The failure is the optimiser, not the information: a 257x faster descent and a benchmark

The gate settles which failure mode each field is in, and refutes the
symmetry hypothesis I proposed. On the caption-omitted field the truth is
a STRICT local minimum -- descent started at the truth does not move at
all -- the anchor bound says the information is 99.7% intact, and our
solver stops 0.44 above it at 4.9% accuracy. That is a pure optimiser
failure. Natural data is the opposite: descent from the truth falls a
further 0.167, so the truth is not even locally optimal, which is the
information-deficit signature the 0.291 bound predicted.

Steepest descent was brute-forcing all 32,640 candidate permutations
through the full energy every step, including a batched cube trace with
the triangle term active -- 203 seconds per descent, which is why the
gates were hopeless. The pairwise term needs one matrix product for the
whole table: swapping p,q changes the alignment sum by
2(C_pq + C_qp - C_pp - C_qq + 2 A_pq B_pq) with C = A @ B. Verified
against brute force to 1e-9 before use, and the fast descent reaches the
same optimum. 203s -> 0.79s.

Adds a matching benchmark with known-reachable answers and the solver
families never tried on these fields: Gromov-Wasserstein, entropic GW
with an annealed regulariser, BAPG.

Co-Authored-By: Claude <noreply@anthropic.com>

1 files changed, 70 insertions, 0 deletions

diff --git a/artifacts/vg_5k/anchor_bound_reprice.json b/artifacts/vg_5k/anchor_bound_reprice.json
new file mode 100644
index 0000000..4571545
--- /dev/null
+++ b/artifacts/vg_5k/anchor_bound_reprice.json
@@