root_transform: { id: "zhe_2 - zhe_3 - zhe_4" },
expected_kind: measured, expected_value: 6.7171381472(21)e-1, expected_digits: "67171381472", expected_digits_label: "SI measured" }
- { recipe_number: 213, constant_id: μ_N/k_B, display_name: "nuclear magneton in K/T", column: "6", island: "7", dimension: "K/T",
external_geometry: { numerator: [ "zhe_1" ], denominator: [ "2" ] }, external_boundary: { numerator: [ "t_p", "q_p", "T_p" ], denominator: [ "m_+" ] },
inversion_geometry: { numerator: [ "-1", "32^0.5" ], denominator: [ "G_Gi^0.5" ] }, root_transform: { id: "zhe_2 - zhe_3 - zhe_4" },
expected_kind: measured, expected_value: 3.6582677706(11)e-4, expected_digits: "36582677706", expected_digits_label: "SI measured" }
- { recipe_number: 214, constant_id: R_∞hc ̈, display_name: "Rydberg constant times hc in J", column: "6", island: "8", dimension: "J",
external_geometry: { numerator: [ "zhe_1^4" ], denominator: [ "2" ] }, external_boundary: { numerator: [ "l_p^2", "m_e" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "35^0.5", "8", "D_d" ], denominator: [ ] }, root_transform: { id: "zhe_2 + zhe_3 + zhe_4" },
expected_kind: measured, expected_value: 2.1798723611030(24)e-18, expected_digits: "21798723611030", expected_digits_label: "SI measured" }
- { recipe_number: 215, constant_id: E_h, display_name: "Hartree energy", column: "6", island: "8", dimension: "J",
external_geometry: { numerator: [ "zhe_1^4" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^2", "m_e" ], denominator: [ "t_p^2" ] },
inversion_geometry: { numerator: [ "35^0.5", "8", "D_d" ], denominator: [ ] }, root_transform: { id: "zhe_2 + zhe_3 + zhe_4" },
expected_kind: measured, expected_value: 4.3597447222060(48)e-18, expected_digits: "43597447222060", expected_digits_label: "SI measured" }
- { recipe_number: 216, constant_id: J⋮E_h, display_name: "joule-hartree relationship", column: "6", island: "8", dimension: "E_h",
external_geometry: { numerator: [ ], denominator: [ "zhe_1^4" ] }, external_boundary: { numerator: [ "joule", "t_p^2" ], denominator: [ "l_p^2", "m_e" ] },
inversion_geometry: { numerator: [ "35^0.5", "-8", "D_d" ], denominator: [ ] }, root_transform: { id: "zhe_2 + zhe_3 + zhe_4" },
expected_kind: measured, expected_value: 2.2937122783969(25)e17, expected_digits: "22937122783969", expected_digits_label: "SI measured" }
- { recipe_number: 217, constant_id: K_J, display_name: "Josephson constant", column: "7", island: "1", dimension: "Hz/V",
external_geometry: { numerator: [ "zhe_1" ], denominator: [ "pi" ] }, external_boundary: { numerator: [ "t_p", "q_p" ], denominator: [ "l_p^2", "m_p" ] },
inversion_geometry: { numerator: [ "-7", "8^2" ], denominator: [ "8", "4^2", "pi^2" ] }, root_transform: { id: "zhe_1^2 + zhe_2^2" },
expected_kind: exact, expected_value: 4.835978484e14, expected_digits: "4835978484", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 218, constant_id: e/ℏ, display_name: "elementary charge over h-bar", column: "7", island: "1", dimension: "A/J",
external_geometry: { numerator: [ "zhe_1" ], denominator: [ ] }, external_boundary: { numerator: [ "t_p", "q_p" ], denominator: [ "l_p^2", "m_p" ] },
inversion_geometry: { numerator: [ "-7", "8^2" ], denominator: [ "8", "4^2", "pi^2" ] }, root_transform: { id: "zhe_1^2 + zhe_2^2" },
expected_kind: exact, expected_value: 1.519267447e15, expected_digits: "1519267447", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 219, constant_id: Φ_0, display_name: "magnetic flux quantum", column: "7", island: "1", dimension: "Wb",
external_geometry: { numerator: [ "pi" ], denominator: [ "zhe_1" ] }, external_boundary: { numerator: [ "l_p^2", "m_p" ], denominator: [ "t_p", "q_p" ] },
inversion_geometry: { numerator: [ "7", "8^2" ], denominator: [ "8", "4^2", "pi^2" ] }, root_transform: { id: "zhe_1^2 + zhe_2^2" },
expected_kind: exact, expected_value: 2.067833848e-15, expected_digits: "2067833848", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 220, constant_id: ℏ¨, display_name: "reduced Planck constant in eV s", column: "7", island: "1", dimension: "eV*s",
external_geometry: { numerator: [ ], denominator: [ "zhe_1" ] }, external_boundary: { numerator: [ "coulomb", "l_p^2", "m_p" ], denominator: [ "t_p", "q_p" ] },
inversion_geometry: { numerator: [ "7", "8^2" ], denominator: [ "8", "4^2", "pi^2" ] }, root_transform: { id: "zhe_1^2 + zhe_2^2" },
expected_kind: exact, expected_value: 6.582119569e-16, expected_digits: "6582119569", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 221, constant_id: h˙, display_name: "Planck constant in eV/Hz", column: "7", island: "1", dimension: "eV/Hz",
external_geometry: { numerator: [ "2", "pi" ], denominator: [ "zhe_1" ] }, external_boundary: { numerator: [ "coulomb", "l_p^2", "m_p" ], denominator: [ "t_p", "q_p" ] },
inversion_geometry: { numerator: [ "7", "8^2" ], denominator: [ "8", "4^2", "pi^2" ] }, root_transform: { id: "zhe_1^2 + zhe_2^2" },
expected_kind: exact, expected_value: 4.135667696e-15, expected_digits: "4135667696", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 222, constant_id: c_1, display_name: "first radiation constant", column: "7", island: "2", dimension: "W*m^2",
external_geometry: { numerator: [ "2^2", "pi^2" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^4", "m_p" ], denominator: [ "t_p^3" ] },
inversion_geometry: { numerator: [ "-1", "4^2", "pi^2" ], denominator: [ "32^2" ] }, root_transform: { id: "zhe_1^2 + zhe_2^2" },
expected_kind: exact, expected_value: 3.741771852e-16, expected_digits: "3741771852", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 223, constant_id: c_1L, display_name: "first radiation constant for spectral radiance", column: "7", island: "2", dimension: "W*m^2/sr",
external_geometry: { numerator: [ "4", "pi" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p^4", "m_p" ], denominator: [ "t_p^3" ] },
inversion_geometry: { numerator: [ "-1", "4^2", "pi^2" ], denominator: [ "32^2" ] }, root_transform: { id: "zhe_1^2 + zhe_2^2" },
expected_kind: exact, expected_value: 1.191042972e-16, expected_digits: "1191042972", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 224, constant_id: γ_he', display_name: "shielded helion gyromagnetic ratio", column: "7", island: "3", dimension: "1/(s*T)",
external_geometry: { numerator: [ "C_CFP^2" ], denominator: [ "7^0.5" ] }, external_boundary: { numerator: [ "q_p" ], denominator: [ "m_he" ] },
inversion_geometry: { numerator: [ "-1", "C_d" ], denominator: [ ] }, root_transform: { id: "zhe_1^2 + zhe_2^2" },
expected_kind: measured, expected_value: 2.0378946078(18)e8, expected_digits: "20378946078", expected_digits_label: "SI measured" }
- { recipe_number: 225, constant_id: γ_he ̇', display_name: "shielded helion gyromagnetic ratio in MHz/T", column: "7", island: "3", dimension: "MHz/T",
external_geometry: { numerator: [ "C_CFP^2" ], denominator: [ "2", "pi", "7^0.5" ] }, external_boundary: { numerator: [ "q_p" ], denominator: [ "MHz", "second", "m_he" ] },
inversion_geometry: { numerator: [ "-1", "C_d" ], denominator: [ ] }, root_transform: { id: "zhe_1^2 + zhe_2^2" },
expected_kind: measured, expected_value: 3.2434100033(28)e1, expected_digits: "32434100033", expected_digits_label: "SI measured" }
- { recipe_number: 226, constant_id: μ_he, display_name: "helion magnetic moment", column: "7", island: "3", dimension: "J/T",
external_geometry: { numerator: [ "C_CFP^2" ], denominator: [ "-2", "7^0.5" ] }, external_boundary: { numerator: [ "l_p^2", "q_p", "m_p" ], denominator: [ "t_p", "m_he" ] },
inversion_geometry: { numerator: [ "5", "16" ], denominator: [ "D_d" ] }, root_transform: { id: "zhe_1^2 + zhe_2^2" },
expected_kind: measured, expected_value: -1.07461755198(93)e-26, expected_digits: "107461755198", expected_digits_label: "SI measured" }
- { recipe_number: 227, constant_id: μ_he', display_name: "shielded helion magnetic moment", column: "7", island: "3", dimension: "J/T",
external_geometry: { numerator: [ "C_CFP^2" ], denominator: [ "-2", "7^0.5" ] }, external_boundary: { numerator: [ "l_p^2", "q_p", "m_p" ], denominator: [ "t_p", "m_he" ] },
inversion_geometry: { numerator: [ "8" ], denominator: [ "7", "4", "pi" ] }, root_transform: { id: "zhe_1^2 + zhe_2^2" },
expected_kind: measured, expected_value: -1.07455311035(93)e-26, expected_digits: "107455311035", expected_digits_label: "SI measured" }
- { recipe_number: 228, constant_id: μ_he'/μ_+, display_name: "shielded helion to proton magnetic moment ratio", column: "7", island: "3", dimension: "-",
external_geometry: { numerator: [ "C_CFP^2", "S" ], denominator: [ "-2", "7^0.5", "zhe_1^2", "zhe_2^2" ] }, external_boundary: { numerator: [ "m_+" ], denominator: [ "m_he" ] },
inversion_geometry: { numerator: [ "-1", "12^0.5", "L^2" ], denominator: [ ] }, root_transform: { id: "zhe_1^2 - zhe_2^2" },
expected_kind: measured, expected_value: -7.6176657721(66)e-1, expected_digits: "76176657721", expected_digits_label: "SI measured" }
- { recipe_number: 229, constant_id: μ_he'/μ_+', display_name: "shielded helion to shielded proton magnetic moment ratio", column: "7", island: "3", dimension: "-",
external_geometry: { numerator: [ "C_CFP^2", "S" ], denominator: [ "-2", "7^0.5", "zhe_1^2", "zhe_2^2" ] }, external_boundary: { numerator: [ "m_+" ], denominator: [ "m_he" ] },
inversion_geometry: { numerator: [ "pi", "L^4" ], denominator: [ "12^0.5"] }, root_transform: { id: "zhe_1^2 + zhe_2^2" },
expected_kind: measured, expected_value: -7.617861334(31)e-1, expected_digits: "7617861334", expected_digits_label: "SI measured" }
- { recipe_number: 230, constant_id: μ_e/μ_he', display_name: "electron to shielded helion magnetic moment ratio", column: "7", island: "3", dimension: "-",
external_geometry: { numerator: [ "2", "7^0.5", "zhe_1^2", "zhe_2^2" ], denominator: [ "C_CFP^2", "P_up" ] }, external_boundary: { numerator: [ "m_he" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ "2", "e^γ", "L^4" ], denominator: [ "12^0.5" ] }, root_transform: { id: "zhe_1^2 + zhe_2^2" },
expected_kind: measured, expected_value: 8.6405823986(70)e2, expected_digits: "86405823986", expected_digits_label: "SI measured" }
- { recipe_number: 231, constant_id: A_mass⋮E_h, display_name: "atomic mass unit-hartree relationship", column: "7", island: "4", dimension: "E_h",
external_geometry: { numerator: [ "18^0.5", "P_up^0.5" ], denominator: [ "32^0.5", "(zhe_1^14)^0.5" ] }, external_boundary: { numerator: [ ], denominator: [ ] },
inversion_geometry: { numerator: [ "zeta(3)" ], denominator: [ "12" ] }, root_transform: { id: "zhe_1^2 - zhe_2^2" },
expected_kind: measured, expected_value: 3.4231776922(11)e7, expected_digits: "34231776922", expected_digits_label: "SI measured" }
- { recipe_number: 232, constant_id: E_h⋮A_mass, display_name: "hartree-atomic mass unit relationship", column: "7", island: "4", dimension: "u",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^14)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ ], denominator: [ ] },
inversion_geometry: { numerator: [ "zeta(3)" ], denominator: [ "-12" ] }, root_transform: { id: "zhe_1^2 - zhe_2^2" },
expected_kind: measured, expected_value: 2.92126231797(91)e-8, expected_digits: "292126231797", expected_digits_label: "SI measured" }
- { recipe_number: 233, constant_id: kg⋮E_h, display_name: "kilogram-hartree relationship", column: "7", island: "4", dimension: "E_h",
external_geometry: { numerator: [ "18^0.5", "P_up^0.5" ], denominator: [ "32^0.5", "(zhe_1^14)^0.5" ] }, external_boundary: { numerator: [ "kilogram" ], denominator: [ "A_mass" ] },
inversion_geometry: { numerator: [ "zeta(3)" ], denominator: [ "12" ] }, root_transform: { id: "zhe_1^2 - zhe_2^2" },
expected_kind: measured, expected_value: 2.0614857887415(22)e34, expected_digits: "20614857887415", expected_digits_label: "SI measured" }
- { recipe_number: 234, constant_id: E_h⋮kg, display_name: "hartree-kilogram relationship", column: "7", island: "4", dimension: "kg",
external_geometry: { numerator: [ "32^0.5", "(zhe_1^14)^0.5" ], denominator: [ "18^0.5", "P_up^0.5" ] }, external_boundary: { numerator: [ "A_mass" ], denominator: [ ] },
inversion_geometry: { numerator: [ "zeta(3)" ], denominator: [ "-12" ] }, root_transform: { id: "zhe_1^2 - zhe_2^2" },
expected_kind: measured, expected_value: 4.8508702095419(53)e-35, expected_digits: "48508702095419", expected_digits_label: "SI measured" }
- { recipe_number: 235, constant_id: K⋮kg, display_name: "kelvin-kilogram relationship", column: "7", island: "5", dimension: "kg",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "kelvin", "m_p" ], denominator: [ "T_p" ] },
inversion_geometry: { numerator: [ "-1", "L_2", "6^0.5", "V_fe^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_3^2 + zhe_4^2" },
expected_kind: exact, expected_value: 1.536179187e-40, expected_digits: "1536179187", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 236, constant_id: kg⋮K, display_name: "kilogram-kelvin relationship", column: "7", island: "5", dimension: "K",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "kilogram", "T_p" ], denominator: [ "m_p" ] },
inversion_geometry: { numerator: [ "L_2", "6^0.5", "V_fe^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_3^2 + zhe_4^2" },
expected_kind: exact, expected_value: 6.509657260e39, expected_digits: "6509657260", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 237, constant_id: K⋮A_mass, display_name: "kelvin-atomic mass unit relationship", column: "7", island: "5", dimension: "u",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "kelvin", "m_p" ], denominator: [ "A_mass", "T_p" ] },
inversion_geometry: { numerator: [ "-1", "L_2", "6^0.5", "V_fe^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_3^2 + zhe_4^2" },
expected_kind: measured, expected_value: 9.2510872884(29)e-14, expected_digits: "92510872884", expected_digits_label: "SI measured" }
- { recipe_number: 238, constant_id: A_mass⋮K, display_name: "atomic mass unit-kelvin relationship", column: "7", island: "5", dimension: "K",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "A_mass", "T_p" ], denominator: [ "m_p" ] },
inversion_geometry: { numerator: [ "L_2", "6^0.5", "V_fe^0.5" ], denominator: [ ] }, root_transform: { id: "zhe_3^2 + zhe_4^2" },
expected_kind: measured, expected_value: 1.08095402067(34)e13, expected_digits: "108095402067", expected_digits_label: "SI measured" }
- { recipe_number: 239, constant_id: kg⋮1/m, display_name: "kilogram-inverse meter relationship", column: "7", island: "6", dimension: "cycles/m",
external_geometry: { numerator: [ ], denominator: [ "2", "pi" ] }, external_boundary: { numerator: [ "kilogram" ], denominator: [ "l_p", "m_p" ] },
inversion_geometry: { numerator: [ "P_up", "i" ], denominator: [ "-8" ] }, root_transform: { id: "zhe_3^2 - zhe_4^2" },
expected_kind: exact, expected_value: 4.524438335e41, expected_digits: "4524438335", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 240, constant_id: A_mass⋮1/m, display_name: "atomic mass unit-inverse meter relationship", column: "7", island: "6", dimension: "cycles/m",
external_geometry: { numerator: [ ], denominator: [ "2", "pi" ] }, external_boundary: { numerator: [ "A_mass" ], denominator: [ "l_p", "m_p" ] },
inversion_geometry: { numerator: [ "P_up", "i" ], denominator: [ "-8" ] }, root_transform: { id: "zhe_3^2 - zhe_4^2" },
expected_kind: measured, expected_value: 7.5130066209(23)e14, expected_digits: "75130066209", expected_digits_label: "SI measured" }
- { recipe_number: 241, constant_id: 1/m⋮kg, display_name: "inverse meter-kilogram relationship", column: "7", island: "6", dimension: "kg",
external_geometry: { numerator: [ "2", "pi" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p", "m_p" ], denominator: [ "meter" ] },
inversion_geometry: { numerator: [ "P_up", "i" ], denominator: [ "8" ] }, root_transform: { id: "zhe_3^2 - zhe_4^2" },
expected_kind: exact, expected_value: 2.210219094e-42, expected_digits: "2210219094", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 242, constant_id: 1/m⋮A_mass, display_name: "inverse meter-atomic mass unit relationship", column: "7", island: "6", dimension: "u",
external_geometry: { numerator: [ "2", "pi" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p", "m_p" ], denominator: [ "meter", "A_mass" ] },
inversion_geometry: { numerator: [ "P_up", "i" ], denominator: [ "8" ] }, root_transform: { id: "zhe_3^2 - zhe_4^2" },
expected_kind: measured, expected_value: 1.33102504824(41)e-15, expected_digits: "133102504824", expected_digits_label: "SI measured" }
- { recipe_number: 243, constant_id: λ_C, display_name: "Compton wavelength", column: "7", island: "6", dimension: "m/cycle",
external_geometry: { numerator: [ "2", "pi" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p", "m_p" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ "P_up", "i" ], denominator: [ "8" ] }, root_transform: { id: "zhe_3^2 - zhe_4^2" },
expected_kind: measured, expected_value: 2.42631023538(76)e-12, expected_digits: "242631023538", expected_digits_label: "SI measured" }
- { recipe_number: 244, constant_id: λ_μ, display_name: "muon Compton wavelength", column: "7", island: "6", dimension: "m/cycle",
external_geometry: { numerator: [ "2", "pi" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p", "m_p" ], denominator: [ "m_μ" ] },
inversion_geometry: { numerator: [ "P_up", "i" ], denominator: [ "8" ] }, root_transform: { id: "zhe_3^2 - zhe_4^2" },
expected_kind: measured, expected_value: 1.173444110(26)e-14, expected_digits: "1173444110", expected_digits_label: "SI measured" }
- { recipe_number: 245, constant_id: λ_+, display_name: "proton Compton wavelength", column: "7", island: "6", dimension: "m/cycle",
external_geometry: { numerator: [ "2", "pi" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p", "m_p" ], denominator: [ "m_+" ] },
inversion_geometry: { numerator: [ "P_up", "i" ], denominator: [ "8" ] }, root_transform: { id: "zhe_3^2 - zhe_4^2" },
expected_kind: measured, expected_value: 1.32140985360(41)e-15, expected_digits: "132140985360", expected_digits_label: "SI measured" }
- { recipe_number: 246, constant_id: λ_n, display_name: "neutron Compton wavelength", column: "7", island: "6", dimension: "m/cycle",
external_geometry: { numerator: [ "2", "pi" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p", "m_p" ], denominator: [ "m_n" ] },
inversion_geometry: { numerator: [ "P_up", "i" ], denominator: [ "8" ] }, root_transform: { id: "zhe_3^2 - zhe_4^2" },
expected_kind: measured, expected_value: 1.31959090382(67)e-15, expected_digits: "131959090382", expected_digits_label: "SI measured" }
- { recipe_number: 247, constant_id: λ_τ, display_name: "tau Compton wavelength", column: "7", island: "6", dimension: "m/cycle",
external_geometry: { numerator: [ "2", "pi" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p", "m_p" ], denominator: [ "m_τ" ] },
inversion_geometry: { numerator: [ "P_up", "i" ], denominator: [ "8" ] }, root_transform: { id: "zhe_3^2 - zhe_4^2" },
expected_kind: measured, expected_value: 6.97771(47)e-16, expected_digits: "697771", expected_digits_label: "SI measured" }
- { recipe_number: 248, constant_id: λ_-, display_name: "reduced Compton wavelength", column: "7", island: "6", dimension: "m/cycle",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p", "m_p" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ "P_up", "i" ], denominator: [ "8" ] }, root_transform: { id: "zhe_3^2 - zhe_4^2" },
expected_kind: measured, expected_value: 3.8615926744(12)e-13, expected_digits: "38615926744", expected_digits_label: "SI measured" }
- { recipe_number: 249, constant_id: λ_μ_-, display_name: "reduced muon Compton wavelength", column: "7", island: "6", dimension: "m/cycle",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p", "m_p" ], denominator: [ "m_μ" ] },
inversion_geometry: { numerator: [ "P_up", "i" ], denominator: [ "8" ] }, root_transform: { id: "zhe_3^2 - zhe_4^2" },
expected_kind: measured, expected_value: 1.867594306(42)e-15, expected_digits: "1867594306", expected_digits_label: "SI measured" }
- { recipe_number: 250, constant_id: λ_+_-, display_name: "reduced proton Compton wavelength", column: "7", island: "6", dimension: "m/cycle",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p", "m_p" ], denominator: [ "m_+" ] },
inversion_geometry: { numerator: [ "P_up", "i" ], denominator: [ "8" ] }, root_transform: { id: "zhe_3^2 - zhe_4^2" },
expected_kind: measured, expected_value: 2.10308910051(66)e-16, expected_digits: "210308910051", expected_digits_label: "SI measured" }
- { recipe_number: 251, constant_id: λ_n_-, display_name: "reduced neutron Compton wavelength", column: "7", island: "6", dimension: "m/cycle",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p", "m_p" ], denominator: [ "m_n" ] },
