constant engine
The Constant Engine is the reproducible computation system used to evaluate the Transform Dictionary expressions in The Logic of Persistence. It computes proposed closed-form expressions, compares them to reference values where available, and reports the numerical structure used throughout this project.
View Code
from __future__ import annotations
import csv
import math
import re
import yaml
import sys
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
# ------------------------------------------------------------
# High precision
# ------------------------------------------------------------
mp.mp.dps = 150 # compute precision
PRINT_DIGITS = 100
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-30)
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
# ------------------------------------------------------------
USE_COLOR = sys.stdout.isatty()
GREEN = "\033[92m" 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:
"""
High-precision numeric formatter.
Unlike sci_pretty(), this does not convert through float.
"""
if isinstance(x, mp.mpc):
if x.imag == 0:
return mp.nstr(x.real, n=sig, strip_zeros=False)
real = mp.nstr(x.real, n=sig, strip_zeros=False)
imag = mp.nstr(abs(x.imag), n=sig, strip_zeros=False)
sign = "+" if x.imag >= 0 else "-"
return f"({real}{sign}{imag}j)"
if isinstance(x, mp.mpf):
return mp.nstr(x, n=sig, strip_zeros=False)
if isinstance(x, complex):
return sci_precise(mp.mpc(x.real, x.imag), sig=sig)
return mp.nstr(mp.mpf(x), n=sig, strip_zeros=False)
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*$")
_BANG_SUBFACT_RE = re.compile(r"^\s*!\s*(\d+)\s*$")
_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 _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":
lines.append(f"digits: {GREEN}full match{RESET} ({match_n}/{sig})")
elif label2 == "almost":
lines.append(f"digits: {ORANGE}almost-full match{RESET} ({match_n}/{sig})")
else:
lines.append(f"digits: {RED}not a match{RESET} ({match_n}/{sig})")
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, _, _, exp = parse_measured_value(expected_value)
lines.append(f"expected: {ev_pretty} {dim} ({codata_label})")
cv = as_display_real(cid, computed.value)
cv_f = float(cv) # reporting
signed_err = cv_f - float(ev)
abs_err = abs(signed_err)
scaled_err = abs_err / (10 ** exp)
ABS_ERR_DECIMALS = 15
mantissa_str = f"{scaled_err:.{ABS_ERR_DECIMALS}f}"
lines.append(f"abs err: {mantissa_str} × 10^{str(exp).translate(_SUPERS)} {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 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_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()
Input Parameters
These are the numerical symbols used by the Constant Engine. Each row gives the token used in the code, its assigned value, and its dimensional type.
| Token | Value | Dimension |
|---|---|---|
| t_p | 5.39125836832313e-44 | s |
| l_p | 1.61625918175645e-35 | m |
| q_p | 1.87554596713962e-18 | C |
| T_p | 1.41678698590795e32 | K |
| m_p | 2.17642683817579e-8 | kg |
| second | 1 | s |
| meter | 1 | m |
| coulomb | 1 | C |
| kelvin | 1 | K |
| kilogram | 1 | kg |
| MHz | 1e6 | Hz |
| fm | 1.00000000000000e-15 | m |
| MeV | 1.60217663422016e-13 | J |
| GeV | 1.60217663422016e-10 | J |
| ampere | 1 | C/2 |
| joule | 1 | J |
| tesla | 1 | T |
| watt | 1 | m^2*kg/s^3 |
| farad | 1 | s^2*C^2/(m^2*kg) |
| henry | 1 | m^2*kg/C^2 |
| ohm | 1 | m^2*kg/s/C^2 |
| volt | 1 | m^2*kg/(s^2*C) |
| pascal | 1 | kg/(s^2*m) |
| IB | 0.999999199973626e-7 | - |
| zhe_1 | 0.0854245431533304 | - |
| zhe_2 | 3.66756753485501 | - |
| zhe_3 | -1.87649603900417+4.06615262615972j | - |
| zhe_4 | -1.87649603900417-4.06615262615972j | - |
| zhe_r | 4.47826244916751 | - |
| zhe_theta | 2.00316562310924 | - |
| G_Gi | 1.01494160640965 | - |
| V_fe | 2.02988321281930 | - |
| K | 0.9159655941772190 | - |
| C_d | 0.291560904030818 | - |
| D_d | 1.79162281206959 | - |
| omega_1 | 0.764977018528596+1.3249790627140867j | - |
| omega_2 | 1.529954037057192 | - |
| Im(omega_1) | 1.3249790627140867 | - |
| i^i^i^... | 0.438282936727032+0.360592471871385j | - |
| i | 1j | - |
| phi_i | 0.5+0.866025403784438j | - |
| G_g | 1.15872847301812 | - |
| pi | 3.14159265358979 | - |
| P_up | 2.29558714939263 | - |
| s | 5.24411510858423 | - |
| L | 2.622057554292119 | - |
| L_1 | 1.31102877714605 | - |
| L_2 | 0.599070117367796 | - |
| C_U | 0.847213084793979 | - |
| G_Ga | 0.834626841674073 | - |
| W_We | 0.47494937998792 | - |
| C_CF | 0.697774657964819 | - |
| C_R1 | 0.998136044598509 | - |
| F_FF | 1.22674201072035 | - |
| M | -1.74756459463318 | - |
| e | 2.71828182845904 | - |
| γ | 0.577215664901532 | - |
| S | 0.822825249678847 | - |
| δ | 1.82282524967884 | - |
| j_01 | 2.404825557695772 | - |
| C_CFP | 1.19967864025773 | - |
| D_Do | 0.739085133215160 | - |
| L_LL | 0.662743419349181 | - |
| α_F | 2.50290787509589 | - |
| δ_F | 4.66920160910299 | - |
| P | 1.32471795724474 | - |
| S* | 3.24697960371714 | - |
| C_Q | 0.605443657196732 | - |
| C_QA | 2.03816937970215 | - |
| C_HSM | 0.353236371854995 | - |
| T_0 | 2.73150000000000e2 | K |
| p_0 | 1.00000000000000e5 | pascal |
| p_1 | 1.01325000000000e5 | pascal |
| E_1 | 6.09110229711386e-24 | J |
| f_1 | 5.40000000000000e14 | Hz |
| lambda_peak | 4.96511423174427 | - |
| nu_peak | 2.82143937212207 | - |
| Re(ipt) | 0.438282936727032 | - |
| Im(ipt) | 0.360592471871385 | - |
| K_-6 | 1.15655237442151 | - |
| L_Li | 0.110001000000000 | - |
| x_infinity | 2.29316628741186 | - |
| φ | 1.61803398874989 | - |
| P* | 0.414682509851111 | - |
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: 9192631770.429694682085234472546258755724510264835296164176798231098459348293467892447658357090667892 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: 241798924253021.0378716753321525222937563112222781128502851653914606902368741347057028023167388647142 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, pi, zeta(2), zhe_theta, IB
computed: 1509190179712698114980147519458844.373297663932583206810787350384179931239390041871354029598826535367 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, zeta(2), zhe_theta, IB
computed: 6.626070149688512981998281366489811795687383972525123505917064682823851516541722774324931892489021650e-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, joule, pi, second, zeta(2), zhe_theta, IB
computed: 0.000000000000004135667696161146721730035237976171763506100617916111302445167989188363673473280225277593152190315434 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, joule, zeta(2), zhe_theta, IB
computed: 0.0000000000000006582119568295178753865440336780212339419709501693377573996415501094715753709062650398265271335667430 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: 1.054571817596582779727697601535391396089483245542510322890679098514632327400568436071168991346026065e-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: 6.626070149688512981998281366489811795687383972525123505917064682823851516541722774324931892489021650e-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: 0.0003636947548007788517467256761222193607080722403912731787049185677067663955649142527764836606109262599 m^2/s
expected: 3.6369475467(11) × 10^⁻⁴ m^2/s (SI measured)
abs err: 0.000000001307789 × 10^⁻⁴ 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: 0.0007273895096015577034934513522444387214161444807825463574098371354135327911298285055529673212218525198 m^2/s
expected: 7.2738950934(22) × 10^⁻⁴ m^2/s (SI measured)
abs err: 0.000000002615577 × 10^⁻⁴ 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: 0.00005788381800313884578380174172322310021110695789564154441482546253362507091232059734985134789672373972 eV/T
expected: 5.7883817982(18) × 10^⁻⁵ eV/T (SI measured)
abs err: 0.000000002113885 × 10^⁻⁵ 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: 0.00000003152451255348451052192517920661216393456776581471277863049608832595674039509945147690010712818818524 eV/T
expected: 3.15245125417(98) × 10^⁻⁸ eV/T (SI measured)
abs err: 0.000000001178451 × 10^⁻⁸ 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: 12906.40373060994822144596313708836735037670503080527457369066753686969206817341378270172030646160418 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: 0.00007748091729287218748187908537408139771018149116084243600540507516191001819447269516218959481873733324 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, zhe_1, zhe_theta, γ, IB
computed: 0.0000000000000000001602176634220160871880950236155269308661129765511122529303520919959331820122619771825512682840752443 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, joule, zhe_1, zhe_theta, γ, IB
computed: 6241509073603085526.641161809009515463191256127896544414292770014425747268309334069728222346289551200 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: -175882000934.6357540694236200399855872353097555149660667778694095592417565258179936834107803364127121 C/kg
expected: -1.75882000838(55) × 10^¹¹ C/kg (SI measured)
abs err: 0.000000000966357 × 10^¹¹ 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: 95788331.48316571725280652047899773268712437868406765426708838230392425740116586927707460802884560497 C/kg
expected: 9.5788331430(29) × 10^⁷ C/kg (SI measured)
abs err: 0.000000005316570 × 10^⁷ 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, tesla, zhe_1, zhe_theta, γ, IB
computed: 13996244924.82033227595090165782970288861827765805618043458112127540006683814850804604968832782138937 Hz/T
expected: 1.39962449171(44) × 10^¹⁰ Hz/T (SI measured)
abs err: 0.000000000772033 × 10^¹⁰ 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: 7.622593223035430894289006771689416688964479062917057776890034021144972159750073807283523710358528074 MHz/T
expected: 7.6225932118(24) × 10^⁰ MHz/T (SI measured)
abs err: 0.000000011235431 × 10^⁰ 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: 0.0000000005431020187637985407497970851706548690396440696715877158754569264734474249505901683220345576501284223 m
expected: 5.431020511(89) × 10^⁻¹⁰ m (SI measured)
