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, 101 insertions, 0 deletions

diff --git a/artifacts/synth_v1/match_battery2.json b/artifacts/synth_v1/match_battery2.json
new file mode 100644
index 0000000..6fd3e2f
--- /dev/null
+++ b/artifacts/synth_v1/match_battery2.json
@@ -0,0 +1,101 @@
+{
+  "protocol": "Blind: the hidden permutation is generated per trial and read only for scoring. Each solver is scored as returned and again after exact steepest-descent refinement.",
+  "rows": [
+    {
+      "field": "omit-size-BOUND0.997",
+      "method": "GW x12 restarts",
+      "raw": 0.018229166666666668,
+      "refined": 0.022135416666666668,
+      "seconds": 0.12735740343729654,
+      "failures": []
+    },
+    {
+      "field": "omit-size-BOUND0.997",
+      "method": "GW kl-loss",
+      "raw": 0.0,
+      "refined": 0.0,
+      "seconds": 0.07698225975036621,
+      "failures": []
+    },
+    {
+      "field": "omit-size-BOUND0.997",
+      "method": "entropic GW deep anneal",
+      "raw": 0.0078125,
+      "refined": 0.033854166666666664,
+      "seconds": 53.124743938446045,
+      "failures": []
+    },
+    {
+      "field": "omit-size-BOUND0.997",
+      "method": "semirelaxed GW",
+      "raw": 0.00390625,
+      "refined": 0.013020833333333334,
+      "seconds": 0.09777029355367024,
+      "failures": []
+    },
+    {
+      "field": "rank8-BOUND0.93",
+      "method": "GW x12 restarts",
+      "raw": 0.82421875,
+      "refined": 0.8815104166666666,
+      "seconds": 0.0817725658416748,
+      "failures": []
+    },
+    {
+      "field": "rank8-BOUND0.93",
+      "method": "GW kl-loss",
+      "raw": 0.21614583333333334,
+      "refined": 0.2513020833333333,
+      "seconds": 0.0778208573659261,
+      "failures": []
+    },
+    {
+      "field": "rank8-BOUND0.93",
+      "method": "entropic GW deep anneal",
+      "raw": 0.0078125,
+      "refined": 0.013020833333333334,
+      "seconds": 554.849017461141,
+      "failures": []
+    },
+    {
+      "field": "rank8-BOUND0.93",
+      "method": "semirelaxed GW",
+      "raw": 0.015625,
+      "refined": 0.044270833333333336,
+      "seconds": 38.94519297281901,
+      "failures": []
+    },
+    {
+      "field": "synth-full-BOUND0.99",
+      "method": "GW x12 restarts",
+      "raw": 0.3697916666666667,
+      "refined": 0.3971354166666667,
+      "seconds": 12.269172191619873,
+      "failures": []
+    },
+    {
+      "field": "synth-full-BOUND0.99",
+      "method": "GW kl-loss",
+      "raw": 0.08463541666666667,
+      "refined": 0.08854166666666667,
+      "seconds": 13.853389739990234,
+      "failures": []
+    },
+    {
+      "field": "synth-full-BOUND0.99",
+      "method": "entropic GW deep anneal",
+      "raw": 0.0078125,
+      "refined": 0.044270833333333336,
+      "seconds": 824.6339288552603,
+      "failures": []
+    },
+    {
+      "field": "synth-full-BOUND0.99",
+      "method": "semirelaxed GW",
+      "raw": 0.022135416666666668,
+      "refined": 0.036458333333333336,
+      "seconds": 60.74571402867635,
+      "failures": []
+    }
+  ]
+}
\ No newline at end of file