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, 21 insertions, 0 deletions

diff --git a/artifacts/spectral_frontier_probe/nmf_adv_prune_control.log b/artifacts/spectral_frontier_probe/nmf_adv_prune_control.log
new file mode 100644
index 0000000..347318c
--- /dev/null
+++ b/artifacts/spectral_frontier_probe/nmf_adv_prune_control.log
@@ -0,0 +1,21 @@
+--- symNMF seed 1, r=42
+  A. symNMF reconstruction, NO pruning (blind)   GW 0.0312 -> clean-desc 0.0391 -> true-desc 0.0391  E=0.6405
+  B. ORACLE prune worst 1 (thr .5)               GW 0.8594 -> clean-desc 0.8594 -> true-desc 0.8672  E=0.3396
+  C0. RANDOM single-column drop (col 32, blind)  GW 0.8359 -> clean-desc 0.8281 -> true-desc 0.8359  E=0.3396
+  C1. RANDOM single-column drop (col 13, blind)  GW 0.0469 -> clean-desc 0.0430 -> true-desc 0.0469  E=0.6486
+  C2. RANDOM single-column drop (col 18, blind)  GW 0.0195 -> clean-desc 0.0156 -> true-desc 0.0156  E=0.6661
+  D. both sides symNMF-reconstructed (blind)     GW 0.0234 -> clean-desc 0.0234 -> true-desc 0.0234  E=0.6020
+--- symNMF seed 2, r=42
+  A. symNMF reconstruction, NO pruning (blind)   GW 0.0156 -> clean-desc 0.0156 -> true-desc 0.0156  E=0.6419
+  B. ORACLE prune worst 4 (thr .5)               GW 0.8203 -> clean-desc 0.8125 -> true-desc 0.8203  E=0.3396
+  C0. RANDOM single-column drop (col 32, blind)  GW 0.0078 -> clean-desc 0.0078 -> true-desc 0.0078  E=0.6720
+  C1. RANDOM single-column drop (col 13, blind)  GW 0.0195 -> clean-desc 0.0195 -> true-desc 0.0195  E=0.7034
+  C2. RANDOM single-column drop (col 18, blind)  GW 0.0039 -> clean-desc 0.0039 -> true-desc 0.0039  E=0.6649
+  D. both sides symNMF-reconstructed (blind)     GW 0.0156 -> clean-desc 0.0156 -> true-desc 0.0156  E=0.7342
+--- symNMF seed 3, r=42
+  A. symNMF reconstruction, NO pruning (blind)   GW 0.1328 -> clean-desc 0.1523 -> true-desc 0.1641  E=0.5919
+  B. ORACLE prune worst 2 (thr .5)               GW 0.0000 -> clean-desc 0.0000 -> true-desc 0.0000  E=0.6669
+  C0. RANDOM single-column drop (col 32, blind)  GW 0.1211 -> clean-desc 0.1172 -> true-desc 0.1211  E=0.5922
+  C1. RANDOM single-column drop (col 13, blind)  GW 0.8125 -> clean-desc 0.8203 -> true-desc 0.8203  E=0.3396
+  C2. RANDOM single-column drop (col 18, blind)  GW 0.0078 -> clean-desc 0.0117 -> true-desc 0.0117  E=0.6752
+  D. both sides symNMF-reconstructed (blind)     GW 0.8398 -> clean-desc 0.8477 -> true-desc 0.8477  E=0.3396