abs err: 0.000000323362015 × 10^⁻¹⁰ 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: 0.0000000001920155601719927612897869420895614647570123473830525650345894687441157271250558283030035704171877801 m
expected: 1.920155716(32) × 10^⁻¹⁰ m (SI measured)
abs err: 0.000000114280072 × 10^⁻¹⁰ m
sigma: -3.57
within 5.2σ: yes
023. R_∞ — Rydberg constant [built on pass 2]
deps: l_p, m_p, V_fe, m_e, pi, zhe_1, zhe_theta, IB
computed: 10973731.56810997339907329579346832123054005941768057343270912700234344277871538609561381344361209229 1/m
expected: 1.0973731568157(12) × 10^⁷ 1/m (SI measured)
abs err: 0.000000000004702 × 10^⁷ 1/m
sigma: -3.92
within 5.2σ: yes
024. 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: 21947463.13621994679814659158693664246108011883536114686541825400468688555743077219122762688722418459 1/m
expected: 2.1947463136314(24) × 10^⁷ 1/m (SI measured)
abs err: 0.000000000009405 × 10^⁷ 1/m
sigma: -3.92
within 5.2σ: yes
025. 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: 0.00000004556335252929196967960709517264102465024697460487805951806882857919377469582243914850453621745824388 E_h
expected: 4.5563352529132(50) × 10^⁻⁸ E_h (SI measured)
abs err: 0.000000000015996 × 10^⁻⁸ E_h
sigma: +3.20
within 5.2σ: yes
026. A_90 — conventional value of ampere-90 [built on pass 1]
deps: S*, ampere, pi, zhe_theta, IB
computed: 1.000000088881727573119905064486936826506917072743047547259178084891334715629995041105799266948094741 A
expected: 1.00000008887000 × 10^⁰ A (SI exact (defined))
digits: almost-full match (11/12)
027. C_90 — conventional value of coulomb-90 [built on pass 1]
deps: S*, coulomb, pi, zhe_theta, IB
computed: 1.000000088881727573119905064486936826506917072743047547259178084891334715629995041105799266948094741 C
expected: 1.00000008887000 × 10^⁰ C (SI exact (defined))
digits: almost-full match (11/12)
028. 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: 46.68644773021157746858865603662789030586163044264257153418581323694520356116736810040705360822067665 1/m*T
expected: 4.6686447719(15) × 10^¹ 1/m*T (SI measured)
abs err: 0.000000001121158 × 10^¹ 1/m*T
sigma: +0.75
within 5.2σ: yes
029. 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: 0.02542623410689399028043851935548649761809999591455814896325157642179791873701947415035409572880656463 1/m*T
expected: 2.54262341009(79) × 10^⁻² 1/m*T (SI measured)
abs err: 0.000000000599399 × 10^⁻² 1/m*T
sigma: +0.76
within 5.2σ: yes
030. κ — Coulomb's constant [built on pass 1]
deps: l_p, t_p, q_p, m_p, C_d, zhe_theta, IB
computed: 8987551793.029847617969204368503335073845568677732078189176789269070400486639646950255480955168242429 m/F
expected: 8.9875517923(14) × 10^⁹ m/F (SI measured)
abs err: 0.000000000729849 × 10^⁹ m/F
sigma: +0.52
within 5.2σ: yes
031. 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: 0.0000000001112650055352702302546615093661230254974973347635146444234863547522815467643531901796084581738225951 F/m
expected: 1.11265005620(17) × 10^⁻¹⁰ F/m (SI measured)
abs err: 0.000000000847298 × 10^⁻¹⁰ F/m
sigma: -4.98
within 5.2σ: yes
032. 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: 0.000000000008854187812042685641587767545934194974531538935595322312159361782662634940053032420816600551167072626 F/m
expected: 8.8541878188(14) × 10^⁻¹² F/m (SI measured)
abs err: 0.000000006757314 × 10^⁻¹² F/m
sigma: -4.83
within 5.2σ: yes
033. 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: 0.00000000000000002418884326574997873035944889971225784196205135126022896893851023720692313729536327039897225196511007 s
expected: 2.4188843265864(26) × 10^⁻¹⁷ s (SI measured)
abs err: 0.000000000011402 × 10^⁻¹⁷ s
sigma: -4.39
within 5.2σ: yes
034. Hz⋮E_h — hertz-hartree relationship [built on pass 2]
deps: t_p, m_p, C_U, C_d, m_e, pi, watt, zhe_1, zhe_theta, IB
computed: 0.0000000000000001519829846050299951678203853356873248338218163650773117727495188271296018433301894767937918175461289 E_h
expected: 1.5198298460574(17) × 10^⁻¹⁶ E_h (SI measured)
abs err: 0.000000000007100 × 10^⁻¹⁶ E_h
sigma: -4.18
within 5.2σ: yes
035. 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: 6579683920520725.038757612362456100559095276119097493993073085972275517457276337707147335637285790667 Hz
expected: 6.5796839204999(72) × 10^¹⁵ Hz (SI measured)
abs err: 0.000000000020825 × 10^¹⁵ Hz
sigma: +2.89
within 5.2σ: yes
036. 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: 3289841960260362.519378806181228050279547638059548746996536542986137758728638168853573667818642895334 Hz
expected: 3.2898419602500(36) × 10^¹⁵ Hz (SI measured)
abs err: 0.000000000010363 × 10^¹⁵ Hz
sigma: +2.88
within 5.2σ: yes
037. μ_n/μ_+ — neutron-proton magnetic moment ratio [built on pass 2]
deps: C_CFP, K, S, m_+, m_n, pi, zhe_r, IB
computed: -0.6849790910856292241193533824764507339320791642552178645127823223445886979762068967789676877903652557 -
expected: -6.8497935(16) × 10^⁻¹ - (SI measured)
abs err: 0.000002589143707 × 10^⁻¹ -
sigma: +1.62
within 5.2σ: yes
038. μ_+/μ_n — proton-neutron magnetic moment ratio [built on pass 2]
deps: C_CFP, K, S, m_+, m_n, pi, zhe_r, IB
computed: -1.459898576488066870938077079793751099597171397105370330279035973163672172676565535692613094554462196 -
expected: -1.45989802(34) × 10^⁰ - (SI measured)
abs err: 0.000000556488067 × 10^⁰ -
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: 960.9201494751148776163983017168514897466039173409368148192111335996545721149774227290444925902221941 -
expected: 9.6092048(23) × 10^² - (SI measured)
abs err: 0.000003305248852 × 10^² -
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: 0.001040669196650972277608071853355560786890570108962764043648478321240785447633234152113105816702410342 -
expected: 1.04066884(24) × 10^⁻³ - (SI measured)
abs err: 0.000000356650972 × 10^⁻³ -
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: 0.00000000000000000000001854802011531276369455971041102538853430447307332571445668958081624379912791104653483898073533277789 J/T
expected: 1.85480201315(58) × 10^⁻²³ J/T (SI measured)
abs err: 0.000000001618724 × 10^⁻²³ 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: 0.000000000000000000000009274010057656381847279855205512694267152236536662857228344790408121899563955523267419490367666388947 J/T
expected: 9.2740100657(29) × 10^⁻²⁴ J/T (SI measured)
abs err: 0.000000008043618 × 10^⁻²⁴ 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: 0.000000000000000000000000005050783734892480442933945769667621080805188398142766084208851693776316232531509531494963312474139686 J/T
expected: 5.0507837393(16) × 10^⁻²⁷ J/T (SI measured)
abs err: 0.000000004407520 × 10^⁻²⁷ 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, pi, s, zhe_1, zhe_2, zhe_3, zhe_4, zhe_r, IB
computed: 0.00000000000000000000000001504609516114368960566004148764204610029909891847999005376260320831040807551674919433095170493718542 J/T
expected: 1.5046095178(30) × 10^⁻²⁶ J/T (SI measured)
abs err: 0.000000001685631 × 10^⁻²⁶ J/T
sigma: -0.56
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: 1.066639917541369176913977523267825208442220022148947183992738458907947900481641204266725848236453832 -
expected: 1.0666399189(21) × 10^⁰ - (SI measured)
abs err: 0.000000001358631 × 10^⁰ -
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: 2.978962475630355691484816642114349331625233588315364792620211496144724457198812300907293250575526000 -
expected: 2.9789624650(59) × 10^⁰ - (SI measured)
abs err: 0.000000010630356 × 10^⁰ -
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: 0.001622393670615784185404844910569703620962561808165033684296846857461095150216270031542001687536084430 -
expected: 1.6223936648(32) × 10^⁻³ - (SI measured)
abs err: 0.000000005815784 × 10^⁻³ -
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: 5.957924951260711382969633284228698663250467176630729585240422992289448914397624601814586501151052001 -
expected: 5.957924930(12) × 10^⁰ - (SI measured)
abs err: 0.000000021260711 × 10^⁰ -
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: 206.7669850416230996807296631905246054702841666660927000898778840782637142421452861738729765250832444 -
expected: 2.067669881(46) × 10^² - (SI measured)
abs err: 0.000000030583769 × 10^² -
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: 0.00000000006674303155045328780957914666544360252795604041632632921118650236791125109293568032541054775409197177 m^3/(s^2*kg)
expected: 6.67430(15) × 10^⁻¹¹ m^3/(s^2*kg) (SI measured)
abs err: 0.000003155045330 × 10^⁻¹¹ 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: 6.708825256046577053113746269321297433377215264696445225335185821462181416549989394521302850988213527e-39 c^4/GeV^2
expected: 6.70883(15) × 10^⁻³⁹ c^4/GeV^2 (SI measured)
abs err: 0.000004743953422 × 10^⁻³⁹ 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: 0.000000000000000000000000001674927498878758719610223732181569067359125529107350733622856517458553853152840459475768060548749960 kg
expected: 1.67492750056(85) × 10^⁻²⁷ kg (SI measured)
abs err: 0.000000001681241 × 10^⁻²⁷ 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: 0.000000000000000000000000001672621925251652155637938564796314660172028713039772192046896644997497090304037262424481290199038812 kg
expected: 1.67262192595(52) × 10^⁻²⁷ kg (SI measured)
abs err: 0.000000000698348 × 10^⁻²⁷ kg
sigma: -1.34
within 5.2σ: yes
054. m_de — deuteron mass [built on pass 2]
deps: A_mass, C_R1, pi, s, x_infinity, zhe_r, IB
computed: 0.000000000000000000000000003343583775363560934655107427384275114049759429707517753508129470397875123340752887411965661272720266 kg
expected: 3.3435837768(10) × 10^⁻²⁷ kg (SI measured)
abs err: 0.000000001436439 × 10^⁻²⁷ kg
sigma: -1.44
within 5.2σ: yes
055. m_μ — muon mass [built on pass 2]
deps: A_mass, K_-6, pi, s, zhe_r, IB
computed: 0.0000000000000000000000000001883531615023630275704811694571397513726379162343979881247497605752430892820908772178976089302482895 kg
expected: 1.883531627(42) × 10^⁻²⁸ kg (SI measured)
abs err: 0.000000011976370 × 10^⁻²⁸ kg
sigma: -0.29
within 5.2σ: yes
056. μ_de/μ_e — deuteron-electron magnetic moment ratio [built on pass 2]
deps: L_1, P_up, m_de, m_e, pi, s, zhe_r, IB
