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, 15 insertions, 0 deletions

diff --git a/artifacts/synth_v1/amplify_pool160.json b/artifacts/synth_v1/amplify_pool160.json
new file mode 100644
index 0000000..1b5ccf8
--- /dev/null
+++ b/artifacts/synth_v1/amplify_pool160.json
@@ -0,0 +1,15 @@
+{
+  "protocol": "Blind. Hidden permutation generated per trial and read only for scoring; the ladder is chosen by energy, never by accuracy.",
+  "pool": 160,
+  "rounds": 4,
+  "ladders": 2,
+  "rows": [
+    {
+      "field": "omit-size-pool160",
+      "size": 256,
+      "chance": 0.00390625,
+      "accuracy_selected_by_energy": 0.5078125,
+      "accuracy_if_oracle_picked_best_ladder": 0.5078125
+    }
+  ]
+}
\ No newline at end of file