inversion_geometry: { numerator: [ "P_up", "i" ], denominator: [ "8" ] }, root_transform: { id: "zhe_3^2 - zhe_4^2" },
expected_kind: measured, expected_value: 2.1001941520(11)e-16, expected_digits: "21001941520", expected_digits_label: "SI measured" }
- { recipe_number: 252, constant_id: λ_τ_-, display_name: "reduced tau Compton wavelength", column: "7", island: "6", dimension: "m/cycle",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "l_p", "m_p" ], denominator: [ "m_τ" ] },
inversion_geometry: { numerator: [ "P_up", "i" ], denominator: [ "8" ] }, root_transform: { id: "zhe_3^2 - zhe_4^2" },
expected_kind: measured, expected_value: 1.110538(75)e-16, expected_digits: "1110538", expected_digits_label: "SI measured" }
- { recipe_number: 253, constant_id: b', display_name: "Wien frequency displacement law constant", column: "8", island: "1", dimension: "Hz/K",
external_geometry: { numerator: [ ], denominator: [ "2", "pi" ] }, external_boundary: { numerator: [ "nu_peak" ], denominator: [ "t_p", "T_p" ] },
inversion_geometry: { numerator: [ "18", "2^2", "pi^2" ], denominator: [ "4^2", "s^2" ] }, root_transform: { id: "zhe_1^2 - zhe_3^2 - zhe_4^2" },
expected_kind: exact, expected_value: 5.878925757E10, expected_digits: "5878925757", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 254, constant_id: k_B ̈, display_name: "Boltzmann constant in Hz/K", column: "8", island: "1", dimension: "Hz/K",
external_geometry: { numerator: [ ], denominator: [ "2", "pi" ] }, external_boundary: { numerator: [ ], denominator: [ "t_p", "T_p" ] },
inversion_geometry: { numerator: [ "18", "2^2", "pi^2" ], denominator: [ "4^2", "s^2" ] }, root_transform: { id: "zhe_1^2 - zhe_3^2 - zhe_4^2" },
expected_kind: exact, expected_value: 2.083661912e10, expected_digits: "2083661912", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 255, constant_id: K⋮Hz, display_name: "kelvin-hertz relationship", column: "8", island: "1", dimension: "Hz",
external_geometry: { numerator: [ ], denominator: [ "2", "pi" ] }, external_boundary: { numerator: [ "kelvin" ], denominator: [ "t_p", "T_p" ] },
inversion_geometry: { numerator: [ "18", "2^2", "pi^2" ], denominator: [ "4^2", "s^2" ] }, root_transform: { id: "zhe_1^2 - zhe_3^2 - zhe_4^2" },
expected_kind: exact, expected_value: 2.083661912e10, expected_digits: "2083661912", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 256, constant_id: Hz⋮K, display_name: "hertz-kelvin relationship", column: "8", island: "1", dimension: "K",
external_geometry: { numerator: [ "2", "pi" ], denominator: [ ] }, external_boundary: { numerator: [ "t_p", "T_p" ], denominator: [ "second" ] },
inversion_geometry: { numerator: [ "-18", "2^2", "pi^2" ], denominator: [ "4^2", "s^2" ] }, root_transform: { id: "zhe_1^2 - zhe_3^2 - zhe_4^2" },
expected_kind: exact, expected_value: 4.799243073e-11, expected_digits: "4799243073", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 257, constant_id: b, display_name: "Wien wavelength displacement law constant", column: "8", island: "2", dimension: "m*K/cycle",
external_geometry: { numerator: [ "2", "pi" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p", "T_p" ], denominator: [ "lambda_peak" ] },
inversion_geometry: { numerator: [ "P^2" ], denominator: [ ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: exact, expected_value: 2.897771955e-3, expected_digits: "2897771955", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 258, constant_id: c_2, display_name: "second radiation constant", column: "8", island: "2", dimension: "m*K",
external_geometry: { numerator: [ "2", "pi" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p", "T_p" ], denominator: [ ] },
inversion_geometry: { numerator: [ "P^2" ], denominator: [ ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: exact, expected_value: 1.438776877e-2, expected_digits: "1438776877", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 259, constant_id: 1/m⋮K, display_name: "inverse meter-kelvin relationship", column: "8", island: "2", dimension: "K",
external_geometry: { numerator: [ "2", "pi" ], denominator: [ ] }, external_boundary: { numerator: [ "l_p", "T_p" ], denominator: [ "meter" ] },
inversion_geometry: { numerator: [ "P^2" ], denominator: [ ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: exact, expected_value: 1.438776877e-2, expected_digits: "1438776877", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 260, constant_id: K⋮1/m, display_name: "kelvin-inverse meter relationship", column: "8", island: "2", dimension: "cycles/m",
external_geometry: { numerator: [ ], denominator: [ "2", "pi" ] }, external_boundary: { numerator: [ "kelvin" ], denominator: [ "l_p", "T_p" ] },
inversion_geometry: { numerator: [ "-1", "P^2" ], denominator: [ ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: exact, expected_value: 6.950348004e1, expected_digits: "6950348004", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 261, constant_id: k_B ̇, display_name: "Boltzmann constant in inverse meter per kelvin", column: "8", island: "2", dimension: "cycles/(m*K)",
external_geometry: { numerator: [ ], denominator: [ "2", "pi" ] }, external_boundary: { numerator: [ ], denominator: [ "l_p", "T_p" ] },
inversion_geometry: { numerator: [ "-1", "P^2" ], denominator: [ ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: exact, expected_value: 6.950348004e1, expected_digits: "6950348004", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 262, constant_id: E_h⋮K, display_name: "Hartree-kelvin relationship", column: "8", island: "3", dimension: "K",
external_geometry: { numerator: [ "zhe_1^4" ], denominator: [ ] }, external_boundary: { numerator: [ "T_p","m_e" ], denominator: [ "m_p" ] },
inversion_geometry: { numerator: [ "s" ], denominator: [ "2^0.5", "pi^0.5" ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: measured, expected_value: 3.1577502480398(34)e5, expected_digits: "31577502480398", expected_digits_label: "SI measured" }
- { recipe_number: 263, constant_id: K⋮E_h, display_name: "kelvin-hartree relationship", column: "8", island: "3", combine: inversion, dimension: "E_h",
external_geometry: { numerator: [ ], denominator: [ "zhe_1^4" ] }, external_boundary: { numerator: [ "kelvin","m_p" ], denominator: [ "T_p","m_e" ] },
inversion_geometry: { numerator:[ "s" ], denominator: [ "2^0.5", "pi^0.5" ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: measured, expected_value: 3.1668115634564(34)e-6, expected_digits: "31668115634564", expected_digits_label: "SI measured" }
- { recipe_number: 264, constant_id: M_e, display_name: "electron molar mass", column: "8", island: "4", dimension: "kg/mol",
external_geometry: { numerator: [ "6", "zhe_1^2" ], denominator: [ "e^γ" ] }, external_boundary: { numerator: [ "coulomb", "kilogram", "m_e" ], denominator: [ "q_p", "m_p" ] },
inversion_geometry: { numerator: [ "18", "C_Q" ], denominator: [ ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: measured, expected_value: 5.4857990962(17)e-7, expected_digits: "54857990962", expected_digits_label: "SI measured" }
- { recipe_number: 265, constant_id: M_μ, display_name: "muon molar mass", column: "8", island: "4", dimension: "kg/mol",
external_geometry: { numerator: [ "6", "zhe_1^2" ], denominator: [ "e^γ" ] }, external_boundary: { numerator: [ "coulomb", "kilogram", "m_μ" ], denominator: [ "q_p", "m_p" ] },
inversion_geometry: { numerator: [ "18", "C_Q" ], denominator: [ ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: measured, expected_value: 1.134289258(25)e-4, expected_digits: "1134289258", expected_digits_label: "SI measured" }
- { recipe_number: 266, constant_id: M_+, display_name: "proton molar mass", column: "8", island: "4", dimension: "kg/mol",
external_geometry: { numerator: [ "6", "zhe_1^2" ], denominator: [ "e^γ" ] }, external_boundary: { numerator: [ "coulomb", "kilogram", "m_+" ], denominator: [ "q_p", "m_p" ] },
inversion_geometry: { numerator: [ "18", "C_Q" ], denominator: [ ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: measured, expected_value: 1.00727646764(31)e-3, expected_digits: "100727646764", expected_digits_label: "SI measured" }
- { recipe_number: 267, constant_id: M_A_mass, display_name: "molar mass constant", column: "8", island: "4", dimension: "kg/mol",
external_geometry: { numerator: [ "6", "zhe_1^2" ], denominator: [ "e^γ" ] }, external_boundary: { numerator: [ "coulomb", "kilogram", "A_mass" ], denominator: [ "q_p", "m_p" ] },
inversion_geometry: { numerator: [ "18", "C_Q" ], denominator: [ ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: measured, expected_value: 1.00000000105(31)e-3, expected_digits: "100000000105", expected_digits_label: "SI measured" }
- { recipe_number: 268, constant_id: M_n, display_name: "neutron molar mass", column: "8", island: "4", dimension: "kg/mol",
external_geometry: { numerator: [ "6", "zhe_1^2" ], denominator: [ "e^γ" ] }, external_boundary: { numerator: [ "coulomb", "kilogram", "m_n" ], denominator: [ "q_p", "m_p" ] },
inversion_geometry: { numerator: [ "18", "C_Q" ], denominator: [ ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: measured, expected_value: 1.00866491712(51)e-3, expected_digits: "100866491712", expected_digits_label: "SI measured" }
- { recipe_number: 269, constant_id: M_τ, display_name: "tau molar mass", column: "8", island: "4", dimension: "kg/mol",
external_geometry: { numerator: [ "6", "zhe_1^2" ], denominator: [ "e^γ" ] }, external_boundary: { numerator: [ "coulomb", "kilogram", "m_τ" ], denominator: [ "q_p", "m_p" ] },
inversion_geometry: { numerator: [ "18", "C_Q" ], denominator: [ ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: measured, expected_value: 1.90754(13)e-3, expected_digits: "190754", expected_digits_label: "SI measured" }
- { recipe_number: 270, constant_id: M_de, display_name: "deuteron molar mass", column: "8", island: "4", dimension: "kg/mol",
external_geometry: { numerator: [ "6", "zhe_1^2" ], denominator: [ "e^γ" ] }, external_boundary: { numerator: [ "coulomb", "kilogram", "m_de" ], denominator: [ "q_p", "m_p" ] },
inversion_geometry: { numerator: [ "18", "C_Q" ], denominator: [ ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: measured, expected_value: 2.01355321466(63)e-3, expected_digits: "201355321466", expected_digits_label: "SI measured" }
- { recipe_number: 271, constant_id: M_he, display_name: "helion molar mass", column: "8", island: "4", dimension: "kg/mol",
external_geometry: { numerator: [ "6", "zhe_1^2" ], denominator: [ "e^γ" ] }, external_boundary: { numerator: [ "coulomb", "kilogram", "m_he" ], denominator: [ "q_p", "m_p" ] },
inversion_geometry: { numerator: [ "18", "C_Q" ], denominator: [ ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: measured, expected_value: 3.01493225010(94)e-3, expected_digits: "301493225010", expected_digits_label: "SI measured" }
- { recipe_number: 272, constant_id: M_tri, display_name: "triton molar mass", column: "8", island: "4", dimension: "kg/mol",
external_geometry: { numerator: [ "6", "zhe_1^2" ], denominator: [ "e^γ" ] }, external_boundary: { numerator: [ "coulomb", "kilogram", "m_tri" ], denominator: [ "q_p", "m_p" ] },
inversion_geometry: { numerator: [ "18", "C_Q" ], denominator: [ ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: measured, expected_value: 3.01550071913(94)e-3, expected_digits: "301550071913", expected_digits_label: "SI measured" }
- { recipe_number: 273, constant_id: M_α, display_name: "alpha particle molar mass", column: "8", island: "4", dimension: "kg/mol",
external_geometry: { numerator: [ "6", "zhe_1^2" ], denominator: [ "e^γ" ] }, external_boundary: { numerator: [ "coulomb", "kilogram", "m_α" ], denominator: [ "q_p", "m_p" ] },
inversion_geometry: { numerator: [ "18", "C_Q" ], denominator: [ ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: measured, expected_value: 4.0015061833(12)e-3, expected_digits: "40015061833", expected_digits_label: "SI measured" }
- { recipe_number: 274, constant_id: M_12_C, display_name: "molar mass of carbon-12", column: "8", island: "4", dimension: "kg/mol",
external_geometry: { numerator: [ "6", "zhe_1^2" ], denominator: [ "e^γ" ] }, external_boundary: { numerator: [ "12", "coulomb", "kilogram", "A_mass" ], denominator: [ "q_p", "m_p" ] },
inversion_geometry: { numerator: [ "18", "C_Q" ], denominator: [ ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: measured, expected_value: 1.20000000126(36)e-2, expected_digits: "120000000126", expected_digits_label: "SI measured" }
- { recipe_number: 275, constant_id: N_A, display_name: "Avogadro constant", column: "8", island: "4", dimension: "1/mol",
external_geometry: { numerator: [ "6", "zhe_1^2" ], denominator: [ "e^γ" ] }, external_boundary: { numerator: [ "coulomb", "kilogram" ], denominator: [ "q_p", "m_p" ] },
inversion_geometry: { numerator: [ "18", "C_Q" ], denominator: [ ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: exact, expected_value: 6.02214076e23, expected_digits: "602214076", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 276, constant_id: ST_0, display_name: "Sackur-Tetrode constant (1K, 100 kPa)", column: "8", island: "5", dimension: "-", combine: "+",
external_geometry: { numerator: [ "(5/2)" ], denominator: [ ] }, external_boundary: { numerator: [ "(log( (((1/(2*pi))*(kelvin*A_mass)/(l_p^2*T_p*m_p))^(3/2)) * (kelvin*l_p^2*m_p/(t_p^2*T_p*p_0)) ))" ], denominator: [ ] },
inversion_geometry: { numerator: [ "j_01", "2", "pi" ], denominator: [ "14" ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: measured, expected_value: -1.15170753496(47), expected_digits: "115170753496", expected_digits_label: "SI measured" }
- { recipe_number: 277, constant_id: ST_1, display_name: "Sackur-Tetrode constant (1K, 101.325 kPa)", column: "8", island: "5", dimension: "-", combine: "+",
external_geometry: { numerator: [ "(5/2)" ], denominator: [ ] }, external_boundary: { numerator: [ "(log( (((1/(2*pi))*(kelvin*A_mass)/(l_p^2*T_p*m_p))^(3/2)) * (kelvin*l_p^2*m_p/(t_p^2*T_p*p_1)) ))" ], denominator: [ ] },
inversion_geometry: { numerator: [ "4", "pi" ], denominator: [ "G_Ga", "14" ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: measured, expected_value: -1.16487052149(47), expected_digits: "116487052149", expected_digits_label: "SI measured" }
- { recipe_number: 278, constant_id: σ, display_name: "Stefan-Boltzmann constant", column: "8", island: "5", dimension: "W/(m^2*K^4)",
external_geometry: { numerator: [ "3", "4^2","pi^2" ], denominator: [ "5", "Γ(5)^2" ] }, external_boundary: { numerator: [ "m_p" ], denominator: [ "t_p^3","T_p^4" ] },
inversion_geometry: { numerator: [ "(18+35)", "2", "K" ], denominator: [ "14" ] }, root_transform: { id: "zhe_1^2 - zhe_3^2 - zhe_4^2" },
expected_kind: exact, expected_value: 5.670374419e-8, expected_digits: "5670374419", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 279, constant_id: V_90, display_name: "conventional value of volt-90", column: "8", island: "6", dimension: "V",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "volt" ], denominator: [ ] },
inversion_geometry: { numerator: [ "L_1" ], denominator: [ "32" ] }, root_transform: { id: "zhe_1^2 - zhe_3^2 - zhe_4^2" },
expected_kind: exact, expected_value: 1.00000010666, expected_digits: "100000010666", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 280, constant_id: W_90, display_name: "conventional value of watt-90", column: "8", island: "6", dimension: "W",
external_geometry: { numerator: [ ], denominator: [ ] }, external_boundary: { numerator: [ "watt" ], denominator: [ ] },
inversion_geometry: { numerator: [ "j_01" ], denominator: [ "-32" ] }, root_transform: { id: "zhe_1^2 + zhe_3^2 + zhe_4^2" },
expected_kind: exact, expected_value: 1.00000019553, expected_digits: "100000019553", expected_digits_label: "SI exact (defined)" }
- { recipe_number: 281, constant_id: A_ef∇, display_name: "atomic unit of electric field gradient", column: "8", island: "7", dimension: "V/m^2",
external_geometry: { numerator: [ "zhe_1^7" ], denominator: [ ] }, external_boundary: { numerator: [ "m_e^3" ], denominator: [ "t_p^2", "q_p", "m_p^2" ] },
inversion_geometry: { numerator: [ "35^0.5", "V_fe" ], denominator: [ "6" ] }, root_transform: { id: "zhe_2^2 + zhe_3^2 + zhe_4^2" },
expected_kind: measured, expected_value: 9.7173624424(30)e21, expected_digits: "97173624424", expected_digits_label: "SI measured" }
- { recipe_number: 282, constant_id: A_current, display_name: "atomic unit of current", column: "8", island: "7", dimension: "A",
external_geometry: { numerator: [ "zhe_1^5" ], denominator: [ ] }, external_boundary: { numerator: [ "q_p", "m_e" ], denominator: [ "t_p", "m_p" ] },
inversion_geometry: { numerator: [ "C_CFP", "V_fe" ], denominator: [ "-8" ] }, root_transform: { id: "zhe_2^2 - zhe_3^2 - zhe_4^2" },
expected_kind: measured, expected_value: 6.6236182375082(72)e-3, expected_digits: "66236182375082", expected_digits_label: "SI measured" }
- { recipe_number: 283, constant_id: A_mfd, display_name: "atomic unit of magnetic flux density", column: "8", island: "8", dimension: "T",
external_geometry: { numerator: [ "zhe_1^3" ], denominator: [ ] }, external_boundary: { numerator: [ "m_e^2" ], denominator: [ "t_p", "q_p", "m_p" ] },
inversion_geometry: { numerator: [ "8^0.5", "4", "pi" ], denominator: [ "35" ] }, root_transform: { id: "zhe_2^2 + zhe_3^2 + zhe_4^2" },
expected_kind: measured, expected_value: 2.35051757077(73)e5, expected_digits: "235051757077", expected_digits_label: "SI measured" }
- { recipe_number: 284, constant_id: A_edm, display_name: "atomic unit of electric dipole moment", column: "8", island: "8", dimension: "m*C",
external_geometry: { numerator: [ ], denominator: [ "zhe_1" ] }, external_boundary: { numerator: [ "l_p", "q_p", "m_p" ], denominator: [ "m_e" ] },
inversion_geometry: { numerator: [ "P", "4", "pi" ], denominator: [ "L_2", "5!" ] }, root_transform: { id: "zhe_2^2 - zhe_3^2 - zhe_4^2" },
expected_kind: measured, expected_value: 8.4783536198(13)e-30, expected_digits: "84783536198", expected_digits_label: "SI measured" }
- { recipe_number: 285, constant_id: A_mag, display_name: "atomic unit of magnetizability", column: "8", island: "8", dimension: "J/T^2",
external_geometry: { numerator: [ ], denominator: [ "zhe_1^2" ] }, external_boundary: { numerator: [ "l_p^2", "q_p^2", "m_p^2" ], denominator: [ "m_e^3" ] },
inversion_geometry: { numerator: [ "L_LL", "4", "pi" ], denominator: [ "18" ] }, root_transform: { id: "zhe_2^2 - zhe_3^2 - zhe_4^2" },
expected_kind: measured, expected_value: 7.8910365794(49)e-29, expected_digits: "78910365794", expected_digits_label: "SI measured" }
- { recipe_number: 286, constant_id: A_eqm, display_name: "atomic unit of electric quadrupole moment", column: "8", island: "8", dimension: "m^2*C",
external_geometry: { numerator: [ ], denominator: [ "zhe_1^3" ] }, external_boundary: { numerator: [ "l_p^2", "q_p", "m_p^2" ], denominator: [ "m_e^2" ] },
inversion_geometry: { numerator: [ "2", "4", "pi" ], denominator: [ "3^0.5", "32" ] }, root_transform: { id: "zhe_2^2 - zhe_3^2 - zhe_4^2" },
expected_kind: measured, expected_value: 4.4865515185(14)e-40, expected_digits: "44865515185", expected_digits_label: "SI measured" }
- { recipe_number: 287, constant_id: A_1^st_hp, display_name: "atomic unit of 1st hyperpolarizability", column: "8", island: "8", dimension: "m^3*C^3/J^2",
external_geometry: { numerator: [ ], denominator: [ "zhe_1^11" ] }, external_boundary: { numerator: [ "t_p^4", "q_p^3", "m_p^3" ], denominator: [ "l_p", "m_e^5" ] },
inversion_geometry: { numerator: [ "-3", "4", "pi" ], denominator: [ "2^0.5", "8" ] }, root_transform: { id: "zhe_2^2 + zhe_3^2 + zhe_4^2" },
expected_kind: measured, expected_value: 3.2063612996(15)e-53, expected_digits: "32063612996", expected_digits_label: "SI measured" }
- { recipe_number: 288, constant_id: A_2^nd_hp, display_name: "atomic unit of 2nd hyperpolarizability", column: "8", island: "8", dimension: "m^4*C^4/J^3",
external_geometry: { numerator: [ ], denominator: [ "zhe_1^16" ] }, external_boundary: { numerator: [ "t_p^6", "q_p^4", "m_p^4" ], denominator: [ "l_p^2", "m_e^7" ] },
inversion_geometry: { numerator: [ "-12", "4", "pi" ], denominator: [ "D_Do", "!5" ] }, root_transform: { id: "zhe_2^2 + zhe_3^2 + zhe_4^2" },
expected_kind: measured, expected_value: 6.2353799735(39)e-65, expected_digits: "62353799735", expected_digits_label: "SI measured" }
Input Parameters
These are the numerical symbols used by the Constant Engine. Each row gives the token used in the code, its name or meaning, its assigned value, and its dimensional type.
