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, 26 insertions, 0 deletions

diff --git a/artifacts/spectral_frontier_probe/nmf_adv_oracle.log b/artifacts/spectral_frontier_probe/nmf_adv_oracle.log
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+E(truth) = 0.339635
+REF: GRAMPA on raw fields -> raw 0.0039 refined 0.0117 E=0.8380
+REF: field correlation (aligned) = 0.8302
+
+=== r=24  [6.2s]  resid V 0.0400  T 0.0331  V(seed2) 0.0447
+  [uniqueness] symNMF(V,seed1) vs symNMF(V,seed2) matched cos: median 0.885  >0.9 10/24  >0.5 24/24  min 0.541
+  [oracle cols] cos: >0.9 10/24  >0.5 23/24  median 0.842  min 0.427
+                sorted: [0.98 0.98 0.97 0.96 0.95 0.94 0.94 0.92 0.91 0.91 0.88 0.86 0.82 0.8
+ 0.79 0.69 0.68 0.68 0.68 0.68 0.68 0.63 0.55 0.43]
+                identity-map fraction (shared-seed artifact check): 0.083
+  [oracle-col row descriptors] Hungarian acc 0.6719 -> descent 0.8320
+  [prune thr=0.5] kept 23/24  rho(cleanV,T)=0.8466 (was 0.8302)  GRAMPA 0.0078 -> clean-descent 0.0547 -> true-descent 0.0547  E=0.6471
+  [prune thr=0.7] kept 15/24  rho(cleanV,T)=0.7684 (was 0.8302)  GRAMPA 0.0039 -> clean-descent 0.0391 -> true-descent 0.0391  E=0.6817
+  [prune thr=0.8] kept 13/24  rho(cleanV,T)=0.7804 (was 0.8302)  GRAMPA 0.0000 -> clean-descent 0.0000 -> true-descent 0.0000  E=0.7292
+
+=== r=42  [32.2s]  resid V 0.0241  T 0.0141  V(seed2) 0.0231
+  [uniqueness] symNMF(V,seed1) vs symNMF(V,seed2) matched cos: median 0.832  >0.9 12/42  >0.5 42/42  min 0.541
+  [oracle cols] cos: >0.9 4/42  >0.5 41/42  median 0.766  min 0.416
+                sorted: [0.97 0.94 0.93 0.9  0.89 0.88 0.88 0.87 0.86 0.86 0.86 0.84 0.84 0.84
+ 0.82 0.81 0.81 0.8  0.79 0.78 0.77 0.76 0.76 0.76 0.75 0.75 0.75 0.74
+ 0.74 0.73 0.72 0.72 0.72 0.71 0.7  0.7  0.69 0.66 0.65 0.63 0.62 0.42]
+                identity-map fraction (shared-seed artifact check): 0.000
+  [oracle-col row descriptors] Hungarian acc 0.8125 -> descent 0.8828
+  [prune thr=0.5] kept 41/42  rho(cleanV,T)=0.8337 (was 0.8302)  GRAMPA 0.0273 -> clean-descent 0.0547 -> true-descent 0.0430  E=0.6804
+  [prune thr=0.7] kept 35/42  rho(cleanV,T)=0.7976 (was 0.8302)  GRAMPA 0.0391 -> clean-descent 0.0625 -> true-descent 0.0859  E=0.6966
+  [prune thr=0.8] kept 17/42  rho(cleanV,T)=0.6036 (was 0.8302)  GRAMPA 0.0000 -> clean-descent 0.0039 -> true-descent 0.0078  E=0.6982