computed: -0.0004664345589721627084870091612060878118068886931805063407900027807149072813890574910153506175644411786 -
expected: -4.664345550(12) × 10^⁻⁴ - (SI measured)
abs err: 0.000000039721627 × 10^⁻⁴ -
sigma: -3.31
within 5.2σ: yes
057. μ_e/μ_de — electron-deuteron magnetic moment ratio [built on pass 2]
deps: L_1, P_up, m_de, m_e, pi, s, zhe_r, IB
computed: -2143.923473860094107485263402454920375988604782781434163763280153413630007028815935898400299885247233 -
expected: -2.1439234921(56) × 10^³ - (SI measured)
abs err: 0.000000018239906 × 10^³ -
sigma: +3.26
within 5.2σ: yes
058. μ_de/μ_+ — deuteron-proton magnetic moment ratio [built on pass 2]
deps: S, m_+, m_de, pi, s, zhe_r, φ, IB
computed: 0.3070122093908253052344334945647896901322920114872606612160993693232697288322953161060110304695107574 -
expected: 3.0701220930(79) × 10^⁻¹ - (SI measured)
abs err: 0.000000000908252 × 10^⁻¹ -
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: -0.4482065896623259907294730732567848320734698975214408000929138478935088538878005083745758487720876129 -
expected: -4.4820652(11) × 10^⁻¹ - (SI measured)
abs err: 0.000000696623260 × 10^⁻¹ -
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: 0.000000000000000000000000004330735059932395245391028229061158999804289649424730419309330183277970283356445990585607389024763953 J/T
expected: 4.330735087(11) × 10^⁻²⁷ J/T (SI measured)
abs err: 0.000000027067604 × 10^⁻²⁷ J/T
sigma: -2.46
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: -0.001158671496948782926960113960423852264286272412015101533892925130497765096876158139067645664669366872 -
expected: -1.15867149457(94) × 10^⁻³ - (SI measured)
abs err: 0.000000002378783 × 10^⁻³ -
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: -2.127497766730559932325758138709578304628593759998913082164487561686695513643503026400685699100710951 -
expected: -2.1274977624(17) × 10^⁰ - (SI measured)
abs err: 0.000000004330560 × 10^⁰ -
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: -4.255250704222979536222114017760897764027698978885909855192926554467824569568831965752615774286133877 dimensionless
expected: -4.2552506995(34) × 10^⁰ dimensionless (SI measured)
abs err: 0.000000004722979 × 10^⁰ dimensionless
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: -2.127625352111489768111057008880448882013849489442954927596463277233912284784415982876307887143066938 -
expected: -2.1276253498(17) × 10^⁰ - (SI measured)
abs err: 0.000000002311490 × 10^⁰ -
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: -0.001158740982118930922523434116682043927825042455007278182109287869273103440290704278764984062693988867 -
expected: -1.15874098083(94) × 10^⁻³ - (SI measured)
abs err: 0.000000001288931 × 10^⁻³ -
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: 0.000001256637061582489760050658683910940916441619508484827847876584549485382971826395318865683938138863921 N/A^2
expected: 1.25663706127(20) × 10^⁻⁶ N/A^2 (SI measured)
abs err: 0.000000000312490 × 10^⁻⁶ 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: 0.0000000000000000000000000000009109383710136370742031131846138441094578530329112556293316312004915821055894177834152064547055232927 kg
expected: 9.1093837139(28) × 10^⁻³¹ kg (SI measured)
abs err: 0.000000003763628 × 10^⁻³¹ 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: 0.000000000000000000000000003167545466689550858717123287193891267182095449041386920425962300856996981456835513036916176522802890 kg
expected: 3.16754(21) × 10^⁻²⁷ kg (SI measured)
abs err: 0.000005466689551 × 10^⁻²⁷ 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: 0.000000000000000000000000005007356748680750293197233730967619243795495261608382991179354733168485822965482817000649187293214357 kg
expected: 5.0073567512(16) × 10^⁻²⁷ kg (SI measured)
abs err: 0.000000002519249 × 10^⁻²⁷ 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: 683.0025030395782953093089626522833633536473497925296987124648011019746686971437842955924080114985739 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: 0.000000000000000000000000005006412784044465673114321201407525622609295394024977668135884158572835044673283609407168891628506934 kg
expected: 5.0064127862(16) × 10^⁻²⁷ kg (SI measured)
abs err: 0.000000002155535 × 10^⁻²⁷ 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: 0.000000000000000000000000006644657342140746109110588097054182735870758083599831563372189767718885530159460362785643368994003735 kg
expected: 6.6446573450(21) × 10^⁻²⁷ kg (SI measured)
abs err: 0.000000002859254 × 10^⁻²⁷ 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), joule, zhe_3, zhe_4, IB
computed: 12208857275407741594.50782890503270684726026391285809662965606072978859564068822466884475726675704462 GeV
expected: 1.220890(14) × 10^¹⁹ GeV (SI measured)
abs err: 0.000004272459226 × 10^¹⁹ GeV
sigma: -0.31
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: 25812.80744939179136926437172874777612269459769504782509025078674511509076151178057217279082339265217 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: 376.7303137120330830449004060905738107322100604362446859062106287012790187117816184129036213181862305 Ohm
expected: 3.76730313412(59) × 10^² Ohm (SI measured)
abs err: 0.000000003000331 × 10^² 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: 29.97924581991528211315092710879476562856491066825456852554041009359378464552473804029547113941531480 Ohm
expected: 2.99792458(45) × 10^¹ Ohm (SI measured)
abs err: 0.000000001991528 × 10^¹ 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: 0.000000003335640953228747859987439592394207660630883280575476111671945531345469014340865460551312606815106827 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: 2187691.263920581791596443974988693419427282599028551891631035076742603345544037826073080877514952275 m/s
expected: 2.18769126216(34) × 10^⁶ m/s (SI measured)
abs err: 0.000000001760582 × 10^⁶ 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: 0.000000000000000000000001992851916236579558708713607550813498028916160760967416861969379462566581375202723919851361904049662 m*kg/s
expected: 1.99285191545(31) × 10^⁻²⁴ m*kg/s (SI measured)
abs err: 0.000000000786580 × 10^⁻²⁴ 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: 0.0000000000000000000002730924532305466820521031926940362486599306217869076862541678323336251508327561014482614671745690629 m*kg/s
expected: 2.73092453446(85) × 10^⁻²² m*kg/s (SI measured)
abs err: 0.000000002154534 × 10^⁻²² m*kg/s
sigma: -2.53
within 5.2σ: yes
081. eV⋮kg — electron volt-kilogram relationship [built on pass 1]
deps: l_p, t_p, Im(ipt), eV, zhe_3, zhe_4, IB
computed: 1.782661923205734590230264630297639872602111138365116177137130870856878823022786551503210694982650555e-36 kg
expected: 1.78266192100000 × 10^⁻³⁶ kg (SI exact (defined))
digits: almost-full match (9/10)
082. J⋮kg — joule-kilogram relationship [built on pass 1]
deps: l_p, t_p, Im(ipt), joule, zhe_3, zhe_4, IB
computed: 0.00000000000000001112650056885533498304629936102120783460034561290621956374251804248240241419848829253737332080924154 kg
expected: 1.11265005600000 × 10^⁻¹⁷ kg (SI exact (defined))
digits: full match (10/10)
083. 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: 6700535254.992636007081128622957049989376788949901129957472499432327773575883107097894303574012781644 u
expected: 6.7005352471(21) × 10^⁹ u (SI measured)
abs err: 0.000000007892635 × 10^⁹ u
sigma: +3.76
within 5.2σ: yes
084. 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: 0.0000000001492418085934802014317106263893640825130469195901517971036050718831185028020809374759107480364851051 J
expected: 1.49241808768(46) × 10^⁻¹⁰ J (SI measured)
abs err: 0.000000001745198 × 10^⁻¹⁰ J
sigma: -3.79
within 5.2σ: yes
085. N_mom ̇ — natural unit of momentum in MeV/c [built on pass 1]
deps: l_p, t_p, Im(ipt), MeV, joule, m_e, meter, second, zhe_3, zhe_4, IB
computed: 0.5109989500280760882464244946922668486282985005948989833790568744137005516117122551256961046348561614 MeV/c
expected: 5.1099895069(16) × 10^⁻¹ MeV/c (SI measured)
abs err: 0.000000006619240 × 10^⁻¹ MeV/c
sigma: -4.14
within 5.2σ: yes
086. 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: 931.4941024971434408719102340568031701806252967452473194067421838275271394510556816281487859331730928 MeV/c
expected: 9.3149410372(29) × 10^² MeV/c (SI measured)
abs err: 0.000000012228567 × 10^² MeV/c
sigma: -4.22
within 5.2σ: yes
087. kg⋮J — kilogram-joule relationship [built on pass 1]
deps: l_p, t_p, Im(ipt), kilogram, zhe_3, zhe_4, IB
computed: 89875517806435918.63219786595620886938756455554801660734053533867056235553643469816349633144280815462 J
expected: 8.98755178700000 × 10^¹⁶ J (SI exact (defined))
digits: almost-full match (9/10)
088. kg⋮eV — kilogram-electron volt relationship [built on pass 1]
deps: l_p, t_p, Im(ipt), eV, joule, kilogram, zhe_3, zhe_4, IB
computed: 560958859883646258843549768353014518.8180207060799781518019203955818726367133032319850344448917504616 eV
expected: 5.60958860300000 × 10^³⁵ eV (SI exact (defined))
digits: almost-full match (7/10)
089. 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: 0.0000000000002072146235770650370525534178584793626100954852129469796317911036855209530198539623962719123860117941 J
expected: 2.07214712(60) × 10^⁻¹³ J (SI measured)
abs err: 0.000000884229349 × 10^⁻¹³ J
sigma: -1.47
within 5.2σ: yes
090. E_∆ ̇ — neutron-proton mass difference energy equivalent in MeV [built on pass 1]
deps: l_p, t_p, Im(ipt), MeV, joule, m_+, m_n, zhe_3, zhe_4, IB
computed: 1.293331953239501811196882964797805104284818873703611928398229177207595822761521641079895139302080364 MeV
expected: 1.29333251(38) × 10^⁰ MeV (SI measured)
abs err: 0.000000556760498 × 10^⁰ MeV
sigma: -1.47
within 5.2σ: yes
091. E_e ̇ — natural unit of energy in MeV [built on pass 1]
deps: l_p, t_p, Im(ipt), MeV, joule, m_e, zhe_3, zhe_4, IB
computed: 0.5109989500280760882464244946922668486282985005948989833790568744137005516117122551256961046348561614 MeV
expected: 5.1099895069(16) × 10^⁻¹ MeV (SI measured)
abs err: 0.000000006619240 × 10^⁻¹ MeV
sigma: -4.14
within 5.2σ: yes
092. E_μ ̇ — muon mass energy equivalent in MeV [built on pass 2]
