N02 · Unit determinant of the stated vacuum

Row

row 2

det(J vac ) φ·1·φ⁻¹ theory 1 experiment 1 deviation 0 · d = exact Theorem (AX1) exact

The experiment cell is an internal normalization check. It is not an independent measured determinant.

Theory value

row 2

At the printed vacuum,

The script multiplies the diagonal entries exactly and obtains 1.

Derivation chain

row 2

1. Take the working diagonal vacuum and its adjoint/inverse as stated in the Roman-surface paragraph. (p1_peirce_gauge_group.tex:116-119).
2. For this diagonal slice the printed determinant is the product of the entries; substitute the reciprocal pair and the middle unit. (p1_peirce_gauge_group.tex:111; p1_peirce_gauge_group.tex:116-118).
3. Distinguish checking this vacuum from selecting it: Appendix E uses unit determinant as hypothesis H0. (appendix_e_vacuum_selector.tex:39-42).

Registrar sync

row 2

LIB2-047 — States the determinant at the working vacuum and distinguishes it from the normalization hypothesis.

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

Calculation

Run python3 N02_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
"""N02 — 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 2 ===')
    print('Scorecard (verbatim): det(J vac ) φ·1·φ⁻¹ theory 1 experiment 1 deviation 0 · d = exact Theorem (AX1) exact')
    phi = (Fraction(0), Fraction(1))
    one = (Fraction(1), Fraction(0))
    inv = (Fraction(-1), Fraction(1))
    result = qmul(qmul(phi, one), inv)
    assert result == one
    print("diagonal_product = " + qstr(result))
    print("theory = 1; internal_reference = 1; signed_percent = 0%")
    print("d = exact (identity label, not a statistical distance)")
    print()


if __name__ == "__main__":
    main()

row 2

Actual stdout for this entry; the text blocks in entry order concatenate to N02_stdout.txt.

=== row 2 ===
Scorecard (verbatim): det(J vac ) φ·1·φ⁻¹ theory 1 experiment 1 deviation 0 · d = exact Theorem (AX1) exact
diagonal_product = 1 + (0)*phi
theory = 1; internal_reference = 1; signed_percent = 0%
d = exact (identity label, not a statistical distance)

Comparison

row 2

Theory 1, internal reference 1, signed deviation 0%. Experimental uncertainty, unit, scheme, scale and experimental edition are not applicable. The equality checks the stated normalization only.

Tier and what this does not show

Literal tier: Theorem (AX1); status: exact. The working vacuum and golden-unit input are consumed. Unit determinant alone does not select that spectrum or its physical ordering.

Sources

LIB2-047; p1_peirce_gauge_group.tex:111; p1_peirce_gauge_group.tex:116-119; appendix_e_vacuum_selector.tex:39-42.