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, 46 insertions, 0 deletions

diff --git a/artifacts/vg_5k/anchor_bound_fixed.json b/artifacts/vg_5k/anchor_bound_fixed.json
new file mode 100644
index 0000000..553feb7
--- /dev/null
+++ b/artifacts/vg_5k/anchor_bound_fixed.json
@@ -0,0 +1,46 @@
+{
+  "protocol": "Half the scenes are anchors with their correspondence given. The rest are described by their field rows against the anchors and matched by Hungarian assignment. Upper-bounds blind recovery, which must additionally discover the anchor correspondence.",
+  "rows": [
+    {
+      "label": "synth-full",
+      "correlation": 0.928480988366389,
+      "probe_scenes": 128,
+      "chance": 0.0078125,
+      "nearest_neighbour": 0.9375,
+      "anchor_bound": 0.9828125,
+      "blind_recovery": 0.958,
+      "search_gap": 0.024812500000000015
+    },
+    {
+      "label": "omit-size",
+      "correlation": 0.8301825436675786,
+      "probe_scenes": 128,
+      "chance": 0.0078125,
+      "nearest_neighbour": 0.8953125,
+      "anchor_bound": 0.9203125,
+      "blind_recovery": 0.837,
+      "search_gap": 0.08331250000000001
+    },
+    {
+      "label": "rank8",
+      "correlation": 0.9058447537972103,
+      "probe_scenes": 128,
+      "chance": 0.0078125,
+      "nearest_neighbour": 0.7484375,
+      "anchor_bound": 0.9296875,
+      "blind_recovery": 0.884,
+      "search_gap": 0.04568749999999999
+    },
+    {
+      "label": "natural-best",
+      "correlation": 0.7157944505313568,
+      "probe_scenes": 128,
+      "chance": 0.0078125,
+      "nearest_neighbour": 0.2,
+      "anchor_bound": 0.3359375,
+      "blind_recovery": 0.0,
+      "search_gap": 0.3359375
+    }
+  ],
+  "reading": "A low bound means the representation does not identify scenes and no solver will help. A high bound with low blind recovery means the information is present and the search or the landscape is at fault."
+}
\ No newline at end of file