N03 · DET-7: evaluation and imposed status

Row

row 3

DET-7 det(Gram) = 7 theory 7 experiment structural deviation — Structural input —

The comparison is “structural,” not an experiment. Computing the Gram determinant at the golden vacuum does not derive why DET-7 must be imposed upstream.

Theory value

row 3

The printed invariant is

On the stated reciprocal spectrum the supplied proof gives s=4 and \det G=s^2-9=7. The computed value is 7.

Derivation chain

row 3

1. Use the working reciprocal spectrum with unit determinant, under the named conditional selector hypotheses. (appendix_x_zero_parameter_input_ledger.tex:63).
2. The supplied DET-7 check uses s=\phi^2+1+\phi^{-2}=4 and \det G=s^2-9. Substitution gives the displayed Gram determinant. (appendix_i_dynamics_bounce.tex:605-609).
3. Keep the logical direction explicit: the algebraic selector imposes DET-7 as a structural postulate. NOT IN SUITE — a first-principles necessity for that postulate; the supplied source itself says it remains open. (appendix_e_vacuum_selector.tex:97-107).

Registrar sync

row 3

LIB2-018 — Carries the imposed-postulate status and the missing necessity, not a physical derivation.

LIB2-019 — Carries the conditional reciprocal golden spectrum used for the evaluation; it does not make DET-7 unconditional.

Comparator NONE — the reference is internal, structural or adopted, not a supplied experimental ledger entry.

LIB2-020 is the alternate arithmetic selector, not needed for this evaluation. LIB2-356 concerns the downstream mismatch identity, not the necessity of DET-7.

Calculation

Run python3 N03_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
"""N03 — 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

# Exact arithmetic in Q(phi), with phi^2=phi+1. A pair is a+b*phi.
def qmul(x, y):
    a, b = x
    c, d = y
    return (a*c + b*d, a*d + b*c + b*d)


def qadd(x, y):
    return (x[0]+y[0], x[1]+y[1])


def qstr(x):
    return str(x[0]) + " + (" + str(x[1]) + ")*phi"

def main():
    print('=== row 3 ===')
    print('Scorecard (verbatim): DET-7 det(Gram) = 7 theory 7 experiment structural deviation — Structural input —')
    phi = (Fraction(0), Fraction(1))
    inv = (Fraction(-1), Fraction(1))
    s = qadd(qadd(qmul(phi,phi), (Fraction(1),Fraction(0))), qmul(inv,inv))
    det = qadd(qmul(s,s), (Fraction(-9),Fraction(0)))
    assert s == (Fraction(4),Fraction(0))
    assert det == (Fraction(7),Fraction(0))
    print("s = " + qstr(s))
    print("gram_diagonal = 4; gram_off_diagonal = 3")
    print("det_Gram = 4*4 - 3*3 = 7")
    print("theory = 7; comparator = structural (not a measurement)")
    print("signed_percent = NOT APPLICABLE; d = NOT APPLICABLE")
    print()


if __name__ == "__main__":
    main()

row 3

Actual stdout for this entry; the text blocks in entry order concatenate to N03_stdout.txt.

=== row 3 ===
Scorecard (verbatim): DET-7 det(Gram) = 7 theory 7 experiment structural deviation — Structural input —
s = 4 + (0)*phi
gram_diagonal = 4; gram_off_diagonal = 3
det_Gram = 4*4 - 3*3 = 7
theory = 7; comparator = structural (not a measurement)
signed_percent = NOT APPLICABLE; d = NOT APPLICABLE

Comparison

row 3

Theory 7; comparator structural. No experimental central value or uncertainty exists for this row, so signed experimental deviation and d are not applicable. The supplied suite treats this as an internal invariant and a structural input, not an empirical agreement.

Tier and what this does not show

Literal tier: Structural input; status: —. The spectrum, normalization and trace/Gram construction are used. Evaluating the postulate on its selected spectrum is not evidence that nature selects the postulate.

Sources

LIB2-018; LIB2-019; appendix_x_zero_parameter_input_ledger.tex:63-64; appendix_i_dynamics_bounce.tex:605-609; appendix_e_vacuum_selector.tex:97-107.