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RUN RECORD · 45/45 PASS · EXIT 0

Source SHA was supplied as prefix a045a02f…; it is preserved as a prefix rather than expanded into an invented full hash.

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Two harness corrections

Spectral norm

The first run used the Frobenius norm for a claim about the operator 2-norm. The corrected check is

$\Gamma=I-K^2/99144$

and

$\|\Gamma^n-P_E\|_2=(15/17)^n$

exactly, with reported values 0.882352941, 0.778546713, 0.606134984, 0.367399619 for n=1,2,4,8. The repaired assertion uses tolerance 1e-9.

Exact √5 identity

The first run imposed a finite floating proximity threshold. The corrected harness uses

$m^2-5u^2=-4 \iff (m/u)^2=5-4/u^2$

exactly, plus monotonic convergence from below. At u=233, the displayed difference from √5 is about 1.6e-5.

Cross-object checks

• Lagrange denominators reconstructed by interpolation: 1,741,824 and −43,545,600.
• Kernel ranks on the identical 125-state carrier: 47, 1, 10.
• Twist defect: 8√3, reported to fifteen digits.

Evidence boundary

The exclusions n=25 and n=243 are explicitly E1 finite-search results through s≤1000. The remaining section-E statements in this record use exact rational arithmetic.

Immutable sources

GitHub formalism note · machine certificate JSON · public Pages record