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Adversarial review of the artifacts found three of my numbers to be
artifacts of my own code. All three reproduced here before acceptance:
- anchor_bound presented probe rows in the same index order on both
sides, so exact twins had their tie broken onto the diagonal. 0.997 ->
0.920 on omit-size. Fixed by scrambling the T-side presentation.
- The truth is not a strict local minimum: 51 transpositions have
exactly zero energy delta. fast_pair_descent only looked stationary
because its break test treats zero as no-improvement.
- scipy's FAQ takes no n_init, so it was swallowed into unknown_options
and 'FAQ x30 restarts' computed bit-identically to plain FAQ. Replaced
with a real restart loop over P0='randomized'.
The blind ceiling for omit-size is 0.836, not 1.0: the text field has 51
exact transposition automorphisms, so T[s,s] is bitwise identical to T
and no objective f(V, P T P^T) can separate an orbit at any order. Every
synthetic accuracy was being divided by the wrong denominator.
The fifteen failed solvers share one property -- all purely quadratic or
purely spectral, none with a node-level term. Eight moments of each
node's own field row, blended with the quadratic term through
Frank-Wolfe, reach 0.837 with an energy gap of exactly zero. The term
must stay in the loop: as a seed for pure-quadratic descent it scores
0.21, pinned through the iterations it scores 0.84 -- which is also why
amplification plateaued, being itself pure-quadratic.
Co-Authored-By: Claude <noreply@anthropic.com>
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