N16 · The electroweak tree-level top-mass value

Row

House note — R84 (S328a). Row 16 now prints the suite's own running endpoint beside the tree value: 0.967 · v_EW/√2 = 168.36 GeV (−2.46% against 172.60; the suite reports y_t(M_Z) ≈ 0.967 at p2_mass_hierarchy_resolvent_quintics.tex:339-340). Whether the row keeps a distance is not yet ruled (R84-f). The Scorecard footer now names this comparator as the direct-measurement (MC) mass, as this note does (H199). 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 16

m t (GeV) v EW /√2 theory 174.104 experiment 172.60 ± 0.27 deviation +0.87% · d = +5.57 Structural cross-scheme

The tree expression is evaluated with the named electroweak anchor. It is not the same object as either a Planck-scale boundary value or the direct/MC mass comparator; those interfaces are not silently filled.

Theory value

row 16

The retained mass expression is

Derivation chain

row 16

1. Take the external electroweak anchor as given by the named operational-anchor inventory. (Appendix X, Table 4, Named operational anchors, PDF p.334).
2. Evaluate the displayed tree-level mass relation. Its physical interpretation inherits the declared Yukawa attachment, rather than the internal eigenvalue theorem. (appendix_x_zero_parameter_input_ledger.tex:93; appendix_a_lagrangian_derivation.tex:231-244).
3. NOT IN SUITE — the scheme/threshold conversion and its uncertainty needed to compare this tree value with a direct/MC top-mass determination. The ledger types the existing distance as cross-scheme and non-status-setting. (appendix_x_zero_parameter_input_ledger.tex:119).

Registrar sync

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LIB2-124 — Carries the external electroweak anchor and its usage inventory.

LIB2-120 — Carries the declared Yukawa attachment inherited by the mass expression.

LIB2-121 — Carries the structural tree-mass expression and cross-scheme comparison boundary.

Comparator LIB2-220 / SL-17 — value 172.60 (+0.27/−0.27) GeV · scheme direct (MC) mass, not MS-bar · edition 2026.

Calculation

Run python3 N16_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
"""N16 — 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 compare(label, theory, reference, lower=None, upper=None):
    """Naive central-value arithmetic, not a likelihood or theory-error model.

    The asymmetric denominator points from the comparator toward the theory:
    lower error below the central value; upper error above it. Any different
    printed convention is audited separately, rather than silently substituted.
    """
    theory, reference = Decimal(str(theory)), Decimal(str(reference))
    if reference == 0:
        raise ValueError("A relative deviation needs a nonzero reference.")
    offset = theory - reference
    percent = 100 * offset / reference
    print(label + ".theory = " + shown(theory))
    print(label + ".reference = " + shown(reference))
    print(label + ".signed_percent = " + shown(percent, signed=True)
          + "%; rounded = " + shown(percent, 2, True) + "%")
    if lower is None or upper is None:
        print(label + ".d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)")
        return
    side = "lower" if offset < 0 else "upper"
    uncertainty = Decimal(str(lower if offset < 0 else upper))
    if uncertainty <= 0:
        raise ValueError("The selected comparator uncertainty must be positive.")
    distance = offset / uncertainty
    print(label + ".uncertainty_used = " + str(uncertainty) + " (" + side + ")")
    print(label + ".d = " + shown(distance, signed=True)
          + "; rounded = " + shown(distance, 2, True))

def main():
    print('=== row 16 ===')
    print('Scorecard (verbatim): m t (GeV) v EW /√2 theory 174.104 experiment 172.60 ± 0.27 deviation +0.87% · d = +5.57 Structural cross-scheme')
    vew = 246.22
    value = vew/math.sqrt(2.0)
    print("external_vEW_GeV = " + shown(vew,2))
    print("theory_at_cell_precision_GeV = " + shown(value,3))
    compare("full_tree_GeV", value, "172.60", "0.27", "0.27")
    compare("printed_tree_GeV", "174.104", "172.60", "0.27", "0.27")
    print("comparison_type = cross-scheme naive distance; no theory/matching uncertainty supplied")
    print()


if __name__ == "__main__":
    main()

row 16

Actual stdout for this entry; the text blocks in entry order concatenate to N16_stdout.txt.

=== row 16 ===
Scorecard (verbatim): m t (GeV) v EW /√2 theory 174.104 experiment 172.60 ± 0.27 deviation +0.87% · d = +5.57 Structural cross-scheme
external_vEW_GeV = 246.22
theory_at_cell_precision_GeV = 174.104
full_tree_GeV.theory = 174.103831664
full_tree_GeV.reference = 172.600000000
full_tree_GeV.signed_percent = +0.871281381%; rounded = +0.87%
full_tree_GeV.uncertainty_used = 0.27 (upper)
full_tree_GeV.d = +5.569746903; rounded = +5.57
printed_tree_GeV.theory = 174.104000000
printed_tree_GeV.reference = 172.600000000
printed_tree_GeV.signed_percent = +0.871378911%; rounded = +0.87%
printed_tree_GeV.uncertainty_used = 0.27 (upper)
printed_tree_GeV.d = +5.570370370; rounded = +5.57
comparison_type = cross-scheme naive distance; no theory/matching uncertainty supplied

Comparison

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Theory 174.104 GeV; comparator 172.60 ±0.27 GeV, PDG 2026 direct/MC mass determination (LIB2-220 / SL-17), not an MS-bar running mass. Signed deviation +0.87%; naive cross-scheme d +5.57. The source supplies neither a matched scale/scheme conversion nor theory uncertainty, so d is not a tension or a status rule.

Tier and what this does not show

Literal tier: Structural; status: cross-scheme. The electroweak anchor and physical attachment are consumed. This arithmetic does not transport a high-scale coupling to the electroweak scale or derive a direct/MC pole proxy.

Sources

LIB2-124; LIB2-120; LIB2-121; LIB2-220; SL-17; Appendix X, Table 4, Named operational anchors, PDF p.334; appendix_x_zero_parameter_input_ledger.tex:93; appendix_x_zero_parameter_input_ledger.tex:119; appendix_a_lagrangian_derivation.tex:231-244.