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, 10 insertions, 4 deletions

diff --git a/worldalign/anchor_bound.py b/worldalign/anchor_bound.py
index 49f4ed3..2920934 100644
--- a/worldalign/anchor_bound.py
+++ b/worldalign/anchor_bound.py
@@ -79,13 +79,19 @@ def analyse(path: str, label: str, repeats: int, blind: float | None) -> dict:
         order = generator.permutation(size)
         half = size // 2
         anchors, probe = order[:half], order[half:]
+        # The two sides must not be presented in the same index order. Exact
+        # twins have identical anchor-restricted rows, and with matched
+        # ordering `linear_sum_assignment` breaks the tie onto the diagonal --
+        # crediting the bound with information it does not have. On the
+        # caption-omitted field that inflated it from 0.920 to 0.997.
+        order = generator.permutation(len(probe))
         left = rows_against(visual, probe, anchors)
-        right = rows_against(text, probe, anchors)
+        right = rows_against(text, probe[order], anchors)
         similarity = left @ right.T / left.shape[1]
-        truth = np.arange(len(probe))
-        nearest.append(float((similarity.argmax(1) == truth).mean()))
+        truth = order
+        nearest.append(float((order[similarity.argmax(1)] == np.arange(len(probe))).mean()))
         _, columns = linear_sum_assignment(-similarity)
-        assigned.append(float((columns == truth).mean()))
+        assigned.append(float((order[columns] == np.arange(len(probe))).mean()))
 
     row = {
         "label": label,