| Token | Name / meaning | Value | Dimension |
|---|---|---|---|
| t_p | Planck time | 5.39125836832312…e-44 | s |
| l_p | Planck length | 1.61625918175645…e-35 | m |
| q_p | Planck charge | 1.87554596713962…e-18 | C |
| T_p | Planck temperature | 1.41678698590794…e+32 | K |
| m_p | Planck mass | 2.17642683817578…e-8 | kg |
| second | second | 1 | s |
| meter | meter | 1 | m |
| coulomb | coulomb | 1 | C |
| kelvin | kelvin | 1 | K |
| kilogram | kilogram | 1 | kg |
| MHz | megahertz | 1e6 | Hz |
| fm | femtometer | 1e-15 | m |
| MeV | megaelectron volt | 1.60217663422016…e-13 | J |
| GeV | gigaelectron volt | 1.60217663422016…e-10 | J |
| ampere | ampere | 1 | C/s |
| joule | joule | 1 | J |
| tesla | tesla | 1 | T |
| watt | watt | 1 | m^2*kg/s^3 |
| farad | farad | 1 | s^2*C^2/(m^2*kg) |
| henry | henry | 1 | m^2*kg/C^2 |
| ohm | ohm | 1 | m^2*kg/s/C^2 |
| volt | volt | 1 | m^2*kg/(s^2*C) |
| pascal | pascal | 1 | kg/(s^2*m) |
| IB | hyperbolic inversion boundary | 9.99999199973622…e-8 | - |
| zhe_1 | 1st hyperbolic partition constant | 0.08542454315333… | - |
| zhe_2 | 2nd hyperbolic partition constant | 3.66756753485501… | - |
| zhe_3 | 3rd hyperbolic partition constant | -1.87649603900417…+4.06615262615972…j | - |
| zhe_4 | 4th hyperbolic partition constant | -1.87649603900417…-4.06615262615972…j | - |
| zhe_r | hyperbolic radius constant | 4.47826244916753… | - |
| zhe_theta | hyperbolic radian constant | 2.00316562310924… | - |
| G_Gi | Gieseking's constant | 1.01494160640965… | - |
| V_fe | figure-eight knot hyperbolic volume | 2.02988321281930… | - |
| K | Catalan's constant | 0.91596559417721… | - |
| C_d | domino tiling constant | 0.29156090403081… | - |
| D_d | dimer constant | 1.79162281206959… | - |
| omega_1 | omega₁ constant | 0.76497701852859…+1.32497906271408…j | - |
| omega_2 | omega₂ constant | 1.52995403705719… | - |
| Im(omega_1) | imaginary part of the omega₁ constant | 1.32497906271408… | - |
| i^i^i^... | infinite power tower of i | 0.43828293672703…+0.36059247187138…j | - |
| i | imaginary unit | 1j | - |
| phi_i | imaginary golden ratio | 0.50000000000000…+0.86602540378443…j | - |
| pi | Archimedes' constant | 3.14159265358979… | - |
| P_up | universal parabolic constant | 2.29558714939263… | - |
| s | arc length of the unit lemniscate | 5.24411510858423… | - |
| L | lemniscate constant | 2.62205755429211… | - |
| L_1 | 1st lemniscate constant | 1.31102877714605… | - |
| L_2 | 2nd lemniscate constant | 0.59907011736779… | - |
| C_U | ubiquitous constant | 0.84721308479397… | - |
| G_Ga | Gauss's constant | 0.83462684167407… | - |
| W_We | Weierstrass constant | 0.47494937998792… | - |
| C_R1 | Ramanujan's 1st continued-fraction constant | 0.99813604459850… | - |
| M | Madelung constant | -1.74756459463318… | - |
| e | Euler's number | 2.71828182845904… | - |
| γ | Euler–Mascheroni constant | 0.57721566490153… | - |
| S | Sierpiński's constant | 0.82282524967884… | - |
| δ | shifted Sierpiński constant | 1.82282524967884… | - |
| j_01 | 1st root of the Bessel function | 2.40482555769577… | - |
| C_CFP | real fixed point of the hyperbolic cotangent | 1.19967864025773… | - |
| D_Do | Dottie number | 0.73908513321516… | - |
| L_LL | Laplace limit | 0.66274341934918… | - |
| α_F | alpha Feigenbaum constant | 2.50290787509589… | - |
| δ_F | delta Feigenbaum constant | 4.66920160910299… | - |
| P | plastic constant | 1.32471795724474… | - |
| S* | silver constant | 3.24697960371746… | - |
| C_Q | QRS constant | 0.60544365719673… | - |
| T_0 | freezing point of water | 273.15 | K |
| p_0 | 1 bar | 1e5 | pascal |
| p_1 | standard atmospheric pressure | 101325.000000000 | pascal |
| E_1 | energy associated with the caesium-133 hyperfine transition | 6.09110229711386e-24 | J |
| f_1 | frequency of maximum light conversion | 5.4e14 | Hz |
| lambda_peak | peak of spectral radiance per unit wavelength | 4.96511423174427… | - |
| nu_peak | peak emission of spectral flux per unit frequency | 2.82143937212207… | - |
| Re(ipt) | real part of the infinite power tower of i | 0.43828293672703… | - |
| Im(ipt) | imaginary part of the infinite power tower of i | 0.36059247187138… | - |
| K_-6 | Khinchin mean of order −6 | 1.15655237442151… | - |
| L_Li | Liouville's constant | 0.11000100000000… | - |
| x_infinity | 1st Foias constant | 2.29316628741186… | - |
| φ | golden ratio | 1.61803398874989… | - |
| P* | prime constant | 0.41468250985111… | - |
Latest Output
This is the latest output generated by the Constant Engine.
=== Build pass 1 ===
=== Build pass 2 ===
=== Build pass 3 ===
=== Build pass 4 ===
288 constants built.
70 exact, 70 passed, 0 failed
218 measured, 218 passed, 0 failed
No further constants can be built.
=== Constants in official order ===
001. Delta_nu_Cs — hyperfine transition frequency of Cs-133 [built on pass 1]
deps: l_p, t_p, m_p, E_1, pi, zeta(2), zhe_theta, IB
computed: 9.19263177042965 × 10^⁹ Hz
expected: 9.19263177000000 × 10^⁹ Hz (SI exact (defined))
digits: full match (10/10)
002. eV⋮Hz — electron volt-hertz relationship [built on pass 2]
deps: l_p, t_p, m_p, eV, pi, zeta(2), zhe_theta, IB
computed: 2.41798924253021 × 10^¹⁴ Hz
expected: 2.41798924200000 × 10^¹⁴ Hz (SI exact (defined))
digits: full match (10/10)
003. J⋮Hz — joule-hertz relationship [built on pass 1]
deps: l_p, t_p, m_p, joule, pi, zeta(2), zhe_theta, IB
computed: 1.50919017971269 × 10^³³ Hz
expected: 1.50919017900000 × 10^³³ Hz (SI exact (defined))
digits: full match (10/10)
004. Hz⋮J — hertz-joule relationship [built on pass 1]
deps: l_p, t_p, m_p, pi, second, zeta(2), zhe_theta, IB
computed: 6.62607014968854 × 10^⁻³⁴ J
expected: 6.62607015000000 × 10^⁻³⁴ J (SI exact (defined))
digits: full match (8/9)
005. Hz⋮eV — hertz-electron volt relationship [built on pass 2]
deps: l_p, t_p, m_p, eV, pi, second, zeta(2), zhe_theta, IB
computed: 4.13566769616115 × 10^⁻¹⁵ eV
expected: 4.13566769600000 × 10^⁻¹⁵ eV (SI exact (defined))
digits: full match (10/10)
006. ℏ̇ — natural unit of action in eV s [built on pass 2]
deps: l_p, t_p, m_p, eV, zeta(2), zhe_theta, IB
computed: 6.58211956829518 × 10^⁻¹⁶ eV s
expected: 6.58211956900000 × 10^⁻¹⁶ eV s (SI exact (defined))
digits: full match (9/10)
007. ℏ — reduced Planck constant [built on pass 1]
deps: l_p, t_p, m_p, zeta(2), zhe_theta, IB
computed: 1.05457181759659 × 10^⁻³⁴ J s
expected: 1.05457181700000 × 10^⁻³⁴ J s (SI exact (defined))
digits: full match (10/10)
008. h — Planck constant [built on pass 1]
deps: l_p, t_p, m_p, pi, zeta(2), zhe_theta, IB
computed: 6.62607014968854 × 10^⁻³⁴ J s
expected: 6.62607015000000 × 10^⁻³⁴ J s (SI exact (defined))
digits: full match (8/9)
009. q_c — quantum of circulation [built on pass 2]
deps: l_p, t_p, m_p, m_e, pi, zeta(2), zhe_theta, IB
computed: 3.63694754800780 × 10^⁻⁴ m^2/s
expected: 3.6369475467(11) × 10^⁻⁴ m^2/s (SI measured)
abs err: 1.30780460243225 × 10^⁻¹³ m^2/s
sigma: +1.19
within 5.2σ: yes
010. 2q_c — quantum of circulation times 2 [built on pass 2]
deps: l_p, t_p, m_p, m_e, pi, zeta(2), zhe_theta, IB
computed: 7.27389509601561 × 10^⁻⁴ m^2/s
expected: 7.2738950934(22) × 10^⁻⁴ m^2/s (SI measured)
abs err: 2.61560920486449 × 10^⁻¹³ m^2/s
sigma: +1.19
within 5.2σ: yes
011. μ_B/e — Bohr magneton in eV/T [built on pass 2]
deps: l_p, t_p, m_p, coulomb, m_e, zeta(2), zhe_theta, IB
computed: 5.78838180031390 × 10^⁻⁵ eV/T
expected: 5.7883817982(18) × 10^⁻⁵ eV/T (SI measured)
abs err: 2.11390421153237 × 10^⁻¹⁴ eV/T
sigma: +1.17
within 5.2σ: yes
012. μ_N/e — nuclear magneton in eV/T [built on pass 2]
deps: l_p, t_p, m_p, coulomb, m_+, zeta(2), zhe_theta, IB
computed: 3.15245125534847 × 10^⁻⁸ eV/T
expected: 3.15245125417(98) × 10^⁻⁸ eV/T (SI measured)
abs err: 1.17847045994894 × 10^⁻¹⁷ eV/T
sigma: +1.20
within 5.2σ: yes
013. G_0^-1 — inverse of conductance quantum [built on pass 1]
deps: l_p, t_p, q_p, m_p, pi, zeta(3), zhe_1, zhe_theta, IB
computed: 1.29064037306099 × 10^⁴ Ohm
expected: 1.29064037200000 × 10^⁴ Ohm (SI exact (defined))
digits: almost-full match (9/10)
014. G_0 — conductance quantum [built on pass 1]
deps: l_p, t_p, q_p, m_p, pi, zeta(3), zhe_1, zhe_theta, IB
computed: 7.74809172928724 × 10^⁻⁵ S
expected: 7.74809172900000 × 10^⁻⁵ S (SI exact (defined))
digits: full match (10/10)
015. eV — electron volt [built on pass 1]
deps: q_p, coulomb, e, joule, zhe_1, zhe_theta, γ, IB
computed: 1.60217663422017 × 10^⁻¹⁹ J
expected: 1.60217663400000 × 10^⁻¹⁹ J (SI exact (defined))
digits: full match (10/10)
016. J⋮eV — joule-electron volt relationship [built on pass 1]
deps: q_p, coulomb, e, zhe_1, zhe_theta, γ, IB
computed: 6.24150907360306 × 10^¹⁸ eV
expected: 6.24150907400000 × 10^¹⁸ eV (SI exact (defined))
digits: full match (9/10)
017. -e/m_e — electron charge to mass quotient [built on pass 2]
deps: q_p, e, m_e, zhe_1, zhe_theta, γ, IB
computed: -1.75882000934636 × 10^¹¹ C/kg
expected: -1.75882000838(55) × 10^¹¹ C/kg (SI measured)
abs err: 9.66363663247235 × 10^¹ C/kg
sigma: -1.76
within 5.2σ: yes
018. e/m_+ — proton charge to mass quotient [built on pass 2]
deps: q_p, e, m_+, zhe_1, zhe_theta, γ, IB
computed: 9.57883314831663 × 10^⁷ C/kg
expected: 9.5788331430(29) × 10^⁷ C/kg (SI measured)
abs err: 5.31663155120871 × 10^⁻² C/kg
sigma: +1.83
within 5.2σ: yes
019. μ_B/h — Bohr magneton in Hz/T [built on pass 2]
deps: q_p, e, m_e, pi, zhe_1, zhe_theta, γ, IB
computed: 1.39962449248204 × 10^¹⁰ Hz/T
expected: 1.39962449171(44) × 10^¹⁰ Hz/T (SI measured)
abs err: 7.72036656986502 × 10^⁰ Hz/T
sigma: +1.75
within 5.2σ: yes
020. μ_N/h — nuclear magneton in MHz/T [built on pass 2]
deps: q_p, MHz, e, m_+, pi, second, zhe_1, zhe_theta, γ, IB
computed: 7.62259322303547 × 10^⁰ MHz/T
expected: 7.6225932118(24) × 10^⁰ MHz/T (SI measured)
abs err: 1.12354706446165 × 10^⁻⁸ MHz/T
sigma: +4.68
within 5.2σ: yes
021. a — lattice parameter of silicon [built on pass 2]
deps: l_p, m_p, m_e, pi, s, zhe_1, zhe_theta, IB
computed: 5.43102018763797 × 10^⁻¹⁰ m
expected: 5.431020511(89) × 10^⁻¹⁰ m (SI measured)
abs err: 3.23362031573218 × 10^⁻¹⁷ m
sigma: -3.63
within 5.2σ: yes
022. d_220 — lattice spacing of ideal Si (220) [built on pass 2]
deps: l_p, m_p, m_e, pi, s, zhe_1, zhe_theta, IB
computed: 1.92015560171992 × 10^⁻¹⁰ m
expected: 1.920155716(32) × 10^⁻¹⁰ m (SI measured)
abs err: 1.14280078390692 × 10^⁻¹⁷ m
sigma: -3.57
within 5.2σ: yes
023. A_90 — conventional value of ampere-90 [built on pass 1]
deps: S*, ampere, pi, zhe_theta, IB
computed: 1.00000008888173 × 10^⁰ A
expected: 1.00000008887000 × 10^⁰ A (SI exact (defined))
digits: almost-full match (11/12)
024. C_90 — conventional value of coulomb-90 [built on pass 1]
deps: S*, coulomb, pi, zhe_theta, IB
computed: 1.00000008888173 × 10^⁰ C
expected: 1.00000008887000 × 10^⁰ C (SI exact (defined))
digits: almost-full match (11/12)
025. μ_B/hc — Bohr magneton in inverse meter per tesla [built on pass 2]
deps: l_p, t_p, q_p, K, S*, m_e, pi, zhe_1, zhe_theta, IB
computed: 4.66864477302116 × 10^¹ 1/m*T
expected: 4.6686447719(15) × 10^¹ 1/m*T (SI measured)
abs err: 1.12115842442852 × 10^⁻⁸ 1/m*T
sigma: +0.75
within 5.2σ: yes
026. μ_N/hc — nuclear magneton in inverse meter per tesla [built on pass 2]
deps: l_p, t_p, q_p, K, S*, m_+, pi, zhe_1, zhe_theta, IB
computed: 2.54262341068941 × 10^⁻² 1/m*T
expected: 2.54262341009(79) × 10^⁻² 1/m*T (SI measured)
abs err: 5.99406426348762 × 10^⁻¹² 1/m*T
sigma: +0.76
within 5.2σ: yes
027. R_∞ — Rydberg constant [built on pass 2]
deps: l_p, m_p, V_fe, m_e, pi, zhe_1, zhe_theta, IB
computed: 1.09737315681100 × 10^⁷ 1/m
expected: 1.0973731568157(12) × 10^⁷ 1/m (SI measured)
abs err: 4.70124151044416 × 10^⁻⁵ 1/m
sigma: -3.92
within 5.2σ: yes
028. E_h⋮1/m — hartree-inverse meter relationship [built on pass 2]
deps: l_p, m_p, V_fe, m_e, pi, zhe_1, zhe_theta, IB
computed: 2.19474631362200 × 10^⁷ 1/m
expected: 2.1947463136314(24) × 10^⁷ 1/m (SI measured)
abs err: 9.40248302088832 × 10^⁻⁵ 1/m
sigma: -3.92
within 5.2σ: yes
029. 1/m⋮E_h — inverse meter-hartree relationship [built on pass 2]
deps: l_p, m_p, V_fe, m_e, meter, pi, zhe_1, zhe_theta, IB
computed: 4.55633525292919 × 10^⁻⁸ E_h
expected: 4.5563352529132(50) × 10^⁻⁸ E_h (SI measured)
abs err: 1.59910779531341 × 10^⁻¹⁹ E_h
sigma: +3.20
within 5.2σ: yes
030. A_time — atomic unit of time [built on pass 2]
deps: t_p, m_p, C_U, C_d, m_e, zhe_1, zhe_theta, IB
computed: 2.41888432657499 × 10^⁻¹⁷ s
expected: 2.4188843265864(26) × 10^⁻¹⁷ s (SI measured)
abs err: 1.14133231595366 × 10^⁻²⁸ s
sigma: -4.39
within 5.2σ: yes
031. Hz⋮E_h — hertz-hartree relationship [built on pass 2]
deps: t_p, m_p, C_U, C_d, m_e, pi, second, zhe_1, zhe_theta, IB
computed: 1.51982984605029 × 10^⁻¹⁶ E_h
expected: 1.5198298460574(17) × 10^⁻¹⁶ E_h (SI measured)
abs err: 7.10551640558465 × 10^⁻²⁸ E_h
sigma: -4.18
within 5.2σ: yes
032. E_h⋮Hz — hartree-hertz relationship [built on pass 2]
deps: t_p, m_p, C_U, C_d, m_e, pi, zhe_1, zhe_theta, IB
computed: 6.57968392052075 × 10^¹⁵ Hz
expected: 6.5796839204999(72) × 10^¹⁵ Hz (SI measured)
abs err: 2.08487113174536 × 10^⁴ Hz
sigma: +2.90
within 5.2σ: yes
033. R_∞_c ̇ — Rydberg constant times c in Hz [built on pass 2]
deps: t_p, m_p, C_U, C_d, m_e, pi, zhe_1, zhe_theta, IB
computed: 3.28984196026037 × 10^¹⁵ Hz
expected: 3.2898419602500(36) × 10^¹⁵ Hz (SI measured)
abs err: 1.03743556587268 × 10^⁴ Hz
sigma: +2.88
within 5.2σ: yes
034. κ — Coulomb's constant [built on pass 1]
deps: l_p, t_p, q_p, m_p, C_d, zhe_theta, IB
computed: 8.98755179302985 × 10^⁹ m/F
expected: 8.9875517923(14) × 10^⁹ m/F (SI measured)
abs err: 7.29850447566695 × 10^⁻¹ m/F
sigma: +0.52
within 5.2σ: yes
035. A_perm — atomic unit of permittivity [built on pass 1]
deps: l_p, t_p, q_p, m_p, C_d, zhe_theta, IB
computed: 1.11265005535270 × 10^⁻¹⁰ F/m
expected: 1.11265005620(17) × 10^⁻¹⁰ F/m (SI measured)
abs err: 8.47298047754766 × 10^⁻²⁰ F/m
sigma: -4.98
within 5.2σ: yes
036. ε_0 — vacuum electric permittivity [built on pass 1]
