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, 6 insertions, 0 deletions

diff --git a/logs/amplify.log b/logs/amplify.log
index f397d0a..f775312 100644
--- a/logs/amplify.log
+++ b/logs/amplify.log
@@ -1,2 +1,8 @@
 
 === omit-size (N=256, chance=0.0039)
+  trial 0: ladders=[0.242, 0.152, 0.207]  picked-by-energy=0.2070
+  trial 1: ladders=[0.02, 0.059, 0.035]  picked-by-energy=0.0195
+  trial 2: ladders=[0.277, 0.273, 0.016]  picked-by-energy=0.2734
+  MEAN selected-by-energy=0.1667  (oracle ladder choice would give 0.1927)
+
+=== synth-full (N=256, chance=0.0039)