deps: l_p, t_p, Im(ipt), MeV, joule, m_μ, zhe_3, zhe_4, IB
computed: 105.6583747318459137503735650070413757656670431558484470973945580148124568843070661249652287887948129 MeV
expected: 1.056583755(23) × 10^² MeV (SI measured)
abs err: 0.000000007681541 × 10^² MeV
sigma: -0.33
within 5.2σ: yes
093. E_+ ̇ — proton mass energy equivalent in MeV [built on pass 1]
deps: l_p, t_p, Im(ipt), MeV, joule, m_+, zhe_3, zhe_4, IB
computed: 938.2720882055566983937312613291441562243051824580023033013952669218662575427553531219775217710261597 MeV
expected: 9.3827208943(29) × 10^² MeV (SI measured)
abs err: 0.000000012244434 × 10^² MeV
sigma: -4.22
within 5.2σ: yes
094. E_n ̇ — neutron mass energy equivalent in MeV [built on pass 1]
deps: l_p, t_p, Im(ipt), MeV, joule, m_n, zhe_3, zhe_4, IB
computed: 939.5654201587962002049281442939419613285900013317059152297934960990738533655168747630574169103282401 MeV
expected: 9.3956542194(48) × 10^² MeV (SI measured)
abs err: 0.000000017812039 × 10^² MeV
sigma: -3.71
within 5.2σ: yes
095. E_τ ̇ — tau energy equivalent [built on pass 1]
deps: l_p, t_p, Im(ipt), MeV, joule, m_τ, zhe_3, zhe_4, IB
computed: 1776.862693623783625228028659503590903487930814189103366820261434104981341050913933214146454165475923 MeV
expected: 1.77686(12) × 10^³ MeV (SI measured)
abs err: 0.000002693623783 × 10^³ MeV
sigma: +0.02
within 5.2σ: yes
096. E_de ̇ — deuteron mass energy equivalent in MeV [built on pass 2]
deps: l_p, t_p, Im(ipt), MeV, joule, m_de, zhe_3, zhe_4, IB
computed: 1875.612942553401766992071093596919234371016366247985099596324771420834568511530440047899253621383399 MeV
expected: 1.87561294500(58) × 10^³ MeV (SI measured)
abs err: 0.000000002446598 × 10^³ MeV
sigma: -4.22
within 5.2σ: yes
097. E_he ̇ — helion mass energy equivalent in MeV [built on pass 2]
deps: l_p, t_p, Im(ipt), MeV, joule, m_he, zhe_3, zhe_4, IB
computed: 2808.391607444496324387679798662401683150600557660248016649622323355490258148026387697937017596398838 MeV
expected: 2.80839161112(88) × 10^³ MeV (SI measured)
abs err: 0.000000003675503 × 10^³ MeV
sigma: -4.18
within 5.2σ: yes
098. E_tri ̇ — triton mass energy equivalent in MeV [built on pass 1]
deps: l_p, t_p, Im(ipt), MeV, joule, m_tri, zhe_3, zhe_4, IB
computed: 2808.921132770637025976132304506784718883320832451545529537988094511561583709388575013906690593216292 MeV
expected: 2.80892113668(88) × 10^³ MeV (SI measured)
abs err: 0.000000003909363 × 10^³ MeV
sigma: -4.44
within 5.2σ: yes
099. E_α ̇ — alpha particle mass energy equivalent in MeV [built on pass 2]
deps: l_p, t_p, Im(ipt), MeV, joule, m_α, zhe_3, zhe_4, IB
computed: 3727.379406964774184840389529488698150420985287218829438774017362413403396362865060531650333602217667 MeV
expected: 3.7273794118(12) × 10^³ MeV (SI measured)
abs err: 0.000000004835226 × 10^³ MeV
sigma: -4.03
within 5.2σ: yes
100. 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: 0.00000000000008187105778460186814007245910295397821165242782243884486512522493234366347361167293366716019192588981 J
expected: 8.1871057880(26) × 10^⁻¹⁴ J (SI measured)
abs err: 0.000000009539814 × 10^⁻¹⁴ J
sigma: -3.67
within 5.2σ: yes
101. 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: 0.00000000001692833792050412864801910309968439817949158252567392586058222772430523302047103331341612573059435150 J
expected: 1.692833804(38) × 10^⁻¹¹ J (SI measured)
abs err: 0.000000011949587 × 10^⁻¹¹ J
sigma: -0.31
within 5.2σ: yes
102. E_+ — proton mass energy equivalent [built on pass 1]
deps: l_p, t_p, Im(ipt), m_+, zhe_3, zhe_4, IB
computed: 0.0000000001503277616263899914067956921695266424814451803653661005637630343355242403473546958011064355798098982 J
expected: 1.50327761802(47) × 10^⁻¹⁰ J (SI measured)
abs err: 0.000000001756100 × 10^⁻¹⁰ J
sigma: -3.74
within 5.2σ: yes
103. 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: 0.0000000001505349762499670564438482455873851218440552758505790475433948254392097613003745497635027074921959100 J
expected: 1.50534976514(76) × 10^⁻¹⁰ J (SI measured)
abs err: 0.000000002640329 × 10^⁻¹⁰ J
sigma: -3.47
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: 0.0000000002846847889941521001640372643069198174339622424814279919782026744733480564970312000186511178654303977 J
expected: 2.84684(19) × 10^⁻¹⁰ J (SI measured)
abs err: 0.000007889941521 × 10^⁻¹⁰ 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: 0.0000000003005063231399979553721565702448785383660709847473230939346550780572978988124657169227980566619165864 J
expected: 3.00506323491(94) × 10^⁻¹⁰ J (SI measured)
abs err: 0.000000003510021 × 10^⁻¹⁰ J
sigma: -3.73
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: 0.0000000004499539413187567959127805241667916015539678071113055301695348054750539817929340726818929229112174874 J
expected: 4.4995394185(14) × 10^⁻¹⁰ J (SI measured)
abs err: 0.000000005312433 × 10^⁻¹⁰ 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: 0.0000000004500387806292338400904993667612248659223328933788647099085453604179691071158882819583296513399780438 J
expected: 4.5003878119(14) × 10^⁻¹⁰ J (SI measured)
abs err: 0.000000005607662 × 10^⁻¹⁰ 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: 0.0000000005971920192712357910275033808139506302495751675236471492469161713609552432577757877022054153682426335 J
expected: 5.9719201997(19) × 10^⁻¹⁰ J (SI measured)
abs err: 0.000000006987643 × 10^⁻¹⁰ 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: 0.8574382359607749302747063221588412239361659759959897348283485782299949029572063743384892469691776191 -
expected: 8.574382335(22) × 10^⁻¹ - (SI measured)
abs err: 0.000000024607750 × 10^⁻¹ -
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: 0.8574382359607749302747063221588412239361659759959897348283485782299949029572063743384892469691776191 -
expected: 8.574382335(22) × 10^⁻¹ - (SI measured)
abs err: 0.000000024607750 × 10^⁻¹ -
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: 0.0004669754581827566938348953901913672729887297045784210208680619680733597725113542478389935049252009304 -
expected: 4.669754568(12) × 10^⁻⁴ - (SI measured)
abs err: 0.000000013827567 × 10^⁻⁴ -
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, L_Li, P_up, m_μ, pi, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: -0.00000000000000000000000004490448330351953019442447133718639576102742562854465948225422125904446364366466601981590174411331569 J/T
expected: -4.49044830(10) × 10^⁻²⁶ J/T (SI measured)
abs err: 0.000000030351953 × 10^⁻²⁶ J/T
sigma: -0.30
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: 0.001159652180254049014214365693332462392504989644997496254329413896306322403584584597329745252489569565 -
expected: 1.15965218046(18) × 10^⁻³ - (SI measured)
abs err: 0.000000000205951 × 10^⁻³ -
sigma: -1.14
within 5.2σ: yes
114. a_μ — muon magnetic moment anomaly [built on pass 1]
deps: K, L_Li, P_up, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 0.001165920601107197395938777289270520053309929579279418811339360608878834865459246099088787845933318052 -
expected: 1.16592062(41) × 10^⁻³ - (SI measured)
abs err: 0.000000018892803 × 10^⁻³ -
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: -2.002331841728403121007191967178882102086057679907529437833544670834226804603947358191732697601990216 -
expected: -2.00233184123(82) × 10^⁰ - (SI measured)
abs err: 0.000000000498403 × 10^⁰ -
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: -0.004841970507911872484750432277430196865917690936385145244801923003135157317900909093883536183166817851 -
expected: -4.84197048(11) × 10^⁻³ - (SI measured)
abs err: 0.000000027911872 × 10^⁻³ -
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: -8.890597092691833122249855563318310573027342840382923828662654366826812225260875395448226776668684988 -
expected: -8.89059704(20) × 10^⁰ - (SI measured)
abs err: 0.000000052691833 × 10^⁰ -
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, meter, zhe_1, zhe_3, zhe_4, γ, IB
computed: 8.314462619781648232267096980718247142681441951913951443120761669696066832713381066894586161374781983 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, 100kPa) [built on pass 1]
deps: l_p, t_p, q_p, T_p, C_d, T_0, coulomb, e, meter, p_0, zhe_1, zhe_3, zhe_4, γ, IB
computed: 0.02271095464593357214643757540283189207023435869165295836688436050077480655355660038422256209979521699 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, 100kPa) [built on pass 1]
deps: l_p, t_p, q_p, T_p, C_d, T_0, coulomb, e, meter, p_1, zhe_1, zhe_3, zhe_4, γ, IB
computed: 0.02241396954940396954990138209013756927731000117607003046324634641083129193541238626619547209454252848 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: -2.002319304360653393430557765357331175429134093864047220424259327501492366418856964847358515821495599 -
expected: -2.00231930436092(36) × 10^⁰ - (SI measured)
abs err: 0.000000000000266 × 10^⁰ -
sigma: +0.74
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: -1.001159652180326696715278882678665587714567046932023610212129663750746183209428482423679257910747799 -
expected: -1.00115965218046(18) × 10^⁰ - (SI measured)
abs err: 0.000000000000133 × 10^⁰ -
sigma: +0.74
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: -1838.281971864662712227702752263168005646404856846813803212891664487985145312530613612741645999599117 -
expected: -1.838281971877(32) × 10^³ - (SI measured)
abs err: 0.000000000012337 × 10^³ -
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: -0.000000000000000000000009284764692071088482298546681304082143989866594761201636858723647933986505648728244429609299662049783 J/T
expected: -9.2847646917(29) × 10^⁻²⁴ J/T (SI measured)
abs err: 0.000000000371090 × 10^⁻²⁴ 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: 176085962907.6197283137091464693231944279378250571329882829091637226595215711540660586518427468424959 1/s*T
expected: 1.76085962784(55) × 10^¹¹ 1/s*T (SI measured)
abs err: 0.000000001236197 × 10^¹¹ 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: 28024.95140584383970011847841494449784404267167259910408750002773245062062132820422440450614458121929 MHz/T
expected: 2.80249513861(87) × 10^⁴ MHz/T (SI measured)