deps: l_p, t_p, q_p, m_p, C_d, pi, zhe_theta, IB
computed: 8.85418781204267 × 10^⁻¹² F/m
expected: 8.8541878188(14) × 10^⁻¹² F/m (SI measured)
abs err: 6.75732627322587 × 10^⁻²¹ F/m
sigma: -4.83
within 5.2σ: yes
037. μ_n/μ_+ — neutron-proton magnetic moment ratio [built on pass 2]
deps: !5, C_CFP, K, S, m_+, m_n, pi, zhe_r, IB
computed: -6.84979091085623 × 10^⁻¹ -
expected: -6.8497935(16) × 10^⁻¹ - (SI measured)
abs err: 2.58914377433736 × 10^⁻⁷ -
sigma: +1.62
within 5.2σ: yes
038. μ_+/μ_n — proton-neutron magnetic moment ratio [built on pass 2]
deps: !5, C_CFP, K, S, m_+, m_n, pi, zhe_r, IB
computed: -1.45989857648808 × 10^⁰ -
expected: -1.45989802(34) × 10^⁰ - (SI measured)
abs err: 5.56488081060851 × 10^⁻⁷ -
sigma: -1.64
within 5.2σ: yes
039. μ_e/μ_n — electron-neutron magnetic moment ratio [built on pass 2]
deps: C_CFP, K, P_up, m_e, m_n, pi, zhe_r, IB
computed: 9.60920149475118 × 10^² -
expected: 9.6092048(23) × 10^² - (SI measured)
abs err: 3.30524881779597 × 10^⁻⁴ -
sigma: -1.44
within 5.2σ: yes
040. μ_n/μ_e — neutron-electron magnetic moment ratio [built on pass 2]
deps: C_CFP, K, P_up, m_e, m_n, pi, zhe_r, IB
computed: 1.04066919665097 × 10^⁻³ -
expected: 1.04066884(24) × 10^⁻³ - (SI measured)
abs err: 3.56650968657396 × 10^⁻¹⁰ -
sigma: +1.49
within 5.2σ: yes
041. A_mdm — atomic unit of magnetic dipole moment [built on pass 2]
deps: l_p, t_p, q_p, m_p, m_e, omega_2, pi, zhe_1, zhe_r, IB
computed: 1.85480201153129 × 10^⁻²³ J/T
expected: 1.85480201315(58) × 10^⁻²³ J/T (SI measured)
abs err: 1.61871065064361 × 10^⁻³² J/T
sigma: -2.79
within 5.2σ: yes
042. μ_B — Bohr magneton [built on pass 2]
deps: l_p, t_p, q_p, m_p, m_e, omega_2, pi, zhe_1, zhe_r, IB
computed: 9.27401005765645 × 10^⁻²⁴ J/T
expected: 9.2740100657(29) × 10^⁻²⁴ J/T (SI measured)
abs err: 8.04355325321805 × 10^⁻³³ J/T
sigma: -2.77
within 5.2σ: yes
043. μ_N — nuclear magneton [built on pass 2]
deps: l_p, t_p, q_p, m_p, m_+, omega_2, pi, zhe_1, zhe_r, IB
computed: 5.05078373489253 × 10^⁻²⁷ J/T
expected: 5.0507837393(16) × 10^⁻²⁷ J/T (SI measured)
abs err: 4.40747024839064 × 10^⁻³⁶ J/T
sigma: -2.75
within 5.2σ: yes
044. μ_tri — triton magnetic moment [built on pass 2]
deps: l_p, t_p, q_p, m_p, D_Do, m_tri, omega_2, pi, zhe_1, zhe_2, zhe_r, IB
computed: 1.50460951924309 × 10^⁻²⁶ J/T
expected: 1.5046095178(30) × 10^⁻²⁶ J/T (SI measured)
abs err: 1.44308666084413 × 10^⁻³⁵ J/T
sigma: +0.48
within 5.2σ: yes
045. μ_tri/μ_+ — triton to proton magnetic moment ratio [built on pass 2]
deps: D_Do, L_LL, S, m_+, m_tri, pi, zhe_r, IB
computed: 1.06663991754138 × 10^⁰ -
expected: 1.0666399189(21) × 10^⁰ - (SI measured)
abs err: 1.35862473585692 × 10^⁻⁹ -
sigma: -0.65
within 5.2σ: yes
046. μ_tri/μ_N — triton magnetic moment to nuclear magneton ratio [built on pass 2]
deps: m_+, m_tri, pi, zhe_1, zhe_2, zhe_r, IB
computed: 2.97896247563038 × 10^⁰ -
expected: 2.9789624650(59) × 10^⁰ - (SI measured)
abs err: 1.06303756147574 × 10^⁻⁸ -
sigma: +1.80
within 5.2σ: yes
047. μ_tri/μ_B — triton magnetic moment to Bohr magneton ratio [built on pass 2]
deps: m_e, m_tri, pi, zhe_1, zhe_2, zhe_r, IB
computed: 1.62239367061580 × 10^⁻³ -
expected: 1.6223936648(32) × 10^⁻³ - (SI measured)
abs err: 5.81579952119730 × 10^⁻¹² -
sigma: +1.82
within 5.2σ: yes
048. g_tri — triton g factor [built on pass 2]
deps: m_+, m_tri, pi, zhe_1, zhe_2, zhe_r, IB
computed: 5.95792495126075 × 10^⁰ -
expected: 5.957924930(12) × 10^⁰ - (SI measured)
abs err: 2.12607512295148 × 10^⁻⁸ -
sigma: +1.77
within 5.2σ: yes
049. μ_e/μ_μ — electron-muon magnetic moment ratio [built on pass 3]
deps: m_e, m_μ, pi, zhe_r, IB
computed: 2.06766985041623 × 10^² -
expected: 2.067669881(46) × 10^² - (SI measured)
abs err: 3.05837693606701 × 10^⁻⁶ -
sigma: -0.66
within 5.2σ: yes
050. G — Newtonian constant of gravitation [built on pass 1]
deps: l_p, t_p, m_p, pi, zhe_r, IB
computed: 6.67430315504538 × 10^⁻¹¹ m^3/(s^2*kg)
expected: 6.67430(15) × 10^⁻¹¹ m^3/(s^2*kg) (SI measured)
abs err: 3.15504537914155 × 10^⁻¹⁷ m^3/(s^2*kg)
sigma: +0.02
within 5.2σ: yes
051. G/ℏc — Newtonian constant of gravitation over h-bar c [built on pass 1]
deps: l_p, t_p, m_p, GeV, pi, zhe_r, IB
computed: 6.70882525604658 × 10^⁻³⁹ c^4/GeV^2
expected: 6.70883(15) × 10^⁻³⁹ c^4/GeV^2 (SI measured)
abs err: 4.74395341755589 × 10^⁻⁴⁵ c^4/GeV^2
sigma: -0.03
within 5.2σ: yes
052. m_n — neutron mass [built on pass 1]
deps: l_p, t_p, GeV, pi, s, zhe_r, φ, IB
computed: 1.67492749887877 × 10^⁻²⁷ kg
expected: 1.67492750056(85) × 10^⁻²⁷ kg (SI measured)
abs err: 1.68123470602965 × 10^⁻³⁶ kg
sigma: -1.98
within 5.2σ: yes
053. m_+ — proton mass [built on pass 1]
deps: l_p, t_p, GeV, e, omega_2, pi, s, zhe_r, γ, IB
computed: 1.67262192525165 × 10^⁻²⁷ kg
expected: 1.67262192595(52) × 10^⁻²⁷ kg (SI measured)
abs err: 6.98352259189495 × 10^⁻³⁷ kg
sigma: -1.34
within 5.2σ: yes
054. μ_de/μ_e — deuteron-electron magnetic moment ratio [built on pass 3]
deps: L_1, P_up, m_de, m_e, pi, s, zhe_r, IB
computed: -4.66434558966557 × 10^⁻⁴ -
expected: -4.664345550(12) × 10^⁻⁴ - (SI measured)
abs err: 3.96655700401982 × 10^⁻¹² -
sigma: -3.31
within 5.2σ: yes
055. μ_e/μ_de — electron-deuteron magnetic moment ratio [built on pass 3]
deps: L_1, P_up, m_de, m_e, pi, s, zhe_r, IB
computed: -2.14392347388586 × 10^³ -
expected: -2.1439234921(56) × 10^³ - (SI measured)
abs err: 1.82141397884307 × 10^⁻⁵ -
sigma: +3.25
within 5.2σ: yes
056. m_μ — muon mass [built on pass 2]
deps: A_mass, K_-6, pi, s, zhe_r, IB
computed: 1.88353161502363 × 10^⁻²⁸ kg
expected: 1.883531627(42) × 10^⁻²⁸ kg (SI measured)
abs err: 1.19763698141403 × 10^⁻³⁶ kg
sigma: -0.29
within 5.2σ: yes
057. m_de — deuteron mass [built on pass 2]
deps: A_mass, K_-6, pi, s, zhe_r, IB
computed: 3.34358377540376 × 10^⁻²⁷ kg
expected: 3.3435837768(10) × 10^⁻²⁷ kg (SI measured)
abs err: 1.39624168889586 × 10^⁻³⁶ kg
sigma: -1.40
within 5.2σ: yes
058. μ_de/μ_+ — deuteron-proton magnetic moment ratio [built on pass 2]
deps: !5, S, m_+, m_de, pi, s, zhe_r, φ, IB
computed: 3.07012209387134 × 10^⁻¹ -
expected: 3.0701220930(79) × 10^⁻¹ - (SI measured)
abs err: 8.71336549833322 × 10^⁻¹¹ -
sigma: +0.11
within 5.2σ: yes
059. μ_de/μ_n — deuteron-neutron magnetic moment ratio [built on pass 2]
deps: C_CFP, Im(omega_1), m_de, m_n, pi, s, zhe_r, IB
computed: -4.48206589656941 × 10^⁻¹ -
expected: -4.4820652(11) × 10^⁻¹ - (SI measured)
abs err: 6.96569409131123 × 10^⁻⁸ -
sigma: -0.63
within 5.2σ: yes
060. μ_de — deuteron magnetic moment [built on pass 2]
deps: l_p, t_p, q_p, m_p, m_de, omega_2, pi, s, zhe_1, zhe_2, zhe_r, IB
computed: 4.33073505988037 × 10^⁻²⁷ J/T
expected: 4.330735087(11) × 10^⁻²⁷ J/T (SI measured)
abs err: 2.71196328964946 × 10^⁻³⁵ J/T
sigma: -2.47
within 5.2σ: yes
061. μ_he'/μ_B — shielded helion magnetic moment to Bohr magneton ratio [built on pass 3]
deps: K, m_he, m_μ, pi, s, zhe_r, IB
computed: -1.15867149694879 × 10^⁻³ -
expected: -1.15867149457(94) × 10^⁻³ - (SI measured)
abs err: 2.37879229059068 × 10^⁻¹² -
sigma: -2.53
within 5.2σ: yes
062. μ_he'/μ_N — shielded helion magnetic moment to nuclear magneton ratio [built on pass 3]
deps: K, m_+, m_e, m_he, m_μ, pi, s, zhe_r, IB
computed: -2.12749776673057 × 10^⁰ -
expected: -2.1274977624(17) × 10^⁰ - (SI measured)
abs err: 4.33057124374067 × 10^⁻⁹ -
sigma: -2.55
within 5.2σ: yes
063. g_he — helion g factor [built on pass 3]
deps: K, m_+, m_e, m_he, m_μ, pi, s, zhe_r, IB
computed: -4.25525070422300 × 10^⁰ -
expected: -4.2552506995(34) × 10^⁰ - (SI measured)
abs err: 4.72300216416685 × 10^⁻⁹ -
sigma: -1.39
within 5.2σ: yes
064. μ_he/μ_N — helion magnetic moment to nuclear magneton ratio [built on pass 3]
deps: K, m_+, m_e, m_he, m_μ, pi, s, zhe_r, IB
computed: -2.12762535211150 × 10^⁰ -
expected: -2.1276253498(17) × 10^⁰ - (SI measured)
abs err: 2.31150108208342 × 10^⁻⁹ -
sigma: -1.36
within 5.2σ: yes
065. μ_he/μ_B — helion magnetic moment to Bohr magneton ratio [built on pass 3]
deps: K, m_he, m_μ, pi, s, zhe_r, IB
computed: -1.15874098211894 × 10^⁻³ -
expected: -1.15874098083(94) × 10^⁻³ - (SI measured)
abs err: 1.28894028773893 × 10^⁻¹² -
sigma: -1.37
within 5.2σ: yes
066. μ_0 — vacuum magnetic permeability [built on pass 1]
deps: l_p, q_p, m_p, G_Ga, pi, s, zhe_r, IB
computed: 1.25663706158249 × 10^⁻⁶ N/A^2
expected: 1.25663706127(20) × 10^⁻⁶ N/A^2 (SI measured)
abs err: 3.12485657655087 × 10^⁻¹⁶ N/A^2
sigma: +1.56
within 5.2σ: yes
067. m_e — electron mass [built on pass 1]
deps: m_p, V_fe, kilogram, s, zhe_r, IB
computed: 9.10938371013637 × 10^⁻³¹ kg
expected: 9.1093837139(28) × 10^⁻³¹ kg (SI measured)
abs err: 3.76362811823937 × 10^⁻⁴⁰ kg
sigma: -1.34
within 5.2σ: yes
068. m_τ — tau mass [built on pass 1]
deps: m_p, L_LL, kilogram, pi, s, zhe_1, zhe_r, IB
computed: 3.16754546668953 × 10^⁻²⁷ kg
expected: 3.16754(21) × 10^⁻²⁷ kg (SI measured)
abs err: 5.46668953450149 × 10^⁻³³ kg
sigma: +0.03
within 5.2σ: yes
069. m_tri — triton mass [built on pass 1]
deps: m_p, G_Ga, K, kilogram, pi, s, zhe_1, zhe_r, IB
computed: 5.00735674868071 × 10^⁻²⁷ kg
expected: 5.0073567512(16) × 10^⁻²⁷ kg (SI measured)
abs err: 2.51928629209690 × 10^⁻³⁶ kg
sigma: -1.57
within 5.2σ: yes
070. K_cd — luminous efficacy [built on pass 2]
deps: l_p, t_p, A_mass, G_Ga, K, f_1, pi, s, zhe_1, zhe_r, IB
computed: 6.83053688789293 × 10^² lm/W
expected: 6.83000000000000 × 10^² lm/W (SI exact (defined))
digits: full match (3/3)
071. m_he — helion mass [built on pass 2]
deps: A_mass, e, pi, s, x_infinity, zhe_r, IB
computed: 5.00641278404442 × 10^⁻²⁷ kg
expected: 5.0064127862(16) × 10^⁻²⁷ kg (SI measured)
abs err: 2.15558219424346 × 10^⁻³⁶ kg
sigma: -1.35
within 5.2σ: yes
072. m_α — alpha particle mass [built on pass 2]
deps: A_mass, V_fe, omega_2, pi, s, x_infinity, zhe_r, IB
computed: 6.64465734214073 × 10^⁻²⁷ kg
expected: 6.6446573450(21) × 10^⁻²⁷ kg (SI measured)
abs err: 2.85927090341242 × 10^⁻³⁶ kg
sigma: -1.36
within 5.2σ: yes
073. E_p ̇ — Planck mass energy equivalent in GeV [built on pass 1]
deps: l_p, t_p, m_p, GeV, Re(ipt), zhe_3, zhe_4, IB
computed: 1.22088626410128 × 10^¹⁹ GeV
expected: 1.220890(14) × 10^¹⁹ GeV (SI measured)
abs err: 3.73589872129398 × 10^¹³ GeV
sigma: -0.27
within 5.2σ: yes
074. R_K — von Klitzing constant [built on pass 1]
deps: l_p, t_p, q_p, m_p, Re(ipt), pi, zhe_1, zhe_3, zhe_4, IB
computed: 2.58128074493917 × 10^⁴ Ohm
expected: 2.58128074500000 × 10^⁴ Ohm (SI exact (defined))
digits: full match (9/10)
075. Z_0 — characteristic impedance of vacuum [built on pass 1]
deps: l_p, t_p, q_p, m_p, Re(ipt), pi, zhe_3, zhe_4, IB
computed: 3.76730313712033 × 10^² Ohm
expected: 3.76730313412(59) × 10^² Ohm (SI measured)
abs err: 3.00032721586267 × 10^⁻⁷ Ohm
sigma: +5.09
within 5.2σ: yes
076. Z_p — Planck electric impedance [built on pass 1]
deps: l_p, t_p, q_p, m_p, Re(ipt), zhe_3, zhe_4, IB
computed: 2.99792458199152 × 10^¹ Ohm
expected: 2.99792458(45) × 10^¹ Ohm (SI measured)
abs err: 1.99152224455407 × 10^⁻⁸ Ohm
sigma: +0.00
within 5.2σ: yes
077. Hz⋮1/m — hertz-inverse meter relationship [built on pass 1]
deps: l_p, t_p, Im(ipt), second, zhe_3, zhe_4, IB
computed: 3.33564095322874 × 10^⁻⁹ cycles/m
expected: 3.33564095100000 × 10^⁻⁹ cycles/m (SI exact (defined))
digits: almost-full match (9/10)
078. A_vel — atomic unit of velocity [built on pass 1]
deps: l_p, t_p, Im(ipt), zhe_1, zhe_3, zhe_4, IB
computed: 2.18769126392059 × 10^⁶ m/s
expected: 2.18769126216(34) × 10^⁶ m/s (SI measured)
abs err: 1.76059056477354 × 10^⁻³ m/s
sigma: +5.18
within 5.2σ: yes
079. A_mom — atomic unit of momentum [built on pass 1]
deps: l_p, t_p, Im(ipt), m_e, zhe_1, zhe_3, zhe_4, IB
computed: 1.99285191623659 × 10^⁻²⁴ m*kg/s
expected: 1.99285191545(31) × 10^⁻²⁴ m*kg/s (SI measured)
abs err: 7.86587799869997 × 10^⁻³⁴ m*kg/s
sigma: +2.54
within 5.2σ: yes
080. N_mom — natural unit of momentum [built on pass 1]
deps: l_p, t_p, Im(ipt), m_e, zhe_3, zhe_4, IB
computed: 2.73092453230547 × 10^⁻²² m*kg/s
expected: 2.73092453446(85) × 10^⁻²² m*kg/s (SI measured)
abs err: 2.15452654265664 × 10^⁻³¹ m*kg/s
sigma: -2.53
within 5.2σ: yes
081. N_mom ̇ — natural unit of momentum in MeV/c [built on pass 1]
deps: l_p, t_p, Im(ipt), MeV, m_e, meter, second, zhe_3, zhe_4, IB
computed: 5.10998950028076 × 10^⁻¹ MeV/c
expected: 5.1099895069(16) × 10^⁻¹ MeV/c (SI measured)
abs err: 6.61923612808745 × 10^⁻¹⁰ MeV/c
sigma: -4.14
within 5.2σ: yes
082. E_A_mass ̇ — atomic mass constant energy equivalent in MeV [built on pass 2]
deps: l_p, t_p, A_mass, Im(ipt), MeV, zhe_3, zhe_4, IB
computed: 9.31494102497143 × 10^² MeV
expected: 9.3149410372(29) × 10^² MeV (SI measured)
abs err: 1.22285675851424 × 10^⁻⁶ MeV
sigma: -4.22
within 5.2σ: yes
083. E_e ̇ — natural unit of energy in MeV [built on pass 1]
deps: l_p, t_p, Im(ipt), MeV, m_e, zhe_3, zhe_4, IB
computed: 5.10998950028076 × 10^⁻¹ MeV
expected: 5.1099895069(16) × 10^⁻¹ MeV (SI measured)
abs err: 6.61923612808745 × 10^⁻¹⁰ MeV
sigma: -4.14
within 5.2σ: yes
084. E_μ ̇ — muon mass energy equivalent in MeV [built on pass 2]
deps: l_p, t_p, Im(ipt), MeV, m_μ, zhe_3, zhe_4, IB
computed: 1.05658374731846 × 10^² MeV
expected: 1.056583755(23) × 10^² MeV (SI measured)
abs err: 7.68154042696809 × 10^⁻⁷ MeV
sigma: -0.33
within 5.2σ: yes
085. E_+ ̇ — proton mass energy equivalent in MeV [built on pass 1]
deps: l_p, t_p, Im(ipt), MeV, m_+, zhe_3, zhe_4, IB
computed: 9.38272088205555 × 10^² MeV
expected: 9.3827208943(29) × 10^² MeV (SI measured)
abs err: 1.22444534662732 × 10^⁻⁶ MeV
sigma: -4.22
within 5.2σ: yes
086. E_n ̇ — neutron mass energy equivalent in MeV [built on pass 1]
deps: l_p, t_p, Im(ipt), MeV, m_n, zhe_3, zhe_4, IB
computed: 9.39565420158800 × 10^² MeV
expected: 9.3956542194(48) × 10^² MeV (SI measured)
abs err: 1.78119967973919 × 10^⁻⁶ MeV
sigma: -3.71
within 5.2σ: yes
087. E_∆ ̇ — neutron-proton mass difference energy equivalent in MeV [built on pass 1]
deps: l_p, t_p, Im(ipt), MeV, m_+, m_n, zhe_3, zhe_4, IB
computed: 1.29333195324567 × 10^⁰ MeV
expected: 1.29333251(38) × 10^⁰ MeV (SI measured)
