N14 · The supplied one-loop gauge coefficients

Row

House note — R84 (S328a). Row 14's tier cell now reads “SM content — not a test of J₃” instead of “no tier assigned” (R84-d). No number moved. The cells quoted below are the Scorecard as it was supplied to the drafting lane; the sealed papers keep their figures until Rev32.12 (= Rev33.0, R156).

row 14

b 1 , b 2 , b 3 41/10, −19/6, −7 theory exact experiment SM one-loop constants deviation 0 · d = exact no tier assigned —

No supplied candidate record carries this coefficient tuple’s derivation. In particular, LIB2-116 concerns a Yukawa trajectory, not the gauge coefficients. The experiment cell names the adopted SM constants rather than independent measurements.

Theory value

row 14

The suite states

The theory entry “exact” refers to this stated rational tuple.

Derivation chain

row 14

1. Use the printed one-loop equation and coefficient tuple. (p6_rg_thresholds.tex:94-98).
2. Retain the GUT-normalized hypercharge convention. The source explicitly excludes the alternative SM-normalized hypercharge coefficient from this calculation. (p6_rg_thresholds.tex:99-102).
3. NOT IN SUITE — in the supplied excerpts, the term-by-term matter and gauge-loop calculation producing the tuple. The script checks the stated rational coefficients and their equivalent inverse-coupling equation; it does not reconstruct that omitted calculation. (p6_rg_thresholds.tex:94-105).

Registrar sync

row 14

NONE — supplied candidates do not state or derive the gauge-coefficient tuple; Paper 6 supplies the equation and constants, not the omitted loop calculation.

Comparator NONE — the reference is internal, structural or adopted, not a supplied experimental ledger entry.

LIB2-116 concerns a different Yukawa-running predicate. The remaining keyword candidates are historical weak-angle material, not this coefficient derivation.

Calculation

Run python3 N14_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N14 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0


def shown(value, places=9, signed=False):
    """Decimal half-up display; never use display-rounded inputs implicitly."""
    value = Decimal(str(value))
    rounded = value.quantize(Decimal(1).scaleb(-places), rounding=ROUND_HALF_UP)
    return format(rounded, ("+" if signed else "") + "." + str(places) + "f")

def main():
    print('=== row 14 ===')
    print('Scorecard (verbatim): b 1 , b 2 , b 3 41/10, −19/6, −7 theory exact experiment SM one-loop constants deviation 0 · d = exact no tier assigned —')
    values = (Fraction(41,10), Fraction(-19,6), Fraction(-7,1))
    reference = (Fraction(41,10), Fraction(-19,6), Fraction(-7,1))
    for i,(value,ref) in enumerate(zip(values,reference),1):
        assert value == ref
        print("b" + str(i) + " = " + str(value)
              + "; decimal = " + shown(float(value),12)
              + "; adopted_reference = " + str(ref)
              + "; signed_percent = 0%")
        print("inverse_alpha_slope_"+str(i)+" = "
              + shown(-float(value)/(2.0*math.pi),12))
    print("normalization = GUT hypercharge; alternative b1=41/6 is not used")
    print("d = exact (same adopted constants, not experimental distances)")
    print("loop_derivation = NOT IN SUITE (supplied excerpts do not provide it)")
    print()


if __name__ == "__main__":
    main()

row 14

Actual stdout for this entry; the text blocks in entry order concatenate to N14_stdout.txt.

=== row 14 ===
Scorecard (verbatim): b 1 , b 2 , b 3 41/10, −19/6, −7 theory exact experiment SM one-loop constants deviation 0 · d = exact no tier assigned —
b1 = 41/10; decimal = 4.100000000000; adopted_reference = 41/10; signed_percent = 0%
inverse_alpha_slope_1 = -0.652535266677
b2 = -19/6; decimal = -3.166666666667; adopted_reference = -19/6; signed_percent = 0%
inverse_alpha_slope_2 = 0.503990653124
b3 = -7; decimal = -7.000000000000; adopted_reference = -7; signed_percent = 0%
inverse_alpha_slope_3 = 1.114084601643
normalization = GUT hypercharge; alternative b1=41/6 is not used
d = exact (same adopted constants, not experimental distances)
loop_derivation = NOT IN SUITE (supplied excerpts do not provide it)

Comparison

row 14

Theory and internal reference are the same adopted rational constants, with 0% arithmetic deviation. They are dimensionless one-loop coefficients in the source’s GUT-normalized convention, not measurements at an experimental edition. No uncertainty or statistical d exists; “exact” is an identity label. Their values alone do not certify the framework’s full matter-loop derivation.

Tier and what this does not show

Literal tier: no tier assigned; status: —. The source adopts the ordinary one-loop coefficients and normalization. No tier is supplied by this note, and no derivation from the exceptional algebra is inferred from the printed match.

Sources

p6_rg_thresholds.tex:94-105.