N17 · The muon tree value and the supplied QED correction

Row

row 17a

m μ tree (MeV) (φ/√5) 8/3 ·√2/10·m τ theory 106.05 experiment 105.6583755 deviation +0.37% Structural / loaded fit gap

row 17b

m μ phys (MeV) tree / (1+δ QED ) theory 105.72 experiment 105.6583755 deviation +0.06% same —

No comparator uncertainty, Registrar comparator ID or SL ID accompanies the precise muon cell. The QED percentage is supplied as a matching input; the script does not claim to derive it from an unspecified electromagnetic coupling.

Theory value

row 17a

The retained tree relation is

row 17b

The suite prints

The script uses the displayed correction, not a newly chosen value of \alpha.

Derivation chain

row 17a

1. Take the tau anchor and retained mass-ratio formula. The source identifies the exponent and geometric normalization but explicitly distinguishes those exact facts from a derivation selecting them as mass coefficients. (appendix_a_lagrangian_derivation.tex:699-704; appendix_x_zero_parameter_input_ledger.tex:419-420).
2. Multiply without first rounding the mass ratio. The residual is the source’s coefficient gap, not an automatically generated radiative correction. (p2_mass_hierarchy_resolvent_quintics.tex:226-233).
3. NOT IN SUITE — the physical exponent/normalization selector. The supplied provenance paragraph expressly retains its target-first origin and blocking formal derivation. (appendix_a_lagrangian_derivation.tex:704).

row 17b

1. Reuse the unrounded structural tree mass; do not absorb its coefficient gap into the matching correction. (p2_mass_hierarchy_resolvent_quintics.tex:226-235).
2. Apply the positive supplied correction by division, as printed. (p2_mass_hierarchy_resolvent_quintics.tex:234-236).
3. NOT IN SUITE — in the supplied excerpts, the fully specified electromagnetic-coupling and matching prescription that reproduces the quoted correction independently. Its numerical value is therefore a declared calculation input here. (appendix_x_zero_parameter_input_ledger.tex:97).

Registrar sync

row 17a

LIB2-122 — Carries the retained ratio and its loaded provenance.

LIB2-123 — Carries the coefficient-gap interpretation of the tree residual.

LIB2-125 — Carries the tau-anchored tree mass.

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

row 17b

LIB2-122 — Carries the inherited structural ratio.

LIB2-125 — Carries its anchored tree mass.

LIB2-126 — Carries the separate QED division and supplied correction.

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

LIB2-127 concerns the downstream electron construction. Superseded empirical mass proposals are not used.

Calculation

Run python3 N17_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
"""N17 — 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 lepton_chain():
    # The printed matching correction is an input, not re-derived here.
    tau = 1776.93
    ratio = (PHI / math.sqrt(5.0))**(8.0/3.0) * math.sqrt(2.0)/10.0
    tree = tau * ratio
    delta = 0.003125
    return tau, ratio, tree, delta, tree / (1.0 + delta)

def main():
    print('=== row 17a ===')
    print('Scorecard (verbatim): m μ tree (MeV) (φ/√5) 8/3 ·√2/10·m τ theory 106.05 experiment 105.6583755 deviation +0.37% Structural / loaded fit gap')
    tau, ratio, tree, delta, physical = lepton_chain()
    print("tau_anchor_MeV = " + shown(tau,2))
    print("mass_ratio = " + shown(ratio,12))
    print("exponent = 8/3; normalization = sqrt(2)/10")
    print("normalization_value = " + shown(math.sqrt(2.0)/10.0,9))
    print("theory_at_cell_precision_MeV = " + shown(tree,2))
    compare("full_tree_MeV", tree, "105.6583755")
    compare("printed_tree_MeV", "106.05", "105.6583755")
    print()
    print('=== row 17b ===')
    print('Scorecard (verbatim): m μ phys (MeV) tree / (1+δ QED ) theory 105.72 experiment 105.6583755 deviation +0.06% same —')
    tau, ratio, tree, delta, physical = lepton_chain()
    print("supplied_delta_QED = " + shown(delta,6) + "; percent = " + shown(100*delta,4)+"%")
    print("full_tree_input_MeV = " + shown(tree,12))
    print("theory_at_cell_precision_MeV = " + shown(physical,2))
    print("alternative_from_rounded_tree_MeV = " + shown(106.05/(1+delta),12))
    compare("full_matching_chain_MeV", physical, "105.6583755")
    compare("printed_physical_cell_MeV", "105.72", "105.6583755")
    print("source_finer_percent_display = +0.058%; rounded-cell rather than full-chain convention")
    print()


