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>

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diff --git a/artifacts/spectral_frontier_probe/eval_impure_anchors.log b/artifacts/spectral_frontier_probe/eval_impure_anchors.log
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+=== (a) PURE random anchors: reproduce the published curve ===
+  K=  12 pure   accuracy 0.589 +- 0.055
+  K=  25 pure   accuracy 0.860 +- 0.058
+  K=  40 pure   accuracy 0.926 +- 0.032
+  K=  50 pure   accuracy 0.949 +- 0.026
+  K=  64 pure   accuracy 0.971 +- 0.017
+  K= 128 pure   accuracy 0.996 +- 0.005
+
+=== (b) IMPURE random anchors: c correct, K-c wrong (wrong = derangement among selected) ===
+  K=  12 prec=1.00 (12/12 right)  accuracy 0.620 +- 0.093
+  K=  12 prec=0.92 (10/12 right)  accuracy 0.390 +- 0.101
+  K=  12 prec=0.88 (10/12 right)  accuracy 0.399 +- 0.109
+  K=  12 prec=0.84 (10/12 right)  accuracy 0.330 +- 0.098
+  K=  12 prec=0.80 (10/12 right)  accuracy 0.408 +- 0.120
+  K=  12 prec=0.72 (9/12 right)  accuracy 0.264 +- 0.068
+  K=  12 prec=0.60 (7/12 right)  accuracy 0.135 +- 0.064
+
+  K=  25 prec=1.00 (25/25 right)  accuracy 0.852 +- 0.049
+  K=  25 prec=0.92 (23/25 right)  accuracy 0.766 +- 0.073
+  K=  25 prec=0.88 (22/25 right)  accuracy 0.746 +- 0.071
+  K=  25 prec=0.84 (21/25 right)  accuracy 0.704 +- 0.079
+  K=  25 prec=0.80 (20/25 right)  accuracy 0.677 +- 0.070
+  K=  25 prec=0.72 (18/25 right)  accuracy 0.527 +- 0.103
+  K=  25 prec=0.60 (15/25 right)  accuracy 0.371 +- 0.091
+
+  K=  40 prec=1.00 (40/40 right)  accuracy 0.933 +- 0.032
+  K=  40 prec=0.92 (37/40 right)  accuracy 0.902 +- 0.038
+  K=  40 prec=0.88 (35/40 right)  accuracy 0.859 +- 0.037
+  K=  40 prec=0.84 (34/40 right)  accuracy 0.835 +- 0.038
+  K=  40 prec=0.80 (32/40 right)  accuracy 0.812 +- 0.047
+  K=  40 prec=0.72 (29/40 right)  accuracy 0.742 +- 0.085
+  K=  40 prec=0.60 (24/40 right)  accuracy 0.574 +- 0.081
+
+  K=  50 prec=1.00 (50/50 right)  accuracy 0.950 +- 0.024
+  K=  50 prec=0.92 (46/50 right)  accuracy 0.920 +- 0.026
+  K=  50 prec=0.88 (44/50 right)  accuracy 0.893 +- 0.033
+  K=  50 prec=0.84 (42/50 right)  accuracy 0.877 +- 0.033
+  K=  50 prec=0.80 (40/50 right)  accuracy 0.855 +- 0.031
+  K=  50 prec=0.72 (36/50 right)  accuracy 0.783 +- 0.055
+  K=  50 prec=0.60 (30/50 right)  accuracy 0.629 +- 0.102
+
+  K= 100 prec=1.00 (100/100 right)  accuracy 0.992 +- 0.009
+  K= 100 prec=0.92 (92/100 right)  accuracy 0.953 +- 0.014
+  K= 100 prec=0.88 (88/100 right)  accuracy 0.933 +- 0.016
+  K= 100 prec=0.84 (84/100 right)  accuracy 0.915 +- 0.018
+  K= 100 prec=0.80 (80/100 right)  accuracy 0.895 +- 0.012
+  K= 100 prec=0.72 (72/100 right)  accuracy 0.852 +- 0.020
+  K= 100 prec=0.60 (60/100 right)  accuracy 0.787 +- 0.021
+
+=== (c) IMPURE with wrong partners drawn from OUTSIDE the anchor set ===
+  K=  25 prec=1.00  accuracy 0.866 +- 0.040
+  K=  25 prec=0.88  accuracy 0.729 +- 0.064
+  K=  25 prec=0.84  accuracy 0.689 +- 0.070
+  K=  25 prec=0.80  accuracy 0.603 +- 0.079
+  K=  25 prec=0.72  accuracy 0.501 +- 0.094
+  K=  50 prec=1.00  accuracy 0.945 +- 0.025
+  K=  50 prec=0.88  accuracy 0.832 +- 0.031
+  K=  50 prec=0.84  accuracy 0.808 +- 0.020
+  K=  50 prec=0.80  accuracy 0.775 +- 0.031
+  K=  50 prec=0.72  accuracy 0.689 +- 0.043