abs err: 0.000000001974384 × 10^⁴ 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: 42.57638528101551271635541760580955086672587037499380105395013537996925886096205644144206596596318313 MHz/T
expected: 4.257638543(17) × 10^¹ MHz/T (SI measured)
abs err: 0.000000014898448 × 10^¹ 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: 267515318.4304936028072407842642747937397323830815942628002019917233520746984112284236250608648188006 1/s*T
expected: 2.675153194(11) × 10^⁸ 1/s*T (SI measured)
abs err: 0.000000009695064 × 10^⁸ 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: 0.00000000000000000000000001410570579397981811213963961608510063689505117100572625068672894235447171397610326046814573471394106 J/T
expected: 1.4105705830(58) × 10^⁻²⁶ J/T (SI measured)
abs err: 0.000000003602018 × 10^⁻²⁶ 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: 0.001521032202552428075019071734701270987151182394696226017170448156629724486311207094618098225156331722 -
expected: 1.52103220230(45) × 10^⁻³ - (SI measured)
abs err: 0.000000000252428 × 10^⁻³ -
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: 2.792847345064704631205912032258814710003766989569280242175202120190520706571573374490910987034120351 -
expected: 2.79284734463(82) × 10^⁰ - (SI measured)
abs err: 0.000000000434704 × 10^⁰ -
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: 5.585694690129409262411824064517629420007533979138560484350404240381041413143146748981821974068240701 -
expected: 5.5856946893(16) × 10^⁰ - (SI measured)
abs err: 0.000000000829409 × 10^⁰ -
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: -0.6849970049032614911147433655973733352412742741608631303341496025369354518524852875711680865255662718 -
expected: -6.8499694(16) × 10^⁻¹ - (SI measured)
abs err: 0.000000649032615 × 10^⁻¹ -
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: -658.2106874904405050823249626817752724261943557367770338848876762588496431579148169577870815682524890 -
expected: -6.5821068789(19) × 10^² - (SI measured)
abs err: 0.000000003995596 × 10^² -
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: -658.2275870290507256835337792922380118557387422567897998895364008518915285693194562083272460895153741 -
expected: -6.582275856(27) × 10^² - (SI measured)
abs err: 0.000000014290507 × 10^² -
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: -3.183345112213159841153660592490404369695637108545311329440554092651510679294302165602025984865319545 -
expected: -3.183345146(71) × 10^⁰ - (SI measured)
abs err: 0.000000033786840 × 10^⁰ -
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: 2.792775622348492058112456290851422365509609298317088612583778960870902231715863715932502606791951094 -
expected: 2.792775648(11) × 10^⁰ - (SI measured)
abs err: 0.000000025651508 × 10^⁰ -
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: 0.001520993141140351030278119535709678311335535450301295284055004499219209800636407188161018501644513782 -
expected: 1.5209931551(62) × 10^⁻³ - (SI measured)
abs err: 0.000000013959649 × 10^⁻³ -
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: 267522187.1704109698910263998445557648342602313542060747285979677316737847012968349105099632715199236 1/s*T
expected: 2.6752218708(11) × 10^⁸ 1/s*T (SI measured)
abs err: 0.000000000904109 × 10^⁸ 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: 42.57747847492617430557331125086311410293572506974301740430485073169412407509935057675414536280943308 MHz/T
expected: 4.2577478461(18) × 10^¹ MHz/T (SI measured)
abs err: 0.000000001392618 × 10^¹ 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, Im(omega_1), S, m_+, s, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 0.00000000000000000000000001410606797163107302086059155945641873038013165589536903055793859035123925458880348581224896666379124 J/T
expected: 1.41060679545(60) × 10^⁻²⁶ J/T (SI measured)
abs err: 0.000000001713107 × 10^⁻²⁶ J/T
sigma: +2.86
within 5.2σ: yes
142. F — Faraday constant [built on pass 1]
deps: m_p, K, e, zhe_1, zhe_2, zhe_3, zhe_4, γ, IB
computed: 96485.33220428574569995244466750878915231947865925568046532257519814605302259873031260261433489655652 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, e, pi, s, second, zhe_1, zhe_2, zhe_3, zhe_4, γ, IB
computed: 0.0000000003990312710622953082351140361638525653746424895509134933928406613128147134336345743250459080650005941 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, D_d, e, m_e, pi, s, zhe_1, zhe_2, zhe_3, zhe_4, γ, IB
computed: 0.00001205883172157723070997191304196957331761416764841897322576582768104487441524880923961216588458608836 m^3/mol
expected: 1.205883199(60) × 10^⁻⁵ m^3/mol (SI measured)
abs err: 0.000000026842277 × 10^⁻⁵ m^3/mol
sigma: -0.45
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: 299792458.0978980671007947735445441313618071755339128483836887639217553683591258521660158616933305505 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: 299792458.0978980671007947735445441313618071755339128483836887639217553683591258521660158616933305505 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: 0.000000000000002817940326994785193411391265369616494126434626034028971555185757653362134146123966706651289268343815 m
expected: 2.8179403205(13) × 10^⁻¹⁵ m (SI measured)
abs err: 0.000000006494785 × 10^⁻¹⁵ 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: 0.00000000005291772105211009553704432456976513981492293914176457540825139320832944460057157567565654776022140897 m
expected: 5.29177210544(82) × 10^⁻¹¹ m (SI measured)
abs err: 0.000000000228990 × 10^⁻¹¹ 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: 0.00000000000000000000000000006652458735897711126498438437289859557832967658927672064409819508063133901361593994280815754614714828 m^2
expected: 6.6524587051(62) × 10^⁻²⁹ m^2 (SI measured)
abs err: 0.000000030797712 × 10^⁻²⁹ 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: 0.00001166378521833528420451914428363850588882905727448713633120970269960795465883610521814728779742032277 1/GeV^2
expected: 1.1663787(06) × 10^⁻⁵ 1/GeV^2 (SI measured)
abs err: 0.000000178166472 × 10^⁻⁵ 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: 0.000000000000000000000000001660539068213224882283845370736915861724620413677450490460344971074809395779072980202853428649664695 kg
expected: 1.66053906892(52) × 10^⁻²⁷ kg (SI measured)
abs err: 0.000000000706775 × 10^⁻²⁷ 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: 602214075623045991946866105.2801624924821082511899787807682249411940235438423492566946209079899639940 u
expected: 6.0221407537(19) × 10^²⁶ u (SI measured)
abs err: 0.000000002530460 × 10^²⁶ 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: 0.0005485799090495407639975880215156877548193279648702991145610454440292111465389946338054415476656962755 -
expected: 5.485799090441(97) × 10^⁻⁴ - (SI measured)
abs err: 0.000000000054407 × 10^⁻⁴ -
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: 1.007276466582263231699749757371604815767549298295159437188786452968084687900578166137666403449441255 -
expected: 1.0072764665789(83) × 10^⁰ - (SI measured)
abs err: 0.000000000003363 × 10^⁰ -
sigma: +0.41
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: 1.008664915472892084456254938218188325781889044404479432484138826104092212079167069700734392666885639 -
expected: 1.00866491606(40) × 10^⁰ - (SI measured)
abs err: 0.000000000587108 × 10^⁰ -
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: 2.013553212548781106948298318285365223114725457402066904919592419901148175884363818082285593229059568 -
expected: 2.013553212544(15) × 10^⁰ - (SI measured)
abs err: 0.000000000004781 × 10^⁰ -
sigma: +0.32
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: 3.014932246930738073334248989182514492761867098045673089166571233786132654016798557198117194062935644 -
expected: 3.014932246932(74) × 10^⁰ - (SI measured)
abs err: 0.000000000001262 × 10^⁰ -
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: 3.015500715721599060637383295273754192278628808176220097160406743986826504901299203685045211435692513 -
expected: 3.01550071597(10) × 10^⁰ - (SI measured)
abs err: 0.000000000248401 × 10^⁰ -
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: 4.001506179129175062788989923077739763476445103590442802119025052917263212234711414700107473554773521 -
expected: 4.001506179129(62) × 10^⁰ - (SI measured)
abs err: 0.000000000000176 × 10^⁰ -
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: 0.0005485799090495407639975880215156877548193279648702991145610454440292111465389946338054415476656962755 u
expected: 5.485799090441(97) × 10^⁻⁴ u (SI measured)
abs err: 0.000000000054407 × 10^⁻⁴ 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: 0.001388448890628852756505180846583510014339746109319995295352373136007524178588903563067989217444383765 u
expected: 1.38844945(40) × 10^⁻³ u (SI measured)
abs err: 0.000000559371147 × 10^⁻³ u
sigma: -1.40
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: 0.1134289250448238433071248605729083494949219123450297348670362190771056780659971688099340599527957561 u
expected: 1.134289257(25) × 10^⁻¹ u (SI measured)
abs err: 0.000000006551762 × 10^⁻¹ 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: 1.007276466582263231699749757371604815767549298295159437188786452968084687900578166137666403449441255 u
expected: 1.0072764665789(83) × 10^⁰ u (SI measured)
abs err: 0.000000000003363 × 10^⁰ u
sigma: +0.41
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: 1.008664915472892084456254938218188325781889044404479432484138826104092212079167069700734392666885639 u
expected: 1.00866491606(40) × 10^⁰ u (SI measured)
abs err: 0.000000000587108 × 10^⁰ 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: 1.907540465216417689878178230514909341046574249313332834928957067513942798658232922896418147875973918 u
expected: 1.90754(13) × 10^⁰ u (SI measured)
abs err: 0.000000465216418 × 10^⁰ 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: 2.013553212548781106948298318285365223114725457402066904919592419901148175884363818082285593229059568 u
expected: 2.013553212544(15) × 10^⁰ u (SI measured)