if __name__ == "__main__":
    main()

row 17a

Actual stdout for this entry; the text blocks in entry order concatenate to N17_stdout.txt.

=== row 17a ===
Scorecard (verbatim): m μ tree (MeV) (φ/√5) 8/3 ·√2/10·m τ theory 106.05 experiment 105.6583755 deviation +0.37% Structural / loaded fit gap
tau_anchor_MeV = 1776.93
mass_ratio = 0.059683648785
exponent = 8/3; normalization = sqrt(2)/10
normalization_value = 0.141421356
theory_at_cell_precision_MeV = 106.05
full_tree_MeV.theory = 106.053666035
full_tree_MeV.reference = 105.658375500
full_tree_MeV.signed_percent = +0.374121345%; rounded = +0.37%
full_tree_MeV.d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)
printed_tree_MeV.theory = 106.050000000
printed_tree_MeV.reference = 105.658375500
printed_tree_MeV.signed_percent = +0.370651638%; rounded = +0.37%
printed_tree_MeV.d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)

row 17b

Actual stdout for this entry; the text blocks in entry order concatenate to N17_stdout.txt.

=== row 17b ===
Scorecard (verbatim): m μ phys (MeV) tree / (1+δ QED ) theory 105.72 experiment 105.6583755 deviation +0.06% same —
supplied_delta_QED = 0.003125; percent = 0.3125%
full_tree_input_MeV = 106.053666035117
theory_at_cell_precision_MeV = 105.72
alternative_from_rounded_tree_MeV = 105.719626168224
full_matching_chain_MeV.theory = 105.723280783
full_matching_chain_MeV.reference = 105.658375500
full_matching_chain_MeV.signed_percent = +0.061429378%; rounded = +0.06%
full_matching_chain_MeV.d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)
printed_physical_cell_MeV.theory = 105.720000000
printed_physical_cell_MeV.reference = 105.658375500
printed_physical_cell_MeV.signed_percent = +0.058324293%; rounded = +0.06%
printed_physical_cell_MeV.d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)
source_finer_percent_display = +0.058%; rounded-cell rather than full-chain convention

Comparison

row 17a

Theory 106.05 MeV; the supplied experimental cell is 105.6583755 MeV, a charged-lepton mass comparator. Signed deviation +0.37%. The precise comparator’s uncertainty and edition/ledger binding are not supplied, so no d is calculated. This is the retained structural fit gap, not a subtraction justified by the next variant.

row 17b

Theory 105.72 MeV against the same 105.6583755 MeV comparator; signed deviation rounds to +0.06%. The source’s finer +0.058% display depends on the rounded-value convention; both paths are printed. No uncertainty or exact edition binding accompanies the comparator, and d is unavailable. No additional renormalization scale is inferred from the label “physical.”

Tier and what this does not show

Row 17a literal tier: Structural / loaded, status fit gap. Row 17b literal tier: same, status —; “same” refers to the preceding tier. The tau anchor, exponent, normalization and quoted correction are consumed. Improved agreement does not derive the physical coefficient selector or erase the original tree gap.

Sources

LIB2-122; LIB2-123; LIB2-125; LIB2-126; appendix_a_lagrangian_derivation.tex:699-704; appendix_x_zero_parameter_input_ledger.tex:97; appendix_x_zero_parameter_input_ledger.tex:419-420; p2_mass_hierarchy_resolvent_quintics.tex:226-236.