abs err: 5.56754333111869 × 10^⁻⁷ MeV
sigma: -1.47
within 5.2σ: yes
088. E_τ ̇ — tau energy equivalent [built on pass 1]
deps: l_p, t_p, Im(ipt), MeV, m_τ, zhe_3, zhe_4, IB
computed: 1.77686269362378 × 10^³ MeV
expected: 1.77686(12) × 10^³ MeV (SI measured)
abs err: 2.69362377526668 × 10^⁻³ MeV
sigma: +0.02
within 5.2σ: yes
089. E_de ̇ — deuteron mass energy equivalent in MeV [built on pass 2]
deps: l_p, t_p, Im(ipt), MeV, m_de, zhe_3, zhe_4, IB
computed: 1.87561294257595 × 10^³ MeV
expected: 1.87561294500(58) × 10^³ MeV (SI measured)
abs err: 2.42404829594202 × 10^⁻⁶ MeV
sigma: -4.18
within 5.2σ: yes
090. E_he ̇ — helion mass energy equivalent in MeV [built on pass 2]
deps: l_p, t_p, Im(ipt), MeV, m_he, zhe_3, zhe_4, IB
computed: 2.80839160744447 × 10^³ MeV
expected: 2.80839161112(88) × 10^³ MeV (SI measured)
abs err: 3.67552923563895 × 10^⁻⁶ MeV
sigma: -4.18
within 5.2σ: yes
091. E_tri ̇ — triton mass energy equivalent in MeV [built on pass 1]
deps: l_p, t_p, Im(ipt), MeV, m_tri, zhe_3, zhe_4, IB
computed: 2.80892113277062 × 10^³ MeV
expected: 2.80892113668(88) × 10^³ MeV (SI measured)
abs err: 3.90938220503340 × 10^⁻⁶ MeV
sigma: -4.44
within 5.2σ: yes
092. E_α ̇ — alpha particle mass energy equivalent in MeV [built on pass 2]
deps: l_p, t_p, Im(ipt), MeV, m_α, zhe_3, zhe_4, IB
computed: 3.72737940696477 × 10^³ MeV
expected: 3.7273794118(12) × 10^³ MeV (SI measured)
abs err: 4.83523364424672 × 10^⁻⁶ MeV
sigma: -4.03
within 5.2σ: yes
093. kg⋮eV — kilogram-electron volt relationship [built on pass 1]
deps: l_p, t_p, Im(ipt), eV, kilogram, zhe_3, zhe_4, IB
computed: 5.60958859883647 × 10^³⁵ eV
expected: 5.60958860300000 × 10^³⁵ eV (SI exact (defined))
digits: almost-full match (7/10)
094. eV⋮kg — electron volt-kilogram relationship [built on pass 1]
deps: l_p, t_p, Im(ipt), eV, zhe_3, zhe_4, IB
computed: 1.78266192320573 × 10^⁻³⁶ kg
expected: 1.78266192100000 × 10^⁻³⁶ kg (SI exact (defined))
digits: almost-full match (9/10)
095. J⋮kg — joule-kilogram relationship [built on pass 1]
deps: l_p, t_p, Im(ipt), joule, zhe_3, zhe_4, IB
computed: 1.11265005688553 × 10^⁻¹⁷ kg
expected: 1.11265005600000 × 10^⁻¹⁷ kg (SI exact (defined))
digits: full match (10/10)
096. J⋮A_mass — joule-atomic mass unit relationship [built on pass 2]
deps: l_p, t_p, A_mass, Im(ipt), joule, zhe_3, zhe_4, IB
computed: 6.70053525499261 × 10^⁹ u
expected: 6.7005352471(21) × 10^⁹ u (SI measured)
abs err: 7.89260963170653 × 10^⁰ u
sigma: +3.76
within 5.2σ: yes
097. kg⋮J — kilogram-joule relationship [built on pass 1]
deps: l_p, t_p, Im(ipt), kilogram, zhe_3, zhe_4, IB
computed: 8.98755178064363 × 10^¹⁶ J
expected: 8.98755178700000 × 10^¹⁶ J (SI exact (defined))
digits: almost-full match (9/10)
098. A_mass⋮J — atomic mass unit-joule relationship [built on pass 2]
deps: l_p, t_p, A_mass, Im(ipt), zhe_3, zhe_4, IB
computed: 1.49241808593481 × 10^⁻¹⁰ J
expected: 1.49241808768(46) × 10^⁻¹⁰ J (SI measured)
abs err: 1.74519211106474 × 10^⁻¹⁹ J
sigma: -3.79
within 5.2σ: yes
099. E_e — electron mass energy equivalent [built on pass 1]
deps: l_p, t_p, Im(ipt), m_e, zhe_3, zhe_4, IB
computed: 8.18710577846023 × 10^⁻¹⁴ J
expected: 8.1871057880(26) × 10^⁻¹⁴ J (SI measured)
abs err: 9.53977441694499 × 10^⁻²³ J
sigma: -3.67
within 5.2σ: yes
100. E_μ — muon mass energy equivalent [built on pass 2]
deps: l_p, t_p, Im(ipt), m_μ, zhe_3, zhe_4, IB
computed: 1.69283379205042 × 10^⁻¹¹ J
expected: 1.692833804(38) × 10^⁻¹¹ J (SI measured)
abs err: 1.19495794115380 × 10^⁻¹⁹ J
sigma: -0.31
within 5.2σ: yes
101. E_+ — proton mass energy equivalent [built on pass 1]
deps: l_p, t_p, Im(ipt), m_+, zhe_3, zhe_4, IB
computed: 1.50327761626390 × 10^⁻¹⁰ J
expected: 1.50327761802(47) × 10^⁻¹⁰ J (SI measured)
abs err: 1.75609712327605 × 10^⁻¹⁹ J
sigma: -3.74
within 5.2σ: yes
102. E_n — neutron mass energy equivalent [built on pass 1]
deps: l_p, t_p, Im(ipt), m_n, zhe_3, zhe_4, IB
computed: 1.50534976249968 × 10^⁻¹⁰ J
expected: 1.50534976514(76) × 10^⁻¹⁰ J (SI measured)
abs err: 2.64031658676316 × 10^⁻¹⁹ J
sigma: -3.47
within 5.2σ: yes
103. E_∆ — neutron-proton mass difference energy equivalent [built on pass 1]
deps: l_p, t_p, Im(ipt), m_+, m_n, zhe_3, zhe_4, IB
computed: 2.07214623578054 × 10^⁻¹³ J
expected: 2.07214712(60) × 10^⁻¹³ J (SI measured)
abs err: 8.84219463487113 × 10^⁻²⁰ J
sigma: -1.47
within 5.2σ: yes
104. E_τ — tau mass energy equivalent [built on pass 1]
deps: l_p, t_p, Im(ipt), m_τ, zhe_3, zhe_4, IB
computed: 2.84684788994152 × 10^⁻¹⁰ J
expected: 2.84684(19) × 10^⁻¹⁰ J (SI measured)
abs err: 7.88994151942521 × 10^⁻¹⁶ J
sigma: +0.04
within 5.2σ: yes
105. E_de — deuteron mass energy equivalent [built on pass 2]
deps: l_p, t_p, Im(ipt), m_de, zhe_3, zhe_4, IB
computed: 3.00506323143612 × 10^⁻¹⁰ J
expected: 3.00506323491(94) × 10^⁻¹⁰ J (SI measured)
abs err: 3.47387899191876 × 10^⁻¹⁹ J
sigma: -3.70
within 5.2σ: yes
106. E_he — helion mass energy equivalent [built on pass 2]
deps: l_p, t_p, Im(ipt), m_he, zhe_3, zhe_4, IB
computed: 4.49953941318755 × 10^⁻¹⁰ J
expected: 4.4995394185(14) × 10^⁻¹⁰ J (SI measured)
abs err: 5.31245431784827 × 10^⁻¹⁹ J
sigma: -3.79
within 5.2σ: yes
107. E_tri — triton mass energy equivalent [built on pass 1]
deps: l_p, t_p, Im(ipt), m_tri, zhe_3, zhe_4, IB
computed: 4.50038780629233 × 10^⁻¹⁰ J
expected: 4.5003878119(14) × 10^⁻¹⁰ J (SI measured)
abs err: 5.60767373234664 × 10^⁻¹⁹ J
sigma: -4.01
within 5.2σ: yes
108. E_α — alpha particle mass energy equivalent [built on pass 2]
deps: l_p, t_p, Im(ipt), m_α, zhe_3, zhe_4, IB
computed: 5.97192019271237 × 10^⁻¹⁰ J
expected: 5.9719201997(19) × 10^⁻¹⁰ J (SI measured)
abs err: 6.98762984769604 × 10^⁻¹⁹ J
sigma: -3.68
within 5.2σ: yes
109. g_de — deuteron g factor [built on pass 1]
deps: K, W_We, pi, zhe_1, zhe_3, zhe_4, IB
computed: 8.57438235960776 × 10^⁻¹ -
expected: 8.574382335(22) × 10^⁻¹ - (SI measured)
abs err: 2.46077580007049 × 10^⁻⁹ -
sigma: +1.12
within 5.2σ: yes
110. μ_de/μ_N — deuteron magnetic moment to nuclear magneton ratio [built on pass 1]
deps: K, W_We, pi, zhe_1, zhe_3, zhe_4, IB
computed: 8.57438235960776 × 10^⁻¹ -
expected: 8.574382335(22) × 10^⁻¹ - (SI measured)
abs err: 2.46077580007049 × 10^⁻⁹ -
sigma: +1.12
within 5.2σ: yes
111. μ_de/μ_B — deuteron magnetic moment to Bohr magneton ratio [built on pass 1]
deps: K, W_We, m_+, m_e, pi, zhe_1, zhe_3, zhe_4, IB
computed: 4.66975458182758 × 10^⁻⁴ -
expected: 4.669754568(12) × 10^⁻⁴ - (SI measured)
abs err: 1.38275845853207 × 10^⁻¹² -
sigma: +1.15
within 5.2σ: yes
112. μ_μ — muon magnetic moment [built on pass 2]
deps: l_p, t_p, q_p, m_p, G_Gi, L_Li, P_up, m_μ, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: -4.49044831883702 × 10^⁻²⁶ J/T
expected: -4.49044830(10) × 10^⁻²⁶ J/T (SI measured)
abs err: 1.88370203702933 × 10^⁻³⁴ J/T
sigma: -0.19
within 5.2σ: yes
113. a_e — electron magnetic moment anomaly [built on pass 1]
deps: L_Li, P_up, V_fe, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 1.15965218025155 × 10^⁻³ -
expected: 1.15965218046(18) × 10^⁻³ - (SI measured)
abs err: 2.08449661758317 × 10^⁻¹³ -
sigma: -1.16
within 5.2σ: yes
114. a_μ — muon magnetic moment anomaly [built on pass 1]
deps: !5, K, L_Li, P_up, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 1.16592060110470 × 10^⁻³ -
expected: 1.16592062(41) × 10^⁻³ - (SI measured)
abs err: 1.88953010287692 × 10^⁻¹¹ -
sigma: -0.05
within 5.2σ: yes
115. g_μ — muon g factor [built on pass 1]
deps: C_d, P_up, zeta(2), zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: -2.00233184172840 × 10^⁰ -
expected: -2.00233184123(82) × 10^⁰ - (SI measured)
abs err: 4.98398123877029 × 10^⁻¹⁰ -
sigma: -0.61
within 5.2σ: yes
116. μ_μ/μ_B — muon magnetic moment to Bohr magneton ratio [built on pass 2]
deps: C_d, P_up, m_e, m_μ, zeta(2), zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: -4.84197050791186 × 10^⁻³ -
expected: -4.84197048(11) × 10^⁻³ - (SI measured)
abs err: 2.79118612376324 × 10^⁻¹¹ -
sigma: -0.25
within 5.2σ: yes
117. μ_μ/μ_N — muon magnetic moment to nuclear magneton ratio [built on pass 2]
deps: C_d, P_up, m_+, m_μ, zeta(2), zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: -8.89059709269179 × 10^⁰ -
expected: -8.89059704(20) × 10^⁰ - (SI measured)
abs err: 5.26917878920461 × 10^⁻⁸ -
sigma: -0.26
within 5.2σ: yes
118. R — molar gas constant [built on pass 1]
deps: l_p, t_p, q_p, T_p, C_d, coulomb, e, kilogram, zhe_1, zhe_3, zhe_4, γ, IB
computed: 8.31446261978168 × 10^⁰ J/mol*K
expected: 8.31446261800000 × 10^⁰ J/mol*K (SI exact (defined))
digits: almost-full match (9/10)
119. V_m_0 — molar volume of ideal gas (273.15 K, 100 kPa) [built on pass 1]
deps: l_p, t_p, q_p, T_p, C_d, T_0, coulomb, e, kilogram, p_0, zhe_1, zhe_3, zhe_4, γ, IB
computed: 2.27109546459337 × 10^⁻² m^3/mol
expected: 2.27109546400000 × 10^⁻² m^3/mol (SI exact (defined))
digits: full match (10/10)
120. V_m_1 — molar volume of ideal gas (273.15 K, 101.325 kPa) [built on pass 1]
deps: l_p, t_p, q_p, T_p, C_d, T_0, coulomb, e, kilogram, p_1, zhe_1, zhe_3, zhe_4, γ, IB
computed: 2.24139695494041 × 10^⁻² m^3/mol
expected: 2.24139695400000 × 10^⁻² m^3/mol (SI exact (defined))
digits: full match (10/10)
121. g_e — electron g factor [built on pass 1]
deps: C_CFP, D_d, P_up, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: -2.00231930436065 × 10^⁰ -
expected: -2.00231930436092(36) × 10^⁰ - (SI measured)
abs err: 2.71601522449349 × 10^⁻¹³ -
sigma: +0.75
within 5.2σ: yes
122. μ_e/μ_B — electron magnetic moment to Bohr magneton ratio [built on pass 1]
deps: C_CFP, D_d, P_up, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: -1.00115965218032 × 10^⁰ -
expected: -1.00115965218046(18) × 10^⁰ - (SI measured)
abs err: 1.35800761224674 × 10^⁻¹³ -
sigma: +0.75
within 5.2σ: yes
123. μ_e/μ_N — electron magnetic moment to nuclear magneton ratio [built on pass 1]
deps: C_CFP, D_d, P_up, m_+, m_e, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: -1.83828197186465 × 10^³ -
expected: -1.838281971877(32) × 10^³ - (SI measured)
abs err: 1.23469556002811 × 10^⁻⁸ -
sigma: +0.39
within 5.2σ: yes
124. μ_e — electron magnetic moment [built on pass 1]
deps: l_p, t_p, q_p, m_p, P_up, m_e, pi, s, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: -9.28476469207113 × 10^⁻²⁴ J/T
expected: -9.2847646917(29) × 10^⁻²⁴ J/T (SI measured)
abs err: 3.71130297186494 × 10^⁻³⁴ J/T
sigma: -0.13
within 5.2σ: yes
125. γ_e — electron gyromagnetic ratio [built on pass 1]
deps: q_p, P_up, m_e, pi, s, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 1.76085962907620 × 10^¹¹ 1/s*T
expected: 1.76085962784(55) × 10^¹¹ 1/s*T (SI measured)
abs err: 1.23619902049640 × 10^² 1/s*T
sigma: +2.25
within 5.2σ: yes
126. γ_e ̇ — electron gyromagnetic ratio in MHz/T [built on pass 1]
deps: q_p, MHz, P_up, m_e, pi, s, second, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 2.80249514058438 × 10^⁴ MHz/T
expected: 2.80249513861(87) × 10^⁴ MHz/T (SI measured)
abs err: 1.97438384619590 × 10^⁻⁵ MHz/T
sigma: +2.27
within 5.2σ: yes
127. γ_+' ̇ — shielded proton gyromagnetic ratio in MHz/T [built on pass 1]
deps: q_p, MHz, S, m_+, pi, s, second, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 4.25763852810158 × 10^¹ MHz/T
expected: 4.257638543(17) × 10^¹ MHz/T (SI measured)
abs err: 1.48984223472690 × 10^⁻⁷ MHz/T
sigma: -0.88
within 5.2σ: yes
128. γ_+' — shielded proton gyromagnetic ratio [built on pass 1]
deps: q_p, S, m_+, s, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 2.67515318430496 × 10^⁸ 1/s*T
expected: 2.675153194(11) × 10^⁸ 1/s*T (SI measured)
abs err: 9.69504463855579 × 10^⁻¹ 1/s*T
sigma: -0.88
within 5.2σ: yes
129. μ_+' — shielded proton magnetic moment [built on pass 1]
deps: l_p, t_p, q_p, m_p, M, S, m_+, s, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 1.41057057939800 × 10^⁻²⁶ J/T
expected: 1.4105705830(58) × 10^⁻²⁶ J/T (SI measured)
abs err: 3.60200303358476 × 10^⁻³⁵ J/T
sigma: -0.62
within 5.2σ: yes
130. μ_+/μ_B — proton magnetic moment to Bohr magneton ratio [built on pass 1]
deps: K, S, m_+, m_e, pi, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 1.52103220255243 × 10^⁻³ -
expected: 1.52103220230(45) × 10^⁻³ - (SI measured)
abs err: 2.52433772433709 × 10^⁻¹³ -
sigma: +0.56
within 5.2σ: yes
131. μ_+/μ_N — proton magnetic moment to nuclear magneton ratio [built on pass 1]
deps: K, S, pi, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 2.79284734506471 × 10^⁰ -
expected: 2.79284734463(82) × 10^⁰ - (SI measured)
abs err: 4.34707371475697 × 10^⁻¹⁰ -
sigma: +0.53
within 5.2σ: yes
132. g_+ — proton g factor [built on pass 1]
deps: K, S, pi, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 5.58569469012941 × 10^⁰ -
expected: 5.5856946893(16) × 10^⁰ - (SI measured)
abs err: 8.29414742951393 × 10^⁻¹⁰ -
sigma: +0.52
within 5.2σ: yes
133. μ_n/μ_+' — neutron to shielded proton magnetic moment ratio [built on pass 1]
deps: C_CFP, S, V_fe, m_+, m_n, pi, zhe_2, zhe_3, zhe_4, IB
computed: -6.84997004903255 × 10^⁻¹ -
expected: -6.8499694(16) × 10^⁻¹ - (SI measured)
abs err: 6.49032548324717 × 10^⁻⁸ -
sigma: -0.41
within 5.2σ: yes
134. μ_e/μ_+ — electron-proton magnetic moment ratio [built on pass 1]
deps: K, P_up, S, m_+, m_e, x_infinity, zhe_2, zhe_3, zhe_4, IB
computed: -6.58210687490436 × 10^² -
expected: -6.5821068789(19) × 10^² - (SI measured)
abs err: 3.99563603304260 × 10^⁻⁷ -
sigma: +2.10
within 5.2σ: yes
135. μ_e/μ_+' — electron to shielded proton magnetic moment ratio [built on pass 1]
deps: K, P_up, S, m_+, m_e, zhe_2, zhe_3, zhe_4, IB
computed: -6.58227587029047 × 10^² -
expected: -6.582275856(27) × 10^² - (SI measured)
abs err: 1.42904661734405 × 10^⁻⁶ -
sigma: -0.53
within 5.2σ: yes
136. μ_μ/μ_+ — muon-proton magnetic moment ratio [built on pass 2]
deps: K, P_up, S, m_+, m_μ, pi, zhe_2, zhe_3, zhe_4, IB
computed: -3.18334511221314 × 10^⁰ -
expected: -3.183345146(71) × 10^⁰ - (SI measured)
abs err: 3.37868594780399 × 10^⁻⁸ -
sigma: +0.48
within 5.2σ: yes