abs err: 0.000000000004781 × 10^⁰ u
sigma: +0.32
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: 3.014932246930738073334248989182514492761867098045673089166571233786132654016798557198117194062935644 u
expected: 3.014932246932(74) × 10^⁰ u (SI measured)
abs err: 0.000000000001262 × 10^⁰ 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: 3.015500715721599060637383295273754192278628808176220097160406743986826504901299203685045211435692513 u
expected: 3.01550071597(10) × 10^⁰ u (SI measured)
abs err: 0.000000000248401 × 10^⁰ 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: 4.001506179129175062788989923077739763476445103590442802119025052917263212234711414700107473554773521 u
expected: 4.001506179129(62) × 10^⁰ u (SI measured)
abs err: 0.000000000000176 × 10^⁰ 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: 0.000000001073544101426670004751568867127015840974311163213670340044015440518877687641594126355600110818021466 u
expected: 1.07354410085(33) × 10^⁻⁹ u (SI measured)
abs err: 0.000000000576670 × 10^⁻⁹ u
sigma: +1.75
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: 931494103.1954453046105749391789430958984169933139794414772921943096687728971754876291686917893210272 eV
expected: 9.3149410372(29) × 10^⁸ eV (SI measured)
abs err: 0.000000005245547 × 10^⁸ eV
sigma: -1.81
within 5.2σ: yes
172. 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: 5034116567783844453122477.231498939764522485276016151636625618969140647502895534274842147826002107258 cycles/m
expected: 5.03411656700000 × 10^²⁴ cycles/m (SI exact (defined))
digits: full match (10/10)
173. 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: 806554.3938843868238196969274254904910620737472800097161565135766053521050297001950358764968003915130 cycles/m
expected: 8.06554393700000 × 10^⁵ cycles/m (SI exact (defined))
digits: almost-full match (9/10)
174. 1/m⋮eV — inverse meter-electron volt relationship [built on pass 1]
deps: l_p, t_p, m_p, eV, joule, meter, pi, zhe_1, zhe_2, δ_F, IB
computed: 0.000001239841984102213603274975008117475829849758102835082144435522382539909326656157165179744735091290898 eV
expected: 1.23984198400000 × 10^⁻⁶ eV (SI exact (defined))
digits: full match (10/10)
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: 0.0000000000000000000000001986445857053730795058661423554909781583511465899933847966828083728495201957694506769862072853758831 J
expected: 1.98644585700000 × 10^⁻²⁵ J (SI exact (defined))
digits: full match (10/10)
176. ℏc ̇ — reduced Planck constant times c in MeV fm [built on pass 1]
deps: l_p, t_p, m_p, MeV, fm, joule, meter, zhe_1, zhe_2, δ_F, IB
computed: 197.3269804227307184264183579366311666623393670965389603657092386175506439612228536797781076617569071 MeV fm
expected: 1.97326980400000 × 10^² MeV fm (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: 27.21138624596085600985121372013538158360454352720655835439990722805850445203290371954482499825890553 V
expected: 2.7211386245981(30) × 10^¹ V (SI measured)
abs err: 0.000000000002015 × 10^¹ 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: 13.60569312298042800492560686006769079180227176360327917719995361402925222601645185977241249912945277 eV
expected: 1.3605693122990(15) × 10^¹ eV (SI measured)
abs err: 0.000000000000957 × 10^¹ eV
sigma: -0.64
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: 27.21138624596085600985121372013538158360454352720655835439990722805850445203290371954482499825890553 eV
expected: 2.7211386245981(30) × 10^¹ eV (SI measured)
abs err: 0.000000000002015 × 10^¹ 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: 0.03674932217567728584731398927463497789802085352687053048424820413372058909007194224343388507498957934 E_h
expected: 3.6749322175665(40) × 10^⁻² E_h (SI measured)
abs err: 0.000000000001228 × 10^⁻² E_h
sigma: +0.31
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: 0.9999999821780258237873644718042483345779503444046957866666666666666666666666666666666666666666666667 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: 1.000000017821974176212635528195751665422049655595304213333333333333333333333333333333333333333333333 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: 1.000000017821974176212635528195751665422049655595304213333333333333333333333333333333333333333333333 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: 0.000000000000000000000000000002305575065252141500038092690582529553565381977767970807662097162983585686454286063661935798002872846 kg
expected: 2.30557461(67) × 10^⁻³⁰ kg (SI measured)
abs err: 0.000000455252141 × 10^⁻³⁰ 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: 0.00005996702991533363587538057061957385062450798263444642021131159731517332770912599405619043206433110635 -
expected: 5.9967029(23) × 10^⁻⁵ - (SI measured)
abs err: 0.000000091533363 × 10^⁻⁵ -
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: 0.00000002393692514640317661483263270790572198863667412361923016293734861641929788983315710942769059719145764 -
expected: 2.39450(20) × 10^⁻⁸ - (SI measured)
abs err: 0.000807485359682 × 10^⁻⁸ -
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: 0.00000001987697451108894685411529295621638024336461596231931309054670418912839817788396809626916702955855342 -
expected: 1.98770(10) × 10^⁻⁸ - (SI measured)
abs err: 0.000002548891105 × 10^⁻⁸ -
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: 0.00002566841247597870727692878098975333084819650974885368140326487837760643385198648653293397556383046358 -
expected: 2.56715(41) × 10^⁻⁵ - (SI measured)
abs err: 0.000308752402129 × 10^⁻⁵ -
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: 1.648777273004234982089672302163506041703886264634228891917316197804524039477389336615906914616160342e-41 m^2*C^2/J
expected: 1.64877727212(51) × 10^⁻⁴¹ m^2*C^2/J (SI measured)
abs err: 0.000000000884235 × 10^⁻⁴¹ 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: 514220674774.7423392794008420826363778207646400007912397256079500742710330832931496862764333208806582 V/m
expected: 5.14220675112(80) × 10^¹¹ V/m (SI measured)
abs err: 0.000000003372577 × 10^¹¹ 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: 0.00000008238723498037706928414578371352092274171281660708131005894758186509358610539487583060975821504975973 N
expected: 8.2387235038(13) × 10^⁻⁸ N (SI measured)
abs err: 0.000000005762292 × 10^⁻⁸ 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: 1081202385617.973668108654475437855887589413370615576568410118002374106784009341886118948376000658090 C/m^3
expected: 1.08120238677(51) × 10^¹² C/m^3 (SI measured)
abs err: 0.000000001152026 × 10^¹² 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: -0.000000000000000000000000009662358187981828644865829652462682953898410894440868095515180706921731683072026836722070330219763879 J/T
expected: -9.6623653(23) × 10^⁻²⁷ J/T (SI measured)
abs err: 0.000007112018171 × 10^⁻²⁷ 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: 29.16468718979309074123815067186103462336656874856303274811339872142775233129014932955198912372463661 MHz/T
expected: 2.91646935(69) × 10^¹ MHz/T (SI measured)
abs err: 0.000000631020691 × 10^¹ 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: 183247134.0393964626410083305246009781890079082336407931421728882372136436523912583849300439714113880 1/(s*T)
expected: 1.83247174(43) × 10^⁸ 1/(s*T) (SI measured)
abs err: 0.000000399606035 × 10^⁸ 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: -0.001041875461652718034391924979369157264394791299132781955464331631885728685597123930049413980319069824 -
expected: -1.04187565(25) × 10^⁻³ - (SI measured)
abs err: 0.000000188347282 × 10^⁻³ -
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: -1.913042414277589833396984403622612756156595054628016102235078614643192590700811392116769422637570200 -
expected: -1.91304276(45) × 10^⁰ - (SI measured)
abs err: 0.000000345722410 × 10^⁰ -
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: -3.826084828555179666793968807245225512313190109256032204470157229286385181401622784233538845275140400 -
expected: -3.82608552(90) × 10^⁰ - (SI measured)
abs err: 0.000000691444820 × 10^⁰ -
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: 7.372497323695148119583146238946040956437834972965725347271029997809829718600845128512919247298064190e-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: 0.000000000000000000000004439821660822536979053475629111042767398451753630386330846259057625295259709438012109814331319547021 u
expected: 4.4398216590(14) × 10^⁻²⁴ u (SI measured)
abs err: 0.000000001822538 × 10^⁻²⁴ 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: 0.000000000000000000001288088666955810355455282724439851048639938546736906048960739790883513000082922016560309780995871766 s
expected: 1.28808866644(40) × 10^⁻²¹ s (SI measured)
abs err: 0.000000000515810 × 10^⁻²¹ 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: 225234272093083596964785.1407790214140104676971563881716447036014356140512686308070359006346968841249 Hz
expected: 2.25234272185(70) × 10^²³ Hz (SI measured)
abs err: 0.000000000919164 × 10^²³ 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: 135639248967168494267965903591166778072494481788549.7009016733829827946632953536305225633614501063569 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: 0.00000000000000000000001380649000092463103116094598340492859453748750669626248764243545439418516013794396853788240530270413 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, joule, pi, s, zhe_2, zhe_3, zhe_4, IB
computed: 0.00008617333261538147876279660420672262683931391889333043132196655412618768648255439261596970722486256965 eV/K
expected: 8.61733326200000 × 10^⁻⁵ eV/K (SI exact (defined))
digits: full match (9/10)
206. 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: 0.00000000000000000000001380649000092463103116094598340492859453748750669626248764243545439418516013794396853788240530270413 J
expected: 1.38064900000000 × 10^⁻²³ J (SI exact (defined))
digits: full match (7/7)
207. K⋮eV — kelvin-electron volt relationship [built on pass 1]
deps: l_p, t_p, T_p, m_p, K, eV, joule, kelvin, pi, s, zhe_2, zhe_3, zhe_4, IB
