Two first-run failures are retained because they identify exactly where a validator can agree with itself while checking the wrong quantity.
The first harness used Frobenius norm, importing complement multiplicity. The repaired assertion uses the operator 2-norm directly at 1e−9.
The ratio approaches √5 from below at O(u⁻²). At u=233 the finite difference is about 1.6×10⁻⁵, so the old 10⁻⁶ proximity assertion was the wrong test. The repaired harness checks the exact rational identity plus monotonicity.
Lagrange denominators: 1,741,824 · −43,545,600
kernel ranks: 47 · 1 · 10 on the same 125-state carrier
twist defect: 8√3
The n=25 and n=243 exclusions are E1 finite searches through s≤1000. They are labeled that way in the record. The remaining section-E identities are exact rational arithmetic.
Formalism and correction note · Machine JSON record · Repository