137. μ_+'/μ_N — shielded proton magnetic moment to nuclear magneton ratio [built on pass 1]
deps: K, S, e, pi, zhe_1, zhe_2, zhe_3, zhe_4, γ, IB
computed: 2.79277562234849 × 10^⁰ -
expected: 2.792775648(11) × 10^⁰ - (SI measured)
abs err: 2.56515052000625 × 10^⁻⁸ -
sigma: -2.33
within 5.2σ: yes
138. μ_+'/μ_B — shielded proton magnetic moment to Bohr magneton ratio [built on pass 1]
deps: K, S, e, m_+, m_e, pi, zhe_1, zhe_2, zhe_3, zhe_4, γ, IB
computed: 1.52099314114036 × 10^⁻³ -
expected: 1.5209931551(62) × 10^⁻³ - (SI measured)
abs err: 1.39596432715682 × 10^⁻¹¹ -
sigma: -2.25
within 5.2σ: yes
139. γ_+ — proton gyromagnetic ratio [built on pass 1]
deps: q_p, S, m_+, pi, s, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 2.67522187170413 × 10^⁸ 1/s*T
expected: 2.6752218708(11) × 10^⁸ 1/s*T (SI measured)
abs err: 9.04129032270680 × 10^⁻² 1/s*T
sigma: +0.82
within 5.2σ: yes
140. γ_+ ̇ — proton gyromagnetic ratio in MHz/T [built on pass 1]
deps: q_p, MHz, S, m_+, pi, s, second, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 4.25774784749264 × 10^¹ MHz/T
expected: 4.2577478461(18) × 10^¹ MHz/T (SI measured)
abs err: 1.39264381152198 × 10^⁻⁸ MHz/T
sigma: +0.77
within 5.2σ: yes
141. μ_+ — proton magnetic moment [built on pass 1]
deps: l_p, t_p, q_p, m_p, G_Gi, S, m_+, pi, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 1.41060679344097 × 10^⁻²⁶ J/T
expected: 1.41060679545(60) × 10^⁻²⁶ J/T (SI measured)
abs err: 2.00902900741469 × 10^⁻³⁵ J/T
sigma: -3.35
within 5.2σ: yes
142. F — Faraday constant [built on pass 1]
deps: m_p, K, coulomb, e, kilogram, zhe_1, zhe_2, zhe_3, zhe_4, γ, IB
computed: 9.64853322042859 × 10^⁴ C/mol
expected: 9.64853321200000 × 10^⁴ C/mol (SI exact (defined))
digits: almost-full match (8/10)
143. M_p — molar Planck constant [built on pass 1]
deps: l_p, t_p, q_p, K, coulomb, e, kilogram, pi, s, zhe_1, zhe_2, zhe_3, zhe_4, γ, IB
computed: 3.99031271062296 × 10^⁻¹⁰ J/(Hz*mol)
expected: 3.99031271200000 × 10^⁻¹⁰ J/(Hz*mol) (SI exact (defined))
digits: almost-full match (9/10)
144. V_m(Si) — molar volume of silicon [built on pass 1]
deps: l_p, q_p, m_p, K, coulomb, e, kilogram, m_e, pi, s, zhe_1, zhe_2, zhe_3, zhe_4, γ, IB
computed: 1.20588329639760 × 10^⁻⁵ m^3/mol
expected: 1.205883199(60) × 10^⁻⁵ m^3/mol (SI measured)
abs err: 9.73976041588576 × 10^⁻¹³ m^3/mol
sigma: +1.62
within 5.2σ: yes
145. c — speed of light [built on pass 1]
deps: l_p, t_p, G_Gi, zhe_1, zhe_2, IB
computed: 2.99792458097899 × 10^⁸ m/s
expected: 2.99792458000000 × 10^⁸ m/s (SI exact (defined))
digits: full match (9/9)
146. 1/m⋮Hz — inverse meter-hertz relationship [built on pass 1]
deps: l_p, t_p, G_Gi, meter, zhe_1, zhe_2, IB
computed: 2.99792458097899 × 10^⁸ Hz
expected: 2.99792458000000 × 10^⁸ Hz (SI exact (defined))
digits: full match (9/9)
147. r_e — classical electron radius [built on pass 1]
deps: l_p, m_p, C_R1, m_e, zhe_1, zhe_2, IB
computed: 2.81794032699479 × 10^⁻¹⁵ m
expected: 2.8179403205(13) × 10^⁻¹⁵ m (SI measured)
abs err: 6.49479306053496 × 10^⁻²⁴ m
sigma: +5.00
within 5.2σ: yes
148. a_0 — atomic unit of length [built on pass 1]
deps: l_p, m_p, C_R1, m_e, zhe_1, zhe_2, IB
computed: 5.29177210521101 × 10^⁻¹¹ m
expected: 5.29177210544(82) × 10^⁻¹¹ m (SI measured)
abs err: 2.28993718870945 × 10^⁻²¹ m
sigma: -0.28
within 5.2σ: yes
149. σ_e — Thomson cross section [built on pass 1]
deps: l_p, m_p, C_R1, m_e, pi, zhe_1, zhe_2, IB
computed: 6.65245873589776 × 10^⁻²⁹ m^2
expected: 6.6524587051(62) × 10^⁻²⁹ m^2 (SI measured)
abs err: 3.07977551287416 × 10^⁻³⁷ m^2
sigma: +4.97
within 5.2σ: yes
150. G_F/(ℏc)^3 — Fermi coupling constant [built on pass 1]
deps: l_p, t_p, m_p, C_R1, GeV, joule, kilogram, pi, zhe_1, zhe_2, IB
computed: 1.16637852183351 × 10^⁻⁵ 1/GeV^2
expected: 1.1663787(06) × 10^⁻⁵ 1/GeV^2 (SI measured)
abs err: 1.78166488606068 × 10^⁻¹² 1/GeV^2
sigma: -0.30
within 5.2σ: yes
151. A_mass — atomic mass constant [built on pass 1]
deps: L, P_up, m_e, zhe_1, zhe_2, IB
computed: 1.66053906821322 × 10^⁻²⁷ kg
expected: 1.66053906892(52) × 10^⁻²⁷ kg (SI measured)
abs err: 7.06776236843576 × 10^⁻³⁷ kg
sigma: -1.36
within 5.2σ: yes
152. kg⋮A_mass — kilogram-atomic mass unit relationship [built on pass 1]
deps: L, P_up, kilogram, m_e, zhe_1, zhe_2, IB
computed: 6.02214075623046 × 10^²⁶ u
expected: 6.0221407537(19) × 10^²⁶ u (SI measured)
abs err: 2.53046397811623 × 10^¹⁷ u
sigma: +1.33
within 5.2σ: yes
153. A_r(e) — electron relative atomic mass [built on pass 1]
deps: L, P_up, zhe_1, zhe_2, IB
computed: 5.48579909049541 × 10^⁻⁴ -
expected: 5.485799090441(97) × 10^⁻⁴ - (SI measured)
abs err: 5.44120235148344 × 10^⁻¹⁵ -
sigma: +0.56
within 5.2σ: yes
154. A_r(+) — proton relative atomic mass [built on pass 1]
deps: L, P_up, m_+, m_e, zhe_1, zhe_2, IB
computed: 1.00727646658226 × 10^⁰ -
expected: 1.0072764665789(83) × 10^⁰ - (SI measured)
abs err: 3.36125188681918 × 10^⁻¹² -
sigma: +0.40
within 5.2σ: yes
155. A_r(n) — neutron relative atomic mass [built on pass 1]
deps: L, P_up, m_e, m_n, zhe_1, zhe_2, IB
computed: 1.00866491547290 × 10^⁰ -
expected: 1.00866491606(40) × 10^⁰ - (SI measured)
abs err: 5.87103276577496 × 10^⁻¹⁰ -
sigma: -1.47
within 5.2σ: yes
156. A_r(de) — deuteron relative atomic mass [built on pass 2]
deps: L, P_up, m_de, m_e, zhe_1, zhe_2, IB
computed: 2.01355321257299 × 10^⁰ -
expected: 2.013553212544(15) × 10^⁰ - (SI measured)
abs err: 2.89898898918387 × 10^⁻¹¹ -
sigma: +1.93
within 5.2σ: yes
157. A_r(he) — helion relative atomic mass [built on pass 2]
deps: L, P_up, m_e, m_he, zhe_1, zhe_2, IB
computed: 3.01493224693071 × 10^⁰ -
expected: 3.014932246932(74) × 10^⁰ - (SI measured)
abs err: 1.28872113586244 × 10^⁻¹² -
sigma: -0.02
within 5.2σ: yes
158. A_r(tri) — triton relative atomic mass [built on pass 1]
deps: L, P_up, m_e, m_tri, zhe_1, zhe_2, IB
computed: 3.01550071572158 × 10^⁰ -
expected: 3.01550071597(10) × 10^⁰ - (SI measured)
abs err: 2.48420939232074 × 10^⁻¹⁰ -
sigma: -2.48
within 5.2σ: yes
159. A_r(α) — alpha particle relative atomic mass [built on pass 2]
deps: L, P_up, m_e, m_α, zhe_1, zhe_2, IB
computed: 4.00150617912917 × 10^⁰ -
expected: 4.001506179129(62) × 10^⁰ - (SI measured)
abs err: 1.67514440412190 × 10^⁻¹³ -
sigma: +0.00
within 5.2σ: yes
160. m_e/A_mass — electron mass in u [built on pass 1]
deps: L, P_up, zhe_1, zhe_2, IB
computed: 5.48579909049541 × 10^⁻⁴ u
expected: 5.485799090441(97) × 10^⁻⁴ u (SI measured)
abs err: 5.44120235148344 × 10^⁻¹⁵ u
sigma: +0.56
within 5.2σ: yes
161. m_∆/A_mass — neutron-proton mass difference in u [built on pass 1]
deps: L, P_up, m_+, m_e, m_n, zhe_1, zhe_2, IB
computed: 1.38844889063547 × 10^⁻³ u
expected: 1.38844948(40) × 10^⁻³ u (SI measured)
abs err: 5.89364528464315 × 10^⁻¹⁰ u
sigma: -1.47
within 5.2σ: yes
162. m_μ/A_mass — muon mass in u [built on pass 2]
deps: L, P_up, m_e, m_μ, zhe_1, zhe_2, IB
computed: 1.13428925044824 × 10^⁻¹ u
expected: 1.134289257(25) × 10^⁻¹ u (SI measured)
abs err: 6.55176085657562 × 10^⁻¹⁰ u
sigma: -0.26
within 5.2σ: yes
163. m_+/A_mass — proton mass in u [built on pass 1]
deps: L, P_up, m_+, m_e, zhe_1, zhe_2, IB
computed: 1.00727646658226 × 10^⁰ u
expected: 1.0072764665789(83) × 10^⁰ u (SI measured)
abs err: 3.36125188681918 × 10^⁻¹² u
sigma: +0.40
within 5.2σ: yes
164. m_n/A_mass — neutron mass in u [built on pass 1]
deps: L, P_up, m_e, m_n, zhe_1, zhe_2, IB
computed: 1.00866491547290 × 10^⁰ u
expected: 1.00866491606(40) × 10^⁰ u (SI measured)
abs err: 5.87103276577496 × 10^⁻¹⁰ u
sigma: -1.47
within 5.2σ: yes
165. m_τ/A_mass — tau mass in u [built on pass 1]
deps: L, P_up, m_e, m_τ, zhe_1, zhe_2, IB
computed: 1.90754046521641 × 10^⁰ u
expected: 1.90754(13) × 10^⁰ u (SI measured)
abs err: 4.65216409124918 × 10^⁻⁷ u
sigma: +0.00
within 5.2σ: yes
166. m_de/A_mass — deuteron mass in u [built on pass 2]
deps: L, P_up, m_de, m_e, zhe_1, zhe_2, IB
computed: 2.01355321257299 × 10^⁰ u
expected: 2.013553212544(15) × 10^⁰ u (SI measured)
abs err: 2.89898898918387 × 10^⁻¹¹ u
sigma: +1.93
within 5.2σ: yes
167. m_he/A_mass — helion mass in u [built on pass 2]
deps: L, P_up, m_e, m_he, zhe_1, zhe_2, IB
computed: 3.01493224693071 × 10^⁰ u
expected: 3.014932246932(74) × 10^⁰ u (SI measured)
abs err: 1.28872113586244 × 10^⁻¹² u
sigma: -0.02
within 5.2σ: yes
168. m_tri/A_mass — triton mass in u [built on pass 1]
deps: L, P_up, m_e, m_tri, zhe_1, zhe_2, IB
computed: 3.01550071572158 × 10^⁰ u
expected: 3.01550071597(10) × 10^⁰ u (SI measured)
abs err: 2.48420939232074 × 10^⁻¹⁰ u
sigma: -2.48
within 5.2σ: yes
169. m_α/A_mass — alpha particle mass in u [built on pass 2]
deps: L, P_up, m_e, m_α, zhe_1, zhe_2, IB
computed: 4.00150617912917 × 10^⁰ u
expected: 4.001506179129(62) × 10^⁰ u (SI measured)
abs err: 1.67514440412190 × 10^⁻¹³ u
sigma: +0.00
within 5.2σ: yes
170. eV⋮A_mass — electron volt-atomic mass unit relationship [built on pass 1]
deps: l_p, t_p, q_p, P_up, coulomb, joule, m_e, zhe_1, zhe_2, α_F, IB
computed: 1.07354410142667 × 10^⁻⁹ u
expected: 1.07354410083(33) × 10^⁻⁹ u (SI measured)
abs err: 5.96669650334830 × 10^⁻¹⁹ u
sigma: +1.81
within 5.2σ: yes
171. A_mass⋮eV — atomic mass unit-electron volt relationship [built on pass 1]
deps: l_p, t_p, q_p, P_up, coulomb, m_e, zhe_1, zhe_2, α_F, IB
computed: 9.31494103195446 × 10^⁸ eV
expected: 9.3149410372(29) × 10^⁸ eV (SI measured)
abs err: 5.24554387868661 × 10^⁻¹ eV
sigma: -1.81
within 5.2σ: yes
172. ℏc ̇ — reduced Planck constant times c in MeV fm [built on pass 1]
deps: l_p, t_p, m_p, MeV, fm, zhe_1, zhe_2, δ_F, IB
computed: 1.97326980422731 × 10^² MeV fm
expected: 1.97326980400000 × 10^² MeV fm (SI exact (defined))
digits: full match (10/10)
173. 1/m⋮eV — inverse meter-electron volt relationship [built on pass 1]
deps: l_p, t_p, m_p, eV, meter, pi, zhe_1, zhe_2, δ_F, IB
computed: 1.23984198410222 × 10^⁻⁶ eV
expected: 1.23984198400000 × 10^⁻⁶ eV (SI exact (defined))
digits: full match (10/10)
174. eV⋮1/m — electron volt-inverse meter relationship [built on pass 1]
deps: l_p, t_p, m_p, eV, pi, zhe_1, zhe_2, δ_F, IB
computed: 8.06554393884384 × 10^⁵ cycles/m
expected: 8.06554393700000 × 10^⁵ cycles/m (SI exact (defined))
digits: almost-full match (9/10)
175. 1/m⋮J — inverse meter-joule relationship [built on pass 1]
deps: l_p, t_p, m_p, meter, pi, zhe_1, zhe_2, δ_F, IB
computed: 1.98644585705374 × 10^⁻²⁵ J
expected: 1.98644585700000 × 10^⁻²⁵ J (SI exact (defined))
digits: full match (10/10)
176. J⋮1/m — joule-inverse meter relationship [built on pass 1]
deps: l_p, t_p, m_p, joule, pi, zhe_1, zhe_2, δ_F, IB
computed: 5.03411656778381 × 10^²⁴ cycles/m
expected: 5.03411656700000 × 10^²⁴ cycles/m (SI exact (defined))
digits: full match (10/10)
177. A_e_pot — atomic unit of electric potential [built on pass 1]
deps: l_p, t_p, q_p, A_mass, P_up, zhe_1, zhe_2, δ_F, IB
computed: 2.72113862459610 × 10^¹ V
expected: 2.7211386245981(30) × 10^¹ V (SI measured)
abs err: 2.00204658332727 × 10^⁻¹¹ V
sigma: -0.67
within 5.2σ: yes
178. R_∞hc ̇ — Rydberg constant times hc in eV [built on pass 1]
deps: l_p, t_p, q_p, A_mass, P_up, coulomb, zhe_1, zhe_2, δ_F, IB
computed: 1.36056931229805 × 10^¹ eV
expected: 1.3605693122990(15) × 10^¹ eV (SI measured)
abs err: 9.51023291663635 × 10^⁻¹² eV
sigma: -0.63
within 5.2σ: yes
179. E_h⋮eV — hartree-electron volt relationship [built on pass 1]
deps: l_p, t_p, q_p, A_mass, P_up, coulomb, zhe_1, zhe_2, δ_F, IB
computed: 2.72113862459610 × 10^¹ eV
expected: 2.7211386245981(30) × 10^¹ eV (SI measured)
abs err: 2.00204658332727 × 10^⁻¹¹ eV
sigma: -0.67
within 5.2σ: yes
180. eV⋮E_h — electron volt-hartree relationship [built on pass 1]
deps: l_p, t_p, q_p, A_mass, P_up, coulomb, zhe_1, zhe_2, δ_F, IB
computed: 3.67493221756771 × 10^⁻² E_h
expected: 3.6749322175665(40) × 10^⁻² E_h (SI measured)
abs err: 1.21190261595540 × 10^⁻¹⁴ E_h
sigma: +0.30
within 5.2σ: yes
181. F_90 — conventional value of farad-90 [built on pass 1]
deps: C_d, farad, zhe_1, zhe_3, zhe_4, IB
computed: 9.99999982178026 × 10^⁻¹ F
expected: 9.99999982200000 × 10^⁻¹ F (SI exact (defined))
digits: almost-full match (9/11)
182. H_90 — conventional value of henry-90 [built on pass 1]
deps: C_d, henry, zhe_1, zhe_3, zhe_4, IB
computed: 1.00000001782197 × 10^⁰ H
expected: 1.00000001779000 × 10^⁰ H (SI exact (defined))
digits: almost-full match (10/12)
183. Ω_90 — conventional value of ohm-90 [built on pass 1]
deps: C_d, ohm, zhe_1, zhe_3, zhe_4, IB
computed: 1.00000001782197 × 10^⁰ Ω
expected: 1.00000001779000 × 10^⁰ Ω (SI exact (defined))
digits: almost-full match (10/12)
184. m_∆ — neutron-proton mass difference [built on pass 1]
deps: C_d, m_+, m_n, zhe_1, zhe_3, zhe_4, IB
computed: 2.30557506526313 × 10^⁻³⁰ kg
expected: 2.30557461(67) × 10^⁻³⁰ kg (SI measured)
abs err: 4.55263130694452 × 10^⁻³⁷ kg
sigma: +0.68
within 5.2σ: yes
185. σ_he — helion shielding shift [built on pass 1]
deps: P, pi, s, zhe_1, zhe_3, zhe_4, IB
computed: 5.99670299153332 × 10^⁻⁵ -
expected: 5.9967029(23) × 10^⁻⁵ - (SI measured)
abs err: 9.15333177932925 × 10^⁻¹³ -
sigma: +0.04
within 5.2σ: yes
186. σ_tp — shielding difference of t and p in HT [built on pass 1]
deps: pi, s, zhe_1, zhe_3, zhe_4, IB
computed: 2.39369251464031 × 10^⁻⁸ -
expected: 2.39450(20) × 10^⁻⁸ - (SI measured)
abs err: 8.07485359685373 × 10^⁻¹² -
sigma: -4.04
within 5.2σ: yes
187. σ_dp — shielding difference of d and p in HD [built on pass 1]
deps: pi, s, zhe_1, zhe_3, zhe_4, IB
computed: 1.98769745110889 × 10^⁻⁸ -
expected: 1.98770(10) × 10^⁻⁸ - (SI measured)
abs err: 2.54889110988370 × 10^⁻¹⁴ -
sigma: -0.03
within 5.2σ: yes
188. σ_+' — proton magnetic shielding correction [built on pass 1]
deps: pi, s, zhe_1, zhe_3, zhe_4, IB
computed: 2.56684124759787 × 10^⁻⁵ -
expected: 2.56715(41) × 10^⁻⁵ - (SI measured)
abs err: 3.08752402125754 × 10^⁻⁹ -
sigma: -0.75
within 5.2σ: yes
189. A_ep — atomic unit of electric polarizability [built on pass 1]
deps: t_p, q_p, m_p, m_e, pi, s, zhe_1, zhe_3, zhe_4, IB