computed: 0.00008617333261538147876279660420672262683931391889333043132196655412618768648255439261596970722486256965 eV
expected: 8.61733326200000 × 10^⁻⁵ eV (SI exact (defined))
digits: full match (9/10)
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: 11604.51812210913615367052652114067525271668912037026240931128550030105866478744950098430558600969312 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: 72429705153935714244060.44822234693982684178128881385287205334731299984378629738552489352295237077531 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: 26516458046471065071960625.37885665012880899919048649199050095087424486318370762786926359983612329317 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: 26867801115586806684164103.66512650074301571842976043800937508847332860762089175393853134253395192681 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: 0.6717138149618068191986614137016816793102378831113950349352121240163894574618691581560962733099796412 K/T
expected: 6.7171381472(21) × 10^⁻¹ K/T (SI measured)
abs err: 0.000000002418068 × 10^⁻¹ 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: 0.0003658267771998760838693309972015718649411820216770468711109174557360347972978652846914536017816000441 K/T
expected: 3.6582677706(11) × 10^⁻⁴ K/T (SI measured)
abs err: 0.000000001398761 × 10^⁻⁴ 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: 0.000000000000000002179872361112194423804079982779732381806677041308389818034942774490816939900110496040399658128766003 J
expected: 2.1798723611030(24) × 10^⁻¹⁸ J (SI measured)
abs err: 0.000000000009194 × 10^⁻¹⁸ J
sigma: +3.83
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: 0.000000000000000004359744722224388847608159965559464763613354082616779636069885548981633879800220992080799316257532007 J
expected: 4.3597447222060(48) × 10^⁻¹⁸ J (SI measured)
abs err: 0.000000000018389 × 10^⁻¹⁸ J
sigma: +3.83
within 5.2σ: yes
216. J⋮E_h — joule-hartree relationship [built on pass 1]
deps: l_p, t_p, D_d, m_e, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 229371227838602555.8783494784140091156927975891514440783395676351802751869378803096618868761345866524 E_h
expected: 2.2937122783969(25) × 10^¹⁷ E_h (SI measured)
abs err: 0.000000000010874 × 10^¹⁷ E_h
sigma: -4.35
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: 483597848424072.4133100413989614775940543247222968764778154510953785415335053583856676117233347834767 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: 1519267447900894.697016839138749349156198672900641432605517013428972803237059097251591434812368125148 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: 0.000000000000002067833848431147128541188740752831811749460145283916702755249279695079336555756301886124706526881298 Wb
expected: 2.06783384800000 × 10^⁻¹⁵ Wb (SI exact (defined))
digits: full match (10/10)
220. ℏ/e — 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: 0.0000000000000006582119569411089714745688515801497352101184815682534394796055959659779456808470481558061900633902347 eV*s
expected: 6.58211956900000 × 10^⁻¹⁶ eV*s (SI exact (defined))
digits: full match (10/10)
221. h/e — 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: 0.000000000000004135667696862294257082377481505663623498920290567833405510498559390158673111512603772249413053762597 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: 0.0000000000000003741771852856867788512506890751025801155500818232263234073182384221959623621459242693193871531894719 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: 0.0000000000000001191042972608582349424564657868746235443622606418786101303454547369096857296680088469822673141220262 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: 203789460.8784158338849071624516445281983769213627609588655018187448099601448742770595652673320159401 1/s*T
expected: 2.0378946078(18) × 10^⁸ 1/s*T (SI measured)
abs err: 0.000000000984158 × 10^⁸ 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: 32.43410004883233634002668950596056887820458522147689690149528445210305126577187724399196262898630812 MHz/T
expected: 3.2434100033(28) × 10^¹ MHz/T (SI measured)
abs err: 0.000000001583233 × 10^¹ 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: -0.00000000000000000000000001074617554202697991053881988275803276800673415326696898188500353907833551907762021923357649474313192 J/T
expected: -1.07461755198(93) × 10^⁻²⁶ J/T (SI measured)
abs err: 0.000000002222698 × 10^⁻²⁶ 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: -0.00000000000000000000000001074553110984421887570502834351551206041944337038805625986475192153014353533884667368470073885435825 J/T
expected: -1.07455311035(93) × 10^⁻²⁶ J/T (SI measured)
abs err: 0.000000000634422 × 10^⁻²⁶ 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: -0.7617665773067863415827653512586698460560288583157908841178140339176909907779830915153180754651387914 -
expected: -7.6176657721(66) × 10^⁻¹ - (SI measured)
abs err: 0.000000000967864 × 10^⁻¹ -
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: -0.7617861346170878796251798675868983207359209359553437052534763577583524977727417429324201687544631611 -
expected: -7.617861334(31) × 10^⁻¹ - (SI measured)
abs err: 0.000000012170879 × 10^⁻¹ -
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: 864.0582365416067132532474783724647943479027112272717690897986276859331766616155927528504294001449527 -
expected: 8.6405823986(70) × 10^² - (SI measured)
abs err: 0.000000033183933 × 10^² -
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: 34231776.90770011008199585450676297590233916253057361067362157181682033868398026375157242232563113989 E_h
expected: 3.4231776922(11) × 10^⁷ E_h (SI measured)
abs err: 0.000000001429989 × 10^⁷ 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: 0.00000002921262319207979677506151158057042493312019325678429487737687519147427664852965896292260564548754782 u
expected: 2.92126231797(91) × 10^⁻⁸ u (SI measured)
abs err: 0.000000001237979 × 10^⁻⁸ 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: 20614857887405338322130732293687395.59218597593895756211322021198472464440620975198959849768236863972 E_h
expected: 2.0614857887415(22) × 10^³⁴ E_h (SI measured)
abs err: 0.000000000000966 × 10^³⁴ 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: 4.850870209544022885982359394477180805428638684224900957947669690471482845136613956493245104534826573e-35 kg
expected: 4.8508702095419(53) × 10^⁻³⁵ kg (SI measured)
abs err: 0.000000000002122 × 10^⁻³⁵ 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: 1.536179186883722841041430213340101745511253893491631646280721627180276398416264767431378238541940762e-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: 6509657262047572173750605919176222081607.147642609866036596023951053707742024189383698130597260827518 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: 0.00000000000009251087290205608346435263296308161343782214020469081805569625712369541508730186868613023669237592277 u
expected: 9.2510872884(29) × 10^⁻¹⁴ u (SI measured)
abs err: 0.000000001805607 × 10^⁻¹⁴ 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: 10809540204307.92817247083795151477335975146921350942815371682146170900934187882029393449340193132783 K
expected: 1.08095402067(34) × 10^¹³ K (SI measured)
abs err: 0.000000000239207 × 10^¹³ 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: 452443833598083488301396266461072868283888.1893756415351339803965847034721535876682790035971573135810 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: 751300661861780.9254091925343124426748773402277046924047088511235264522665176388297815354186290151758 cycles/m
expected: 7.5130066209(23) × 10^¹⁴ cycles/m (SI measured)
abs err: 0.000000002282191 × 10^¹⁴ 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: 2.210219094040204244780910433049013156605669413619671760761595339619220342388023841142485603666588845e-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: 0.000000000000001331025048641852601969255115014769196077931280931349012081346677071790256240828898303298510301796481 u
expected: 1.33102504824(41) × 10^⁻¹⁵ u (SI measured)
abs err: 0.000000000401853 × 10^⁻¹⁵ 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: 0.000000000002426310236092927160328761818699365739856733145766061364345217120937724367606106436546084296981078933 m/cycle
expected: 2.42631023538(76) × 10^⁻¹² m/cycle (SI measured)
abs err: 0.000000000712927 × 10^⁻¹² 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: 0.00000000000001173444117640932422977601951002182773325899063935917940537836097647617735984746840112840569778729455 m/cycle
expected: 1.173444110(26) × 10^⁻¹⁴ m/cycle (SI measured)
abs err: 0.000000007640932 × 10^⁻¹⁴ 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: 0.000000000000001321409853997739869720508132127588945057926691816882863768657542505383151470449154474897603065188377 m/cycle
expected: 1.32140985360(41) × 10^⁻¹⁵ m/cycle (SI measured)
abs err: 0.000000000397740 × 10^⁻¹⁵ 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: 0.000000000000001319590904991281139442774749756234612501120555045987404112363790966393882218440273795174089051142946 m/cycle
expected: 1.31959090382(67) × 10^⁻¹⁵ m/cycle (SI measured)
abs err: 0.000000001171281 × 10^⁻¹⁵ 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: 0.0000000000000006977702821579818635290220737298159136492718208175277339737114214138238444806406772774411674319210901 m/cycle
expected: 6.97771(47) × 10^⁻¹⁶ m/cycle (SI measured)
abs err: 0.000007178420181 × 10^⁻¹⁶ 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: 0.0000000000003861592675486533567968783526577886946421787989424674938416755513325235550143884776780148550470980125 m/cycle
expected: 3.8615926744(12) × 10^⁻¹³ m/cycle (SI measured)
abs err: 0.000000001086533 × 10^⁻¹³ 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: 0.000000000000001867594317646621279605853786198097962660252988019131038146522299385340233340956436321930802629533557 m/cycle
expected: 1.867594306(42) × 10^⁻¹⁵ m/cycle (SI measured)
