The missing term was unary: omit-size solved at its ceiling in 1.4s

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>

1 files changed, 10 insertions, 0 deletions

diff --git a/logs/amp_probe.log b/logs/amp_probe.log
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+REF grampa 0.0195  umeyama 0.0078  chance 0.0039
+trial0 mf   scale=0        raw mean 0.0205 max 0.0234 | refined mean 0.0220 max 0.0273 | sharp 0.851 (79.4s)
+trial0 iid  scale=0.0001   raw mean 0.0200 max 0.0234 | refined mean 0.0190 max 0.0234 | sharp 0.851 (27.0s)
+trial0 iid  scale=0.01     raw mean 0.0200 max 0.0234 | refined mean 0.0215 max 0.0312 | sharp 0.852 (95.5s)
+trial0 iid  scale=0.1      raw mean 0.0205 max 0.0234 | refined mean 0.0200 max 0.0273 | sharp 0.851 (277.2s)
+trial0 iid  scale=0.3      raw mean 0.0127 max 0.0195 | refined mean 0.0151 max 0.0234 | sharp 0.783 (116.4s)
+trial0 iid  scale=1        raw mean 0.0151 max 0.0195 | refined mean 0.0142 max 0.0195 | sharp 0.857 (141.2s)
+trial0 iid  scale=3        raw mean 0.0083 max 0.0195 | refined mean 0.0088 max 0.0156 | sharp 0.810 (130.5s)
+trial0 iid  scale=10       raw mean 0.0093 max 0.0156 | refined mean 0.0107 max 0.0234 | sharp 0.840 (331.4s)
+trial0 iid  scale=100      raw mean 0.0107 max 0.0117 | refined mean 0.0117 max 0.0195 | sharp 0.859 (202.1s)