N13 · The fenced structural weak-angle target

Row

row 13

sin²θ W φ⁻³ = √5 − 2 theory 0.236068 experiment 0.23122 ± 0.00006 (MS-bar, M Z ; PDG 2026) deviation +2.10% · d = no d — fenced Structural (~2% target) —

The generic request to print d does not override this row’s explicit “no d — fenced” rule. A better upstream record, LIB2-200, is supplied among another note’s candidates and carries the named scalar readout.

Theory value

row 13

The suite prints the declared readout

The agreement quoted here is a structural percentage comparison, not a scheme-matched weak-angle measurement.

Derivation chain

row 13

1. Take the independent AX6_{\rm pol} postulate and its stated scalar readout. It is not the retired Det-squared object. (appendix_x_zero_parameter_input_ledger.tex:90; p4_higgs_ewsb.tex:360-369).
2. Evaluate the printed reciprocal-power and radical expressions and check their equality numerically. (p4_higgs_ewsb.tex:367-368).
3. NOT IN SUITE — a derived matching scale and threshold map to the measured scheme. The source explicitly retains the structural target and bars a significance calculation. (p4_higgs_ewsb.tex:361-365; p6_rg_thresholds.tex:198-207).

Registrar sync

row 13

LIB2-200 — Carries the independent AX6-pol scalar readout and its distinction from the retired object.

LIB2-199 — Carries the retained reciprocal-power target and the scheme/scale fence.

Comparator LIB2-209 / SL-06 — value 0.23122 (+0.00006/−0.00006) · scheme MZ MS-bar · edition 2026 (A1546 lined).

LIB2-249 and the historical candidates do not replace the current readout. LIB2-200 is explicitly taken from the supplied cross-note material, not invented as a mapping.

Calculation

Run python3 N13_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
"""N13 — 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 13 ===')
    print('Scorecard (verbatim): sin²θ W φ⁻³ = √5 − 2 theory 0.236068 experiment 0.23122 ± 0.00006 (MS-bar, M Z ; PDG 2026) deviation +2.10% · d = no d — fenced Structural (~2% target) —')
    readout = 3.0/(4.0+(6.0*PHI-1.0))
    value = PHI**(-3)
    assert abs(readout-value) < 1e-14
    assert abs(value-(math.sqrt(5.0)-2.0)) < 1e-14
    print("readout = " + shown(readout,12))
    print("radical = " + shown(math.sqrt(5.0)-2.0,12))
    print("theory_at_cell_precision = " + shown(value,6))
    for label, theory in (("structural_full_formula", Decimal(str(value))),
                          ("structural_printed_cell", Decimal("0.236068"))):
        offset_percent = 100*(theory-Decimal("0.23122"))/Decimal("0.23122")
        print(label+".theory = "+shown(theory,12))
        print(label+".signed_percent = "+shown(offset_percent,9,True)+"%"
              +"; rounded = "+shown(offset_percent,2,True)+"%")
    print("comparator_uncertainty_as_printed = 0.00006")
    print("d_policy = NOT COMPUTED: explicit suite fence; missing scheme/scale matching")
    print()


if __name__ == "__main__":
    main()

row 13

Actual stdout for this entry; the text blocks in entry order concatenate to N13_stdout.txt.

=== row 13 ===
Scorecard (verbatim): sin²θ W φ⁻³ = √5 − 2 theory 0.236068 experiment 0.23122 ± 0.00006 (MS-bar, M Z ; PDG 2026) deviation +2.10% · d = no d — fenced Structural (~2% target) —
readout = 0.236067977500
radical = 0.236067977500
theory_at_cell_precision = 0.236068
structural_full_formula.theory = 0.236067977500
structural_full_formula.signed_percent = +2.096694706%; rounded = +2.10%
structural_printed_cell.theory = 0.236068000000
structural_printed_cell.signed_percent = +2.096704437%; rounded = +2.10%
comparator_uncertainty_as_printed = 0.00006
d_policy = NOT COMPUTED: explicit suite fence; missing scheme/scale matching

Comparison

row 13

Theory 0.236068; comparator 0.23122 ±0.00006, dimensionless, MS-bar at M_Z, PDG 2026 (LIB2-209 / SL-06). Signed structural offset +2.10%. The theoretical effective target is not supplied in that matched scheme and scale. No d is assigned despite the comparator’s small reported uncertainty.

Tier and what this does not show

Literal tier: Structural (~2% target); status: —. The independent readout postulate is consumed; matching is missing. The percentage agreement neither derives an electroweak matching scale nor licenses a sigma-level comparison.

Sources

LIB2-200; LIB2-199; LIB2-209; SL-06; appendix_x_zero_parameter_input_ledger.tex:90; p4_higgs_ewsb.tex:360-369; p6_rg_thresholds.tex:198-207.