computed: 1.64877727300423 × 10^⁻⁴¹ m^2*C^2/J
expected: 1.64877727212(51) × 10^⁻⁴¹ m^2*C^2/J (SI measured)
abs err: 8.84231404075842 × 10^⁻⁵¹ m^2*C^2/J
sigma: +1.73
within 5.2σ: yes
190. A_ef — atomic unit of electric field [built on pass 1]
deps: l_p, t_p, q_p, m_p, m_e, pi, s, zhe_1, zhe_3, zhe_4, IB
computed: 5.14220674774745 × 10^¹¹ V/m
expected: 5.14220675112(80) × 10^¹¹ V/m (SI measured)
abs err: 3.37255008444560 × 10^² V/m
sigma: -4.22
within 5.2σ: yes
191. A_force — atomic unit of force [built on pass 1]
deps: l_p, t_p, m_p, m_e, pi, s, zhe_1, zhe_3, zhe_4, IB
computed: 8.23872349803778 × 10^⁻⁸ N
expected: 8.2387235038(13) × 10^⁻⁸ N (SI measured)
abs err: 5.76222086716750 × 10^⁻¹⁷ N
sigma: -4.43
within 5.2σ: yes
192. A_cd — atomic unit of charge density [built on pass 1]
deps: l_p, q_p, m_p, m_e, pi, s, zhe_1, zhe_3, zhe_4, IB
computed: 1.08120238561798 × 10^¹² C/m^3
expected: 1.08120238677(51) × 10^¹² C/m^3 (SI measured)
abs err: 1.15202042696524 × 10^³ C/m^3
sigma: -2.26
within 5.2σ: yes
193. μ_n — neutron magnetic moment [built on pass 1]
deps: l_p, t_p, q_p, m_p, C_CFP, m_n, pi, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: -9.66235818798184 × 10^⁻²⁷ J/T
expected: -9.6623653(23) × 10^⁻²⁷ J/T (SI measured)
abs err: 7.11201816146704 × 10^⁻³³ J/T
sigma: +3.09
within 5.2σ: yes
194. γ_n ̇ — neutron gyromagnetic ratio in MHz/T [built on pass 1]
deps: q_p, C_CFP, MHz, m_n, pi, second, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 2.91646871897930 × 10^¹ MHz/T
expected: 2.91646935(69) × 10^¹ MHz/T (SI measured)
abs err: 6.31020701204704 × 10^⁻⁶ MHz/T
sigma: -0.91
within 5.2σ: yes
195. γ_n — neutron gyromagnetic ratio [built on pass 1]
deps: q_p, C_CFP, m_n, pi, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 1.83247134039396 × 10^⁸ 1/(s*T)
expected: 1.83247174(43) × 10^⁸ 1/(s*T) (SI measured)
abs err: 3.99606039942993 × 10^¹ 1/(s*T)
sigma: -0.93
within 5.2σ: yes
196. μ_n/μ_B — neutron magnetic moment to Bohr magneton ratio [built on pass 1]
deps: C_CFP, m_e, m_n, pi, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: -1.04187546165271 × 10^⁻³ -
expected: -1.04187565(25) × 10^⁻³ - (SI measured)
abs err: 1.88347288190430 × 10^⁻¹⁰ -
sigma: +0.75
within 5.2σ: yes
197. μ_n/μ_N — neutron magnetic moment to nuclear magneton ratio [built on pass 1]
deps: C_CFP, m_+, m_n, pi, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: -1.91304241427757 × 10^⁰ -
expected: -1.91304276(45) × 10^⁰ - (SI measured)
abs err: 3.45722426885087 × 10^⁻⁷ -
sigma: +0.77
within 5.2σ: yes
198. g_n — neutron g factor [built on pass 1]
deps: C_CFP, m_+, m_n, pi, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: -3.82608482855515 × 10^⁰ -
expected: -3.82608552(90) × 10^⁰ - (SI measured)
abs err: 6.91444853770174 × 10^⁻⁷ -
sigma: +0.77
within 5.2σ: yes
199. Hz⋮kg — hertz-kilogram relationship [built on pass 1]
deps: t_p, m_p, C_CFP, pi, second, zhe_2, zhe_3, zhe_4, IB
computed: 7.37249732369515 × 10^⁻⁵¹ kg
expected: 7.37249732300000 × 10^⁻⁵¹ kg (SI exact (defined))
digits: full match (10/10)
200. Hz⋮A_mass — hertz-atomic mass unit relationship [built on pass 1]
deps: t_p, m_p, A_mass, C_CFP, pi, second, zhe_2, zhe_3, zhe_4, IB
computed: 4.43982166082254 × 10^⁻²⁴ u
expected: 4.4398216590(14) × 10^⁻²⁴ u (SI measured)
abs err: 1.82253969380120 × 10^⁻³³ u
sigma: +1.30
within 5.2σ: yes
201. N_time — natural unit of time [built on pass 1]
deps: t_p, m_p, C_CFP, m_e, zhe_2, zhe_3, zhe_4, IB
computed: 1.28808866695581 × 10^⁻²¹ s
expected: 1.28808866644(40) × 10^⁻²¹ s (SI measured)
abs err: 5.15808785982723 × 10^⁻³¹ s
sigma: +1.29
within 5.2σ: yes
202. A_mass⋮Hz — atomic mass unit-hertz relationship [built on pass 1]
deps: t_p, m_p, A_mass, C_CFP, pi, zhe_2, zhe_3, zhe_4, IB
computed: 2.25234272093083 × 10^²³ Hz
expected: 2.25234272185(70) × 10^²³ Hz (SI measured)
abs err: 9.19165407556627 × 10^¹³ Hz
sigma: -1.31
within 5.2σ: yes
203. kg⋮Hz — kilogram-hertz relationship [built on pass 1]
deps: t_p, m_p, C_CFP, kilogram, pi, zhe_2, zhe_3, zhe_4, IB
computed: 1.35639248967169 × 10^⁵⁰ Hz
expected: 1.35639248900000 × 10^⁵⁰ Hz (SI exact (defined))
digits: full match (10/10)
204. k_B — Boltzmann constant [built on pass 1]
deps: l_p, t_p, T_p, m_p, K, pi, s, zhe_2, zhe_3, zhe_4, IB
computed: 1.38064900009247 × 10^⁻²³ J/K
expected: 1.38064900000000 × 10^⁻²³ J/K (SI exact (defined))
digits: full match (7/7)
205. k_B ⃛ — Boltzmann constant in eV/K [built on pass 1]
deps: l_p, t_p, T_p, m_p, K, eV, pi, s, zhe_2, zhe_3, zhe_4, IB
computed: 8.61733326153817 × 10^⁻⁵ eV/K
expected: 8.61733326200000 × 10^⁻⁵ eV/K (SI exact (defined))
digits: full match (9/10)
206. K⋮eV — kelvin-electron volt relationship [built on pass 1]
deps: l_p, t_p, T_p, m_p, K, eV, kelvin, pi, s, zhe_2, zhe_3, zhe_4, IB
computed: 8.61733326153817 × 10^⁻⁵ eV
expected: 8.61733326200000 × 10^⁻⁵ eV (SI exact (defined))
digits: full match (9/10)
207. K⋮J — kelvin-joule relationship [built on pass 1]
deps: l_p, t_p, T_p, m_p, K, kelvin, pi, s, zhe_2, zhe_3, zhe_4, IB
computed: 1.38064900009247 × 10^⁻²³ J
expected: 1.38064900000000 × 10^⁻²³ J (SI exact (defined))
digits: full match (7/7)
208. eV⋮K — electron volt-kelvin relationship [built on pass 1]
deps: l_p, t_p, T_p, m_p, K, eV, pi, s, zhe_2, zhe_3, zhe_4, IB
computed: 1.16045181221091 × 10^⁴ K
expected: 1.16045181200000 × 10^⁴ K (SI exact (defined))
digits: full match (10/10)
209. J⋮K — joule-kelvin relationship [built on pass 1]
deps: l_p, t_p, T_p, m_p, K, joule, pi, s, zhe_2, zhe_3, zhe_4, IB
computed: 7.24297051539353 × 10^²² K
expected: 7.24297051600000 × 10^²² K (SI exact (defined))
digits: full match (9/10)
210. n_0 — Loschmidt constant (273.15 K, 100 kPa) [built on pass 1]
deps: l_p, t_p, T_p, m_p, K, T_0, p_0, pi, s, zhe_2, zhe_3, zhe_4, IB
computed: 2.65164580464709 × 10^²⁵ 1/m^3
expected: 2.65164580400000 × 10^²⁵ 1/m^3 (SI exact (defined))
digits: full match (10/10)
211. n_1 — Loschmidt constant (273.15 K, 101.325 kPa) [built on pass 1]
deps: l_p, t_p, T_p, m_p, K, T_0, p_1, pi, s, zhe_2, zhe_3, zhe_4, IB
computed: 2.68678011155866 × 10^²⁵ 1/m^3
expected: 2.68678011100000 × 10^²⁵ 1/m^3 (SI exact (defined))
digits: full match (10/10)
212. μ_B/k_B — Bohr magneton in K/T [built on pass 1]
deps: t_p, q_p, T_p, G_Gi, m_e, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 6.71713814961807 × 10^⁻¹ K/T
expected: 6.7171381472(21) × 10^⁻¹ K/T (SI measured)
abs err: 2.41807261743172 × 10^⁻¹⁰ K/T
sigma: +1.15
within 5.2σ: yes
213. μ_N/k_B — nuclear magneton in K/T [built on pass 1]
deps: t_p, q_p, T_p, G_Gi, m_+, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 3.65826777199877 × 10^⁻⁴ K/T
expected: 3.6582677706(11) × 10^⁻⁴ K/T (SI measured)
abs err: 1.39877336244444 × 10^⁻¹³ K/T
sigma: +1.27
within 5.2σ: yes
214. R_∞hc ̈ — Rydberg constant times hc in J [built on pass 1]
deps: l_p, t_p, D_d, m_e, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 2.17987236111221 × 10^⁻¹⁸ J
expected: 2.1798723611030(24) × 10^⁻¹⁸ J (SI measured)
abs err: 9.21218017783575 × 10^⁻³⁰ J
sigma: +3.84
within 5.2σ: yes
215. E_h — Hartree energy [built on pass 1]
deps: l_p, t_p, D_d, m_e, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 4.35974472222442 × 10^⁻¹⁸ J
expected: 4.3597447222060(48) × 10^⁻¹⁸ J (SI measured)
abs err: 1.84243603556715 × 10^⁻²⁹ J
sigma: +3.84
within 5.2σ: yes
216. J⋮E_h — joule-hartree relationship [built on pass 1]
deps: l_p, t_p, D_d, joule, m_e, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 2.29371227838601 × 10^¹⁷ E_h
expected: 2.2937122783969(25) × 10^¹⁷ E_h (SI measured)
abs err: 1.08931248849758 × 10^⁶ E_h
sigma: -4.36
within 5.2σ: yes
217. K_J — Josephson constant [built on pass 1]
deps: l_p, t_p, q_p, m_p, pi, zhe_1, zhe_2, IB
computed: 4.83597848424072 × 10^¹⁴ Hz/V
expected: 4.83597848400000 × 10^¹⁴ Hz/V (SI exact (defined))
digits: full match (10/10)
218. e/ℏ — elementary charge over h-bar [built on pass 1]
deps: l_p, t_p, q_p, m_p, pi, zhe_1, zhe_2, IB
computed: 1.51926744790089 × 10^¹⁵ A/J
expected: 1.51926744700000 × 10^¹⁵ A/J (SI exact (defined))
digits: full match (10/10)
219. Φ_0 — magnetic flux quantum [built on pass 1]
deps: l_p, t_p, q_p, m_p, pi, zhe_1, zhe_2, IB
computed: 2.06783384843115 × 10^⁻¹⁵ Wb
expected: 2.06783384800000 × 10^⁻¹⁵ Wb (SI exact (defined))
digits: full match (10/10)
220. ℏ¨ — reduced Planck constant in eV s [built on pass 1]
deps: l_p, t_p, q_p, m_p, coulomb, pi, zhe_1, zhe_2, IB
computed: 6.58211956941109 × 10^⁻¹⁶ eV*s
expected: 6.58211956900000 × 10^⁻¹⁶ eV*s (SI exact (defined))
digits: full match (10/10)
221. h˙ — Planck constant in eV/Hz [built on pass 1]
deps: l_p, t_p, q_p, m_p, coulomb, pi, zhe_1, zhe_2, IB
computed: 4.13566769686230 × 10^⁻¹⁵ eV/Hz
expected: 4.13566769600000 × 10^⁻¹⁵ eV/Hz (SI exact (defined))
digits: full match (10/10)
222. c_1 — first radiation constant [built on pass 1]
deps: l_p, t_p, m_p, pi, zhe_1, zhe_2, IB
computed: 3.74177185285691 × 10^⁻¹⁶ W*m^2
expected: 3.74177185200000 × 10^⁻¹⁶ W*m^2 (SI exact (defined))
digits: full match (10/10)
223. c_1L — first radiation constant for spectral radiance [built on pass 1]
deps: l_p, t_p, m_p, pi, zhe_1, zhe_2, IB
computed: 1.19104297260859 × 10^⁻¹⁶ W*m^2/sr
expected: 1.19104297200000 × 10^⁻¹⁶ W*m^2/sr (SI exact (defined))
digits: full match (10/10)
224. γ_he' — shielded helion gyromagnetic ratio [built on pass 2]
deps: q_p, C_CFP, C_d, m_he, zhe_1, zhe_2, IB
computed: 2.03789460878420 × 10^⁸ 1/(s*T)
expected: 2.0378946078(18) × 10^⁸ 1/(s*T) (SI measured)
abs err: 9.84196460516671 × 10^⁻² 1/(s*T)
sigma: +0.55
within 5.2σ: yes
225. γ_he ̇' — shielded helion gyromagnetic ratio in MHz/T [built on pass 2]
deps: q_p, C_CFP, C_d, MHz, m_he, pi, second, zhe_1, zhe_2, IB
computed: 3.24341000488329 × 10^¹ MHz/T
expected: 3.2434100033(28) × 10^¹ MHz/T (SI measured)
abs err: 1.58329096310154 × 10^⁻⁸ MHz/T
sigma: +0.57
within 5.2σ: yes
226. μ_he — helion magnetic moment [built on pass 2]
deps: l_p, t_p, q_p, m_p, C_CFP, D_d, m_he, zhe_1, zhe_2, IB
computed: -1.07461755420272 × 10^⁻²⁶ J/T
expected: -1.07461755198(93) × 10^⁻²⁶ J/T (SI measured)
abs err: 2.22272187229305 × 10^⁻³⁵ J/T
sigma: -2.39
within 5.2σ: yes
227. μ_he' — shielded helion magnetic moment [built on pass 2]
deps: l_p, t_p, q_p, m_p, C_CFP, m_he, pi, zhe_1, zhe_2, IB
computed: -1.07455311098445 × 10^⁻²⁶ J/T
expected: -1.07455311035(93) × 10^⁻²⁶ J/T (SI measured)
abs err: 6.34445767722769 × 10^⁻³⁶ J/T
sigma: -0.68
within 5.2σ: yes
228. μ_he'/μ_+ — shielded helion to proton magnetic moment ratio [built on pass 2]
deps: C_CFP, L, S, m_+, m_he, zhe_1, zhe_2, IB
computed: -7.61766577306795 × 10^⁻¹ -
expected: -7.6176657721(66) × 10^⁻¹ - (SI measured)
abs err: 9.67950862565528 × 10^⁻¹¹ -
sigma: -0.15
within 5.2σ: yes
229. μ_he'/μ_+' — shielded helion to shielded proton magnetic moment ratio [built on pass 2]
deps: C_CFP, L, S, m_+, m_he, pi, zhe_1, zhe_2, IB
computed: -7.61786134617097 × 10^⁻¹ -
expected: -7.617861334(31) × 10^⁻¹ - (SI measured)
abs err: 1.21709662454072 × 10^⁻⁹ -
sigma: -0.39
within 5.2σ: yes
230. μ_e/μ_he' — electron to shielded helion magnetic moment ratio [built on pass 2]
deps: C_CFP, L, P_up, e, m_e, m_he, zhe_1, zhe_2, γ, IB
computed: 8.64058236541591 × 10^² -
expected: 8.6405823986(70) × 10^² - (SI measured)
abs err: 3.31840859893994 × 10^⁻⁶ -
sigma: -4.74
within 5.2σ: yes
231. A_mass⋮E_h — atomic mass unit-hartree relationship [built on pass 1]
deps: P_up, zeta(3), zhe_1, zhe_2, IB
computed: 3.42317769077000 × 10^⁷ E_h
expected: 3.4231776922(11) × 10^⁷ E_h (SI measured)
abs err: 1.43000340097083 × 10^⁻² E_h
sigma: -1.30
within 5.2σ: yes
232. E_h⋮A_mass — hartree-atomic mass unit relationship [built on pass 1]
deps: P_up, zeta(3), zhe_1, zhe_2, IB
computed: 2.92126231920799 × 10^⁻⁸ u
expected: 2.92126231797(91) × 10^⁻⁸ u (SI measured)
abs err: 1.23799197396587 × 10^⁻¹⁷ u
sigma: +1.36
within 5.2σ: yes
233. kg⋮E_h — kilogram-hartree relationship [built on pass 1]
deps: A_mass, P_up, kilogram, zeta(3), zhe_1, zhe_2, IB
computed: 2.06148578874053 × 10^³⁴ E_h
expected: 2.0614857887415(22) × 10^³⁴ E_h (SI measured)
abs err: 9.73455844986858 × 10^²¹ E_h
sigma: -0.44
within 5.2σ: yes
234. E_h⋮kg — hartree-kilogram relationship [built on pass 1]
deps: A_mass, P_up, zeta(3), zhe_1, zhe_2, IB
computed: 4.85087020954404 × 10^⁻³⁵ kg
expected: 4.8508702095419(53) × 10^⁻³⁵ kg (SI measured)
abs err: 2.14003546935669 × 10^⁻⁴⁷ kg
sigma: +0.40
within 5.2σ: yes
235. K⋮kg — kelvin-kilogram relationship [built on pass 1]
deps: T_p, m_p, L_2, V_fe, kelvin, zhe_3, zhe_4, IB
computed: 1.53617918688373 × 10^⁻⁴⁰ kg
expected: 1.53617918700000 × 10^⁻⁴⁰ kg (SI exact (defined))
digits: full match (9/10)
236. kg⋮K — kilogram-kelvin relationship [built on pass 1]
deps: T_p, m_p, L_2, V_fe, kilogram, zhe_3, zhe_4, IB
computed: 6.50965726204756 × 10^³⁹ K
expected: 6.50965726000000 × 10^³⁹ K (SI exact (defined))
digits: almost-full match (9/10)
237. K⋮A_mass — kelvin-atomic mass unit relationship [built on pass 1]
deps: T_p, m_p, A_mass, L_2, V_fe, kelvin, zhe_3, zhe_4, IB
computed: 9.25108729020563 × 10^⁻¹⁴ u
expected: 9.2510872884(29) × 10^⁻¹⁴ u (SI measured)
abs err: 1.80563057575806 × 10^⁻²³ u
sigma: +0.62
within 5.2σ: yes
238. A_mass⋮K — atomic mass unit-kelvin relationship [built on pass 1]
deps: T_p, m_p, A_mass, L_2, V_fe, zhe_3, zhe_4, IB
computed: 1.08095402043079 × 10^¹³ K
expected: 1.08095402067(34) × 10^¹³ K (SI measured)
abs err: 2.39209780163912 × 10^³ K
sigma: -0.70
within 5.2σ: yes
239. kg⋮1/m — kilogram-inverse meter relationship [built on pass 1]
deps: l_p, m_p, P_up, i, kilogram, pi, zhe_3, zhe_4, IB
computed: 4.52443833598082 × 10^⁴¹ cycles/m
expected: 4.52443833500000 × 10^⁴¹ cycles/m (SI exact (defined))
digits: full match (10/10)
240. A_mass⋮1/m — atomic mass unit-inverse meter relationship [built on pass 1]
deps: l_p, m_p, A_mass, P_up, i, pi, zhe_3, zhe_4, IB
computed: 7.51300661861779 × 10^¹⁴ cycles/m
expected: 7.5130066209(23) × 10^¹⁴ cycles/m (SI measured)
