N21 · The light constituent-mass proxy

Row

House correction — R77 (S327h). The Scorecard printed −1.49%, computed from the displayed 331 MeV. At full precision (Λ_G2·√φ = 330.725 MeV against the ~336 MeV constituent target) it is −1.57%; the theory cell still displays 331. The suite's Appendix X table prints −1.4% with no stated convention; that is queued for Rev32.12 (= Rev33.0, R156). The cell quoted below, and the cell the script echoes, are the text as it was supplied to the drafting lane (the Scorecard through S327g). Scorecard and Registrar are unchanged in every other respect; the sealed papers keep the earlier figure until Rev32.12 (= Rev33.0, R156).

row 21

m u const (MeV) Λ G2 ·√φ theory 331 experiment ~336 (constituent target) deviation −1.49% Structural constituent

The quoted percentage is calculated from the displayed integer-MeV theory value. The full proxy gives a different rounded percentage. The supplied suite table also prints a coarser percentage that does not equal either audit at the same precision.

Theory value

row 21

The suite prints

The script uses the stated central anchor without treating its approximate value as exact physical knowledge.

Derivation chain

row 21

1. Load the named approximate hadronic anchor, not an algebraically derived scale. (appendix_x_zero_parameter_input_ledger.tex:89; Appendix X, Table 4, Named operational anchors, PDF p.334).
2. Apply the printed constituent proxy and round only for the cell display. (appendix_x_zero_parameter_input_ledger.tex:94; appendix_x_zero_parameter_input_ledger.tex:425).
3. Keep the constituent/current-mass distinction. NOT IN SUITE — a supplied uncertainty and unique scheme/scale definition for the approximate constituent comparison, or a conversion to a current-quark mass. (Appendix X, Table 4, Constituent/current-mass boundary, PDF p.334).

Registrar sync

row 21

LIB2-124 — Carries the externally supplied hadronic anchor.

LIB2-128 — Carries the light constituent proxy and its distinction from a current-quark mass.

Comparator NONE — no matching comparator record is supplied for this exact entry; the stated cell is retained without inventing an ID.

LIB2-129 concerns the strange proxy; its quoted constituent/current-mass boundary is relevant, but its formula does not derive the up-constituent row.

Calculation

Run python3 N21_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
"""N21 — 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 21 ===')
    print('Scorecard (verbatim): m u const (MeV) Λ G2 ·√φ theory 331 experiment ~336 (constituent target) deviation −1.49% Structural constituent')
    anchor = 260.0
    value = anchor*math.sqrt(PHI)
    print("external_hadronic_anchor_MeV = approximately 260 (used as 260.0)")
    print("full_constituent_proxy_MeV = " + shown(value,12))
    print("theory_at_cell_precision_MeV = " + shown(value,0))
    print("reference_type = approximate constituent target; 336 used for arithmetic only")
    compare("full_proxy_MeV", value, "336")
    compare("printed_cell_MeV", "331", "336")
    print("suite_table_percent_as_printed = -1.4%; precision convention not specified")
    print()


if __name__ == "__main__":
    main()

row 21

Actual stdout for this entry; the text blocks in entry order concatenate to N21_stdout.txt.

=== row 21 ===
Scorecard (verbatim): m u const (MeV) Λ G2 ·√φ theory 331 experiment ~336 (constituent target) deviation −1.49% Structural constituent
external_hadronic_anchor_MeV = approximately 260 (used as 260.0)
full_constituent_proxy_MeV = 330.725108873658
theory_at_cell_precision_MeV = 331
reference_type = approximate constituent target; 336 used for arithmetic only
full_proxy_MeV.theory = 330.725108874
full_proxy_MeV.reference = 336.000000000
full_proxy_MeV.signed_percent = -1.569908073%; rounded = -1.57%
full_proxy_MeV.d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)
printed_cell_MeV.theory = 331.000000000
printed_cell_MeV.reference = 336.000000000
printed_cell_MeV.signed_percent = -1.488095238%; rounded = -1.49%
printed_cell_MeV.d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)
suite_table_percent_as_printed = -1.4%; precision convention not specified

Comparison

row 21

Theory cell 331 MeV, approximate constituent target ~336 MeV. Rounded-cell offset −1.49%; full-formula offset −1.57%. The suite table’s −1.4% is retained as a separate print discrepancy. No comparator uncertainty, experimental edition, unique constituent scheme/scale, or comparator record is supplied. No d is available; this is not a current-quark PDG comparison.

Tier and what this does not show

Literal tier: Structural; status: constituent. The approximate hadronic anchor and constituent reading are consumed. Agreement with an approximate constituent target neither determines the anchor independently nor derives a current-quark mass or matching prescription.

Sources

LIB2-124; LIB2-128; LIB2-129; appendix_x_zero_parameter_input_ledger.tex:89; appendix_x_zero_parameter_input_ledger.tex:94; appendix_x_zero_parameter_input_ledger.tex:425; Appendix X, Table 4, Named operational anchors, PDF p.334; Appendix X, Table 4, Constituent/current-mass boundary, PDF p.334.