N20 · The constituent-anchored charm bridge

Row

row 20

m c (MeV) (7/3)·m s const theory 1291.9 experiment 1272.9 ± 4.5 (m c (m c ), MS-bar) deviation +1.49% · d = +4.22 Structural cross-scheme

The printed charm cell is obtained by retaining the full strange-constituent formula before applying the bridge. Multiplying the displayed rounded strange value instead changes the final decimal. The approximate hadronic anchor has no supplied uncertainty.

Theory value

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The source prints

The supplied explicit form is m_s^{\rm const}=260\phi\,3^{1/4} MeV. Keeping its intermediate precision gives 1291.9 MeV at cell precision.

Derivation chain

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1. Take the approximate external hadronic anchor and the source’s constituent prescription. The explicit formula supplies the fourth-root factor numerically. (p0_framework_foundations.tex:529; appendix_x_zero_parameter_input_ledger.tex:428).
2. Apply the retained invariant/rank bridge to the unrounded constituent proxy. (appendix_x_zero_parameter_input_ledger.tex:96; appendix_x_zero_parameter_input_ledger.tex:424).
3. NOT IN SUITE — a constituent-to-MS-bar conversion with uncertainty or a physical matching theorem for this bridge. The source explicitly retains that gap. (appendix_x_zero_parameter_input_ledger.tex:96; p2_mass_hierarchy_resolvent_quintics.tex:437-441).

Registrar sync

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LIB2-018 — Carries the imposed invariant used by the bridge.

LIB2-124 — Carries the named external hadronic anchor.

LIB2-129 — Carries the strange-constituent proxy and its modifier.

LIB2-131 — Carries the retained charm bridge and missing-conversion boundary.

Comparator LIB2-218 / SL-15 — value 1272.9 (+4.5/−4.5) MeV · scheme MS-bar at m_c · edition 2026.

LIB2-132 does not supply the missing conversion. Historical mass offsets do not replace the current comparator.

Calculation

Run python3 N20_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
"""N20 — 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 20 ===')
    print('Scorecard (verbatim): m c (MeV) (7/3)·m s const theory 1291.9 experiment 1272.9 ± 4.5 (m c (m c ), MS-bar) deviation +1.49% · d = +4.22 Structural cross-scheme')
    anchor = 260.0
    strange = anchor*PHI*3.0**0.25
    charm = (7.0/3.0)*strange
    rounded_strange_bridge = Decimal(7)*Decimal("553.7")/Decimal(3)
    print("external_hadronic_anchor_MeV = approximately 260 (used as 260.0)")
    print("strange_full_formula_MeV = " + shown(strange,12))
    print("strange_display_MeV = " + shown(strange,1))
    print("bridge_coefficient = 7/3")
    print("theory_at_cell_precision_MeV = " + shown(charm,1))
    print("bridge_from_rounded_strange_MeV = " + shown(rounded_strange_bridge,9)
          + "; rounded = " + shown(rounded_strange_bridge,1))
    compare("full_constituent_bridge_MeV", charm, "1272.9", "4.5", "4.5")
    compare("printed_cell_MeV", "1291.9", "1272.9", "4.5", "4.5")
    print("comparison_type = constituent-anchored versus MS-bar; no conversion uncertainty")
    print()


if __name__ == "__main__":
    main()

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Actual stdout for this entry; the text blocks in entry order concatenate to N20_stdout.txt.

=== row 20 ===
Scorecard (verbatim): m c (MeV) (7/3)·m s const theory 1291.9 experiment 1272.9 ± 4.5 (m c (m c ), MS-bar) deviation +1.49% · d = +4.22 Structural cross-scheme
external_hadronic_anchor_MeV = approximately 260 (used as 260.0)
strange_full_formula_MeV = 553.657646013577
strange_display_MeV = 553.7
bridge_coefficient = 7/3
theory_at_cell_precision_MeV = 1291.9
bridge_from_rounded_strange_MeV = 1291.966666667; rounded = 1292.0
full_constituent_bridge_MeV.theory = 1291.867840698
full_constituent_bridge_MeV.reference = 1272.900000000
full_constituent_bridge_MeV.signed_percent = +1.490128109%; rounded = +1.49%
full_constituent_bridge_MeV.uncertainty_used = 4.5 (upper)
full_constituent_bridge_MeV.d = +4.215075711; rounded = +4.22
printed_cell_MeV.theory = 1291.900000000
printed_cell_MeV.reference = 1272.900000000
printed_cell_MeV.signed_percent = +1.492654568%; rounded = +1.49%
printed_cell_MeV.uncertainty_used = 4.5 (upper)
printed_cell_MeV.d = +4.222222222; rounded = +4.22
comparison_type = constituent-anchored versus MS-bar; no conversion uncertainty

Comparison

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Theory 1291.9 MeV; comparator 1272.9 ±4.5 MeV, PDG 2026, m_c(m_c) in MS-bar (LIB2-218 / SL-15). Signed offset +1.49%, naive d +4.22. The theory is constituent-anchored and has no supplied conversion uncertainty; the offset is not a physics tension. The approximate anchor is not secretly adjusted to the comparator.

Tier and what this does not show

Literal tier: Structural; status: cross-scheme. The hadronic anchor, constituent prescription and bridge attachment are consumed. Numerical agreement does not derive a current-quark mass from a constituent proxy or establish the absent matching relation.

Sources

LIB2-018; LIB2-124; LIB2-129; LIB2-131; LIB2-218; SL-15; p0_framework_foundations.tex:529; appendix_x_zero_parameter_input_ledger.tex:96; appendix_x_zero_parameter_input_ledger.tex:424; appendix_x_zero_parameter_input_ledger.tex:428; p2_mass_hierarchy_resolvent_quintics.tex:437-441; s194.