abs err: 2.28221265830764 × 10^⁵ cycles/m
sigma: -0.99
within 5.2σ: yes
241. 1/m⋮kg — inverse meter-kilogram relationship [built on pass 1]
deps: l_p, m_p, P_up, i, meter, pi, zhe_3, zhe_4, IB
computed: 2.21021909404021 × 10^⁻⁴² kg
expected: 2.21021909400000 × 10^⁻⁴² kg (SI exact (defined))
digits: full match (10/10)
242. 1/m⋮A_mass — inverse meter-atomic mass unit relationship [built on pass 1]
deps: l_p, m_p, A_mass, P_up, i, meter, pi, zhe_3, zhe_4, IB
computed: 1.33102504864186 × 10^⁻¹⁵ u
expected: 1.33102504824(41) × 10^⁻¹⁵ u (SI measured)
abs err: 4.01856484030615 × 10^⁻²⁵ u
sigma: +0.98
within 5.2σ: yes
243. λ_C — Compton wavelength [built on pass 1]
deps: l_p, m_p, P_up, i, m_e, pi, zhe_3, zhe_4, IB
computed: 2.42631023609293 × 10^⁻¹² m/cycle
expected: 2.42631023538(76) × 10^⁻¹² m/cycle (SI measured)
abs err: 7.12932298101346 × 10^⁻²² m/cycle
sigma: +0.94
within 5.2σ: yes
244. λ_μ — muon Compton wavelength [built on pass 2]
deps: l_p, m_p, P_up, i, m_μ, pi, zhe_3, zhe_4, IB
computed: 1.17344411764094 × 10^⁻¹⁴ m/cycle
expected: 1.173444110(26) × 10^⁻¹⁴ m/cycle (SI measured)
abs err: 7.64093511056515 × 10^⁻²³ m/cycle
sigma: +0.29
within 5.2σ: yes
245. λ_+ — proton Compton wavelength [built on pass 1]
deps: l_p, m_p, P_up, i, m_+, pi, zhe_3, zhe_4, IB
computed: 1.32140985399775 × 10^⁻¹⁵ m/cycle
expected: 1.32140985360(41) × 10^⁻¹⁵ m/cycle (SI measured)
abs err: 3.97746320983782 × 10^⁻²⁵ m/cycle
sigma: +0.97
within 5.2σ: yes
246. λ_n — neutron Compton wavelength [built on pass 1]
deps: l_p, m_p, P_up, i, m_n, pi, zhe_3, zhe_4, IB
computed: 1.31959090499128 × 10^⁻¹⁵ m/cycle
expected: 1.31959090382(67) × 10^⁻¹⁵ m/cycle (SI measured)
abs err: 1.17127891920464 × 10^⁻²⁴ m/cycle
sigma: +1.75
within 5.2σ: yes
247. λ_τ — tau Compton wavelength [built on pass 1]
deps: l_p, m_p, P_up, i, m_τ, pi, zhe_3, zhe_4, IB
computed: 6.97770282157987 × 10^⁻¹⁶ m/cycle
expected: 6.97771(47) × 10^⁻¹⁶ m/cycle (SI measured)
abs err: 7.17842012968331 × 10^⁻²² m/cycle
sigma: -0.02
within 5.2σ: yes
248. λ_- — reduced Compton wavelength [built on pass 1]
deps: l_p, m_p, P_up, i, m_e, zhe_3, zhe_4, IB
computed: 3.86159267548654 × 10^⁻¹³ m/cycle
expected: 3.8615926744(12) × 10^⁻¹³ m/cycle (SI measured)
abs err: 1.08653776432418 × 10^⁻²² m/cycle
sigma: +0.91
within 5.2σ: yes
249. λ_μ_- — reduced muon Compton wavelength [built on pass 2]
deps: l_p, m_p, P_up, i, m_μ, zhe_3, zhe_4, IB
computed: 1.86759431764662 × 10^⁻¹⁵ m/cycle
expected: 1.867594306(42) × 10^⁻¹⁵ m/cycle (SI measured)
abs err: 1.16466236318533 × 10^⁻²³ m/cycle
sigma: +0.28
within 5.2σ: yes
250. λ_+_- — reduced proton Compton wavelength [built on pass 1]
deps: l_p, m_p, P_up, i, m_+, zhe_3, zhe_4, IB
computed: 2.10308910114081 × 10^⁻¹⁶ m/cycle
expected: 2.10308910051(66) × 10^⁻¹⁶ m/cycle (SI measured)
abs err: 6.30810400660681 × 10^⁻²⁶ m/cycle
sigma: +0.96
within 5.2σ: yes
251. λ_n_- — reduced neutron Compton wavelength [built on pass 1]
deps: l_p, m_p, P_up, i, m_n, zhe_3, zhe_4, IB
computed: 2.10019415388470 × 10^⁻¹⁶ m/cycle
expected: 2.1001941520(11) × 10^⁻¹⁶ m/cycle (SI measured)
abs err: 1.88469661174855 × 10^⁻²⁵ m/cycle
sigma: +1.71
within 5.2σ: yes
252. λ_τ_- — reduced tau Compton wavelength [built on pass 1]
deps: l_p, m_p, P_up, i, m_τ, zhe_3, zhe_4, IB
computed: 1.11053589548070 × 10^⁻¹⁶ m/cycle
expected: 1.110538(75) × 10^⁻¹⁶ m/cycle (SI measured)
abs err: 2.10451929822612 × 10^⁻²² m/cycle
sigma: -0.03
within 5.2σ: yes
253. b' — Wien frequency displacement law constant [built on pass 1]
deps: t_p, T_p, nu_peak, pi, s, zhe_1, zhe_3, zhe_4, IB
computed: 5.87892575796312 × 10^¹⁰ Hz/K
expected: 5.87892575700000 × 10^¹⁰ Hz/K (SI exact (defined))
digits: full match (10/10)
254. k_B ̈ — Boltzmann constant in Hz/K [built on pass 1]
deps: t_p, T_p, pi, s, zhe_1, zhe_3, zhe_4, IB
computed: 2.08366191244486 × 10^¹⁰ Hz/K
expected: 2.08366191200000 × 10^¹⁰ Hz/K (SI exact (defined))
digits: full match (10/10)
255. K⋮Hz — kelvin-hertz relationship [built on pass 1]
deps: t_p, T_p, kelvin, pi, s, zhe_1, zhe_3, zhe_4, IB
computed: 2.08366191244486 × 10^¹⁰ Hz
expected: 2.08366191200000 × 10^¹⁰ Hz (SI exact (defined))
digits: full match (10/10)
256. Hz⋮K — hertz-kelvin relationship [built on pass 1]
deps: t_p, T_p, pi, s, second, zhe_1, zhe_3, zhe_4, IB
computed: 4.79924307302319 × 10^⁻¹¹ K
expected: 4.79924307300000 × 10^⁻¹¹ K (SI exact (defined))
digits: full match (10/10)
257. b — Wien wavelength displacement law constant [built on pass 1]
deps: l_p, T_p, P, lambda_peak, pi, zhe_1, zhe_3, zhe_4, IB
computed: 2.89777195379426 × 10^⁻³ m*K/cycle
expected: 2.89777195500000 × 10^⁻³ m*K/cycle (SI exact (defined))
digits: almost-full match (9/10)
258. c_2 — second radiation constant [built on pass 1]
deps: l_p, T_p, P, pi, zhe_1, zhe_3, zhe_4, IB
computed: 1.43877687681333 × 10^⁻² m*K
expected: 1.43877687700000 × 10^⁻² m*K (SI exact (defined))
digits: full match (9/10)
259. 1/m⋮K — inverse meter-kelvin relationship [built on pass 1]
deps: l_p, T_p, P, meter, pi, zhe_1, zhe_3, zhe_4, IB
computed: 1.43877687681333 × 10^⁻² K
expected: 1.43877687700000 × 10^⁻² K (SI exact (defined))
digits: full match (9/10)
260. K⋮1/m — kelvin-inverse meter relationship [built on pass 1]
deps: l_p, T_p, P, kelvin, pi, zhe_1, zhe_3, zhe_4, IB
computed: 6.95034800805251 × 10^¹ cycles/m
expected: 6.95034800400000 × 10^¹ cycles/m (SI exact (defined))
digits: almost-full match (9/10)
261. k_B ̇ — Boltzmann constant in inverse meter per kelvin [built on pass 1]
deps: l_p, T_p, P, pi, zhe_1, zhe_3, zhe_4, IB
computed: 6.95034800805251 × 10^¹ cycles/(m*K)
expected: 6.95034800400000 × 10^¹ cycles/(m*K) (SI exact (defined))
digits: almost-full match (9/10)
262. E_h⋮K — Hartree-kelvin relationship [built on pass 1]
deps: T_p, m_p, m_e, pi, s, zhe_1, zhe_3, zhe_4, IB
computed: 3.15775024803817 × 10^⁵ K
expected: 3.1577502480398(34) × 10^⁵ K (SI measured)
abs err: 1.62540214698891 × 10^⁻⁷ K
sigma: -0.48
within 5.2σ: yes
263. K⋮E_h — kelvin-hartree relationship [built on pass 1]
deps: T_p, m_p, kelvin, m_e, pi, s, zhe_1, zhe_3, zhe_4, IB
computed: 3.16681156345811 × 10^⁻⁶ E_h
expected: 3.1668115634564(34) × 10^⁻⁶ E_h (SI measured)
abs err: 1.70798970087561 × 10^⁻¹⁸ E_h
sigma: +0.50
within 5.2σ: yes
264. M_e — electron molar mass [built on pass 1]
deps: q_p, m_p, C_Q, coulomb, e, kilogram, m_e, zhe_1, zhe_3, zhe_4, γ, IB
computed: 5.48579909796586 × 10^⁻⁷ kg/mol
expected: 5.4857990962(17) × 10^⁻⁷ kg/mol (SI measured)
abs err: 1.76586473568613 × 10^⁻¹⁶ kg/mol
sigma: +1.04
within 5.2σ: yes
265. M_μ — muon molar mass [built on pass 2]
deps: q_p, m_p, C_Q, coulomb, e, kilogram, m_μ, zhe_1, zhe_3, zhe_4, γ, IB
computed: 1.13428925199289 × 10^⁻⁴ kg/mol
expected: 1.134289258(25) × 10^⁻⁴ kg/mol (SI measured)
abs err: 6.00710818745417 × 10^⁻¹³ kg/mol
sigma: -0.24
within 5.2σ: yes
266. M_+ — proton molar mass [built on pass 1]
deps: q_p, m_p, C_Q, coulomb, e, kilogram, m_+, zhe_1, zhe_3, zhe_4, γ, IB
computed: 1.00727646795395 × 10^⁻³ kg/mol
expected: 1.00727646764(31) × 10^⁻³ kg/mol (SI measured)
abs err: 3.13950423793081 × 10^⁻¹³ kg/mol
sigma: +1.01
within 5.2σ: yes
267. M_A_mass — molar mass constant [built on pass 1]
deps: q_p, m_p, A_mass, C_Q, coulomb, e, kilogram, zhe_1, zhe_3, zhe_4, γ, IB
computed: 1.00000000136176 × 10^⁻³ kg/mol
expected: 1.00000000105(31) × 10^⁻³ kg/mol (SI measured)
abs err: 3.11761559789688 × 10^⁻¹³ kg/mol
sigma: +1.01
within 5.2σ: yes
268. M_n — neutron molar mass [built on pass 1]
deps: q_p, m_p, C_Q, coulomb, e, kilogram, m_n, zhe_1, zhe_3, zhe_4, γ, IB
computed: 1.00866491684648 × 10^⁻³ kg/mol
expected: 1.00866491712(51) × 10^⁻³ kg/mol (SI measured)
abs err: 2.73523342430464 × 10^⁻¹³ kg/mol
sigma: -0.54
within 5.2σ: yes
269. M_τ — tau molar mass [built on pass 1]
deps: q_p, m_p, C_Q, coulomb, e, kilogram, m_τ, zhe_1, zhe_3, zhe_4, γ, IB
computed: 1.90754046781406 × 10^⁻³ kg/mol
expected: 1.90754(13) × 10^⁻³ kg/mol (SI measured)
abs err: 4.67814060006199 × 10^⁻¹⁰ kg/mol
sigma: +0.00
within 5.2σ: yes
270. M_de — deuteron molar mass [built on pass 2]
deps: q_p, m_p, C_Q, coulomb, e, kilogram, m_de, zhe_1, zhe_3, zhe_4, γ, IB
computed: 2.01355321531501 × 10^⁻³ kg/mol
expected: 2.01355321466(63) × 10^⁻³ kg/mol (SI measured)
abs err: 6.55006833973671 × 10^⁻¹³ kg/mol
sigma: +1.04
within 5.2σ: yes
271. M_he — helion molar mass [built on pass 2]
deps: q_p, m_p, C_Q, coulomb, e, kilogram, m_he, zhe_1, zhe_3, zhe_4, γ, IB
computed: 3.01493225103639 × 10^⁻³ kg/mol
expected: 3.01493225010(94) × 10^⁻³ kg/mol (SI measured)
abs err: 9.36386388278733 × 10^⁻¹³ kg/mol
sigma: +1.00
within 5.2σ: yes
272. M_tri — triton molar mass [built on pass 1]
deps: q_p, m_p, C_Q, coulomb, e, kilogram, m_tri, zhe_1, zhe_3, zhe_4, γ, IB
computed: 3.01550071982803 × 10^⁻³ kg/mol
expected: 3.01550071913(94) × 10^⁻³ kg/mol (SI measured)
abs err: 6.98028299739669 × 10^⁻¹³ kg/mol
sigma: +0.74
within 5.2σ: yes
273. M_α — alpha particle molar mass [built on pass 2]
deps: q_p, m_p, C_Q, coulomb, e, kilogram, m_α, zhe_1, zhe_3, zhe_4, γ, IB
computed: 4.00150618457834 × 10^⁻³ kg/mol
expected: 4.0015061833(12) × 10^⁻³ kg/mol (SI measured)
abs err: 1.27833949385866 × 10^⁻¹² kg/mol
sigma: +1.07
within 5.2σ: yes
274. M_12_C — molar mass of carbon-12 [built on pass 1]
deps: q_p, m_p, A_mass, C_Q, coulomb, e, kilogram, zhe_1, zhe_3, zhe_4, γ, IB
computed: 1.20000000163411 × 10^⁻² kg/mol
expected: 1.20000000126(36) × 10^⁻² kg/mol (SI measured)
abs err: 3.74113871747626 × 10^⁻¹² kg/mol
sigma: +1.04
within 5.2σ: yes
275. N_A — Avogadro constant [built on pass 1]
deps: q_p, m_p, C_Q, coulomb, e, kilogram, zhe_1, zhe_3, zhe_4, γ, IB
computed: 6.02214076443130 × 10^²³ 1/mol
expected: 6.02214076000000 × 10^²³ 1/mol (SI exact (defined))
digits: full match (9/9)
276. ST_0 — Sackur-Tetrode constant (1K, 100 kPa) [built on pass 1]
deps: l_p, t_p, T_p, m_p, A_mass, j_01, kelvin, p_0, pi, zhe_1, zhe_3, zhe_4, IB
computed: -1.15170753432429 × 10^⁰ -
expected: -1.15170753496(47) × 10^⁰ - (SI measured)
abs err: 6.35707560424961 × 10^⁻¹⁰ -
sigma: +1.35
within 5.2σ: yes
277. ST_1 — Sackur-Tetrode constant (1K, 101.325 kPa) [built on pass 1]
deps: l_p, t_p, T_p, m_p, A_mass, G_Ga, kelvin, p_1, pi, zhe_1, zhe_3, zhe_4, IB
computed: -1.16487052045596 × 10^⁰ -
expected: -1.16487052149(47) × 10^⁰ - (SI measured)
abs err: 1.03404479671049 × 10^⁻⁹ -
sigma: +2.20
within 5.2σ: yes
278. σ — Stefan-Boltzmann constant [built on pass 1]
deps: t_p, T_p, m_p, K, pi, zhe_1, zhe_3, zhe_4, Γ(5), IB
computed: 5.67037441987324 × 10^⁻⁸ W/(m^2*K^4)
expected: 5.67037441900000 × 10^⁻⁸ W/(m^2*K^4) (SI exact (defined))
digits: full match (10/10)
279. V_90 — conventional value of volt-90 [built on pass 1]
deps: L_1, volt, zhe_1, zhe_3, zhe_4, IB
computed: 1.00000010665218 × 10^⁰ V
expected: 1.00000010666000 × 10^⁰ V (SI exact (defined))
digits: full match (11/12)
280. W_90 — conventional value of watt-90 [built on pass 1]
deps: j_01, watt, zhe_1, zhe_3, zhe_4, IB
computed: 1.00000019552285 × 10^⁰ W
expected: 1.00000019553000 × 10^⁰ W (SI exact (defined))
digits: full match (11/12)
281. A_ef∇ — atomic unit of electric field gradient [built on pass 1]
deps: t_p, q_p, m_p, V_fe, m_e, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 9.71736242779307 × 10^²¹ V/m^2
expected: 9.7173624424(30) × 10^²¹ V/m^2 (SI measured)
abs err: 1.46069257304486 × 10^¹³ V/m^2
sigma: -4.87
within 5.2σ: yes
282. A_current — atomic unit of current [built on pass 1]
deps: t_p, q_p, m_p, C_CFP, V_fe, m_e, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 6.62361823748097 × 10^⁻³ A
expected: 6.6236182375082(72) × 10^⁻³ A (SI measured)
abs err: 2.72277329797713 × 10^⁻¹⁴ A
sigma: -3.78
within 5.2σ: yes
283. A_mfd — atomic unit of magnetic flux density [built on pass 1]
deps: t_p, q_p, m_p, m_e, pi, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 2.35051756883524 × 10^⁵ T
expected: 2.35051757077(73) × 10^⁵ T (SI measured)
abs err: 1.93475935048898 × 10^⁻⁴ T
sigma: -2.65
within 5.2σ: yes
284. A_edm — atomic unit of electric dipole moment [built on pass 1]
deps: l_p, q_p, m_p, 5!, L_2, P, m_e, pi, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 8.47835362016677 × 10^⁻³⁰ m*C
expected: 8.4783536198(13) × 10^⁻³⁰ m*C (SI measured)
abs err: 3.66767849445790 × 10^⁻⁴⁰ m*C
sigma: +0.28
within 5.2σ: yes
285. A_mag — atomic unit of magnetizability [built on pass 1]
deps: l_p, q_p, m_p, L_LL, m_e, pi, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 7.89103656936022 × 10^⁻²⁹ J/T^2
expected: 7.8910365794(49) × 10^⁻²⁹ J/T^2 (SI measured)
abs err: 1.00397820514135 × 10^⁻³⁷ J/T^2
sigma: -2.05
within 5.2σ: yes
286. A_eqm — atomic unit of electric quadrupole moment [built on pass 1]
deps: l_p, q_p, m_p, m_e, pi, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 4.48655151529887 × 10^⁻⁴⁰ m^2*C
expected: 4.4865515185(14) × 10^⁻⁴⁰ m^2*C (SI measured)
abs err: 3.20113232111466 × 10^⁻⁴⁹ m^2*C
sigma: -2.29
within 5.2σ: yes
287. A_1^st_hp — atomic unit of 1st hyperpolarizability [built on pass 1]
deps: l_p, t_p, q_p, m_p, m_e, pi, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 3.20636129566258 × 10^⁻⁵³ m^3*C^3/J^2
expected: 3.2063612996(15) × 10^⁻⁵³ m^3*C^3/J^2 (SI measured)
abs err: 3.93741604795674 × 10^⁻⁶² m^3*C^3/J^2
sigma: -2.62
within 5.2σ: yes
288. A_2^nd_hp — atomic unit of 2nd hyperpolarizability [built on pass 1]
deps: l_p, t_p, q_p, m_p, !5, D_Do, m_e, pi, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 6.23537998029124 × 10^⁻⁶⁵ m^4*C^4/J^3
expected: 6.2353799735(39) × 10^⁻⁶⁵ m^4*C^4/J^3 (SI measured)
abs err: 6.79123572287357 × 10^⁻⁷⁴ m^4*C^4/J^3
sigma: +1.74
within 5.2σ: yes
Build complete.
Run Locally
To run the Constant Engine locally, use:
source /Users/thadroberts/manim-venv/bin/activate
cd /Users/thadroberts/physics-monastery-site
python constant_engine/src/build_all.py > public/code/constant-engine/latest-output.txt 2>&1Then refresh this page and open Latest Output.