N15 · The declared unit top-Yukawa boundary value

Row

row 15

y t (tree) cubic invariant / Peirce ½ theory 1 experiment y t (M Z ) ≈ 0.967 deviation — Structural (declared) —

The “experiment” cell is a reported running result, not a measured comparator at the boundary scale. The attached excerpts do not supply a complete numerical RGE initial-value specification reproducing that result.

Theory value

row 15

The source’s internal extraction gives the middle carrier weight \lambda_2=1, read as the declared boundary value

The separately reported low-scale result is y_t(M_Z)\approx0.967.

Derivation chain

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1. Take the cubic invariant and the stated carrier Higgs direction in the specified Peirce block; the supplied theorem extracts the middle weight. (appendix_a_lagrangian_derivation.tex:231-236).
2. Read that weight as a physical, scale- and scheme-specific Yukawa only through the declared attachment. NOT IN SUITE — the Higgs-direction, coupling-scheme and Planck-scale identifications; the source explicitly says none is proved. (appendix_a_lagrangian_derivation.tex:237-244).
3. Keep the reported running endpoint separate. NOT IN SUITE — in the supplied excerpts, all boundary couplings, matching choices and numerical integration data needed to reproduce that endpoint. (p0_framework_foundations.tex:1002).

Registrar sync

row 15

LIB2-120 — Carries the internal eigenvalue and the declared rather than derived physical attachment.

LIB2-139 — Carries the reported low-scale endpoint, not an experimental comparator or a reproduced integration.

Comparator NONE — the comparison cell is a reported scale-dependent calculation, not an experimental ledger entry.

Calculation

Run python3 N15_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
"""N15 — 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 15 ===')
    print('Scorecard (verbatim): y t (tree) cubic invariant / Peirce ½ theory 1 experiment y t (M Z ) ≈ 0.967 deviation — Structural (declared) —')
    carrier_diagonal = (PHI, 1.0, PHI**(-1))
    unit = carrier_diagonal[1]
    assert unit == 1.0
    print("carrier_middle_weight = " + shown(unit,0))
    print("declared_boundary_y_t = 1")
    print("reported_running_y_t_MZ = approximately 0.967 (source report; not rerun)")
    print("running_inputs = NOT IN SUITE (complete initial-value data absent from excerpts)")
    print("signed_percent = NOT ASSIGNED (different scales; no experimental comparator)")
    print("d = NOT ASSIGNED (not an experimental comparison)")
    print()


if __name__ == "__main__":
    main()

row 15

Actual stdout for this entry; the text blocks in entry order concatenate to N15_stdout.txt.

=== row 15 ===
Scorecard (verbatim): y t (tree) cubic invariant / Peirce ½ theory 1 experiment y t (M Z ) ≈ 0.967 deviation — Structural (declared) —
carrier_middle_weight = 1
declared_boundary_y_t = 1
reported_running_y_t_MZ = approximately 0.967 (source report; not rerun)
running_inputs = NOT IN SUITE (complete initial-value data absent from excerpts)
signed_percent = NOT ASSIGNED (different scales; no experimental comparator)
d = NOT ASSIGNED (not an experimental comparison)

Comparison

row 15

Boundary theory 1 versus reported low-scale running ≈0.967. Both are dimensionless, but the first is a declared Planck-scale attachment and the second is labelled M_Z. The supplied row does not identify a common renormalization scheme, measurement uncertainty or experimental edition. A difference between scales is not an experimental deviation; percentage and d remain unassigned.

Tier and what this does not show

Literal tier: Structural (declared); status: —. The physical Higgs, coupling and scale identifications are consumed. The internal unit eigenvalue does not by itself derive the physical top coupling or validate its running.

Sources

LIB2-120; LIB2-139; appendix_a_lagrangian_derivation.tex:231-244; p0_framework_foundations.tex:1002.