abs err: 0.000000011646621 × 10^⁻¹⁵ 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: 0.0000000000000002103089101140802301093459703693810849591409697667094968615656413997568564131926561688174106036106037 m/cycle
expected: 2.10308910051(66) × 10^⁻¹⁶ m/cycle (SI measured)
abs err: 0.000000000630802 × 10^⁻¹⁶ 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: 0.0000000000000002100194153884702310320247356771939323081642272312003406246482097901015410405965668036127774170945940 m/cycle
expected: 2.1001941520(11) × 10^⁻¹⁶ m/cycle (SI measured)
abs err: 0.000000001884703 × 10^⁻¹⁶ 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: 0.0000000000000001110535895480694693313427304313139186105523637890447372228798674683651309157022236249635669249807362 m/cycle
expected: 1.110538(75) × 10^⁻¹⁶ m/cycle (SI measured)
abs err: 0.000002104519305 × 10^⁻¹⁶ 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: 58789257579.63094156321955698820617721532519620679598115570163499460259299985609330915430092847525333 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: 20836619124.44858852940757707212621766806859063567886168166944979781093210853418005916504009452554591 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: 20836619124.44858852940757707212621766806859063567886168166944979781093210853418005916504009452554591 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: 0.00000000004799243073023195820460900703090291629479969567582026987374696057256132960017993586615838985233300613 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: 0.002897771953794263988572863232447310724552401995140878556830869234505528072723347976562693878964645311 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: 0.01438776876813329930788440147461592835416761220426938520528719277983598472721412734308229204066026815 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: 0.01438776876813329930788440147461592835416761220426938520528719277983598472721412734308229204066026815 cycles/m
expected: 1.43877687700000 × 10^⁻² cycles/m (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: 69.50348008052510925719712468760956561421110552357723341028763839123048398195897303968091432028068868 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, kelvin, pi, zhe_1, zhe_3, zhe_4, IB
computed: 69.50348008052510925719712468760956561421110552357723341028763839123048398195897303968091432028068868 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: 315775.0248038168893653535122242969926548616896537681972085748059361585570656249823089412567655484627 K
expected: 3.1577502480398(34) × 10^⁵ K (SI measured)
abs err: 0.000000000001631 × 10^⁵ 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: 0.000003166811563458113710268824897125260921765194728659564144137361843006400365840390846904555328478108208 E_h
expected: 3.1668115634564(34) × 10^⁻⁶ E_h (SI measured)
abs err: 0.000000000001714 × 10^⁻⁶ 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, e, m_e, zhe_1, zhe_3, zhe_4, γ, IB
computed: 0.0000005485799097965875893830724432255587262146966972669153180285661568562105047546868997971461457477189038 kg/mol
expected: 5.4857990962(17) × 10^⁻⁷ kg/mol (SI measured)
abs err: 0.000000001765876 × 10^⁻⁷ 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, e, m_μ, zhe_1, zhe_3, zhe_4, γ, IB
computed: 0.0001134289251992894315719903446440412638741284623531255609886745339971957629233948335940709594160924465 kg/mol
expected: 1.134289258(25) × 10^⁻⁴ kg/mol (SI measured)
abs err: 0.000000006007106 × 10^⁻⁴ kg/mol
sigma: -0.24
within 5.2σ: yes
266. M_A_mass — molar mass constant [built on pass 1]
deps: q_p, m_p, A_mass, C_Q, e, zhe_1, zhe_3, zhe_4, γ, IB
computed: 0.001000000001361764392865288626410988144108235714605785205361896912203796726124192386565652989790104149 kg/mol
expected: 1.00000000105(31) × 10^⁻³ kg/mol (SI measured)
abs err: 0.000000000311764 × 10^⁻³ kg/mol
sigma: +1.01
within 5.2σ: yes
267. M_+ — proton molar mass [built on pass 1]
deps: q_p, m_p, C_Q, e, m_+, zhe_1, zhe_3, zhe_4, γ, IB
computed: 0.001007276467953955257296394536902724096176794203831040216467321374725006158334034769069920837770790739 kg/mol
expected: 1.00727646764(31) × 10^⁻³ kg/mol (SI measured)
abs err: 0.000000000313955 × 10^⁻³ 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, e, m_n, zhe_1, zhe_3, zhe_4, γ, IB
computed: 0.001008664916846474876227241352491894920569292959711831014764101571808706530427784988056362164459683127 kg/mol
expected: 1.00866491712(51) × 10^⁻³ kg/mol (SI measured)
abs err: 0.000000000273525 × 10^⁻³ 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, e, m_τ, zhe_1, zhe_3, zhe_4, γ, IB
computed: 0.001907540467814073975364902151411013058833738312076000250204745644967729404596241638255244275331311877 kg/mol
expected: 1.90754(13) × 10^⁻³ kg/mol (SI measured)
abs err: 0.000000467814074 × 10^⁻³ 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, e, m_de, zhe_1, zhe_3, zhe_4, γ, IB
computed: 0.002013553215290803755545639826789150703482395343819794288872588047009386448784247845414101329495377852 kg/mol
expected: 2.01355321466(63) × 10^⁻³ kg/mol (SI measured)
abs err: 0.000000000630804 × 10^⁻³ kg/mol
sigma: +1.00
within 5.2σ: yes
271. M_he — helion molar mass [built on pass 2]
deps: q_p, m_p, C_Q, e, m_he, zhe_1, zhe_3, zhe_4, γ, IB
computed: 0.003014932251036421724279866433392001496125160281031066483224629974692175598904549887253357991800266786 kg/mol
expected: 3.01493225010(94) × 10^⁻³ kg/mol (SI measured)
abs err: 0.000000000936422 × 10^⁻³ 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, e, m_tri, zhe_1, zhe_3, zhe_4, γ, IB
computed: 0.003015500719828056842750653608073434288513325239327393488032064197256703270909204087574527520372164284 kg/mol
expected: 3.01550071913(94) × 10^⁻³ kg/mol (SI measured)
abs err: 0.000000000698057 × 10^⁻³ 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, e, m_α, zhe_1, zhe_3, zhe_4, γ, IB
computed: 0.004001506184578358378776767168341075486960158661073316748609663900326302727818304415560131893152314157 kg/mol
expected: 4.0015061833(12) × 10^⁻³ kg/mol (SI measured)
abs err: 0.000000001278358 × 10^⁻³ 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, e, zhe_1, zhe_3, zhe_4, γ, IB
computed: 0.01200000001634117271438346351693185772929882857526942246434276294644556071349030863878783587748124979 kg/mol
expected: 1.20000000126(36) × 10^⁻² kg/mol (SI measured)
abs err: 0.000000000374117 × 10^⁻² 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, e, zhe_1, zhe_3, zhe_4, γ, IB
computed: 602214076443130916631964.1081823651954198950560659493601490014120154043236272000256305048436059009846 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: -1.151707534324295179552989171818971494063331675174147828437828213715561167933935550882945902351869602 -
expected: -1.15170753496(47) × 10^⁰ - (SI measured)
abs err: 0.000000000635705 × 10^⁰ -
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: -1.164870520455957943261923581118726050256454499904769120028994999513988379877981703369364913912434826 -
expected: -1.16487052149(47) × 10^⁰ - (SI measured)
abs err: 0.000000001034042 × 10^⁰ -
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: 0.00000005670374419873165667663806664606519299097145700989492267508540673752032652532002624171284871871342069 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: 1.000000106652175107921655813058060892600436137071076009752740495654900000000000000000000000000000000 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: 1.000000195522849642363414518612025826933041019355395947516270929353464000000000000000000000000000000 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: 9717362427793018139509.448756036338940570794263153016449598868363324060259068307766931780751724493840 V/m^2
expected: 9.7173624424(30) × 10^²¹ V/m^2 (SI measured)
abs err: 0.000000014606982 × 10^²¹ 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: 0.006623618237480917722613938508122427764122572575698427196796525703359934498625234988733819349911502239 A
expected: 6.6236182375082(72) × 10^⁻³ A (SI measured)
abs err: 0.000000000027282 × 10^⁻³ A
sigma: -3.79
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: 235051.7567706029583717894958060221013457030372880713379415115072106186001419282246195977946142244599 T
expected: 2.35051757077(73) × 10^⁵ T (SI measured)
abs err: 0.000000003063971 × 10^⁵ T
sigma: -4.20
within 5.2σ: yes
284. A_edm — atomic unit of electric dipole moment [built on pass 1]
deps: l_p, q_p, m_p, L_2, P, m_e, pi, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 0.000000000000000000000000000008478353620166742518220840169885475970646355564597441465354195879307481518637170847786888575274752786 m*C
expected: 8.4783536198(13) × 10^⁻³⁰ m*C (SI measured)
abs err: 0.000000000366742 × 10^⁻³⁰ 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: 0.00000000000000000000000000007891036569360171782998212940951052970545810222243849267425020822087123546968642369801296864440155877 J/T^2
expected: 7.8910365794(49) × 10^⁻²⁹ J/T^2 (SI measured)
abs err: 0.000000010039828 × 10^⁻²⁹ 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, γ, IB
computed: 4.486551513426490239268678452321974558852592301005030666921899916886040888603079411215008794847182460e-40 m*C
expected: 4.4865515185(14) × 10^⁻⁴⁰ m*C (SI measured)
abs err: 0.000000005073509 × 10^⁻⁴⁰ m*C
sigma: -3.62
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: 3.206361295662607448083271936832356012102613772328940657691896462747191188253395449374049973966069561e-53 m^3*C^3/J^2
expected: 3.2063612996(15) × 10^⁻⁵³ m^3*C^3/J^2 (SI measured)
abs err: 0.000000003937393 × 10^⁻⁵³ 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, D_Do, m_e, pi, zhe_1, zhe_2, zhe_3, zhe_4, IB
computed: 6.235379980291313576577344321626049396928674216594536790644261156859382108960911918695386556787534164e-65 m^4*C^4/J^3
expected: 6.2353799735(39) × 10^⁻⁶⁵ m^4*C^4/J^3 (SI measured)
abs err: 0.000000006791314 × 10^⁻⁶⁵ m^4*C^4/J^3
sigma: +1.74
within 5.2σ: yes
Build complete.
Run Locally
To run the Constant Engine locally from the project folder, use:
python constant_engine/src/build_all.py > public/code/constant-engine/latest-output.txt 2>&1Then refresh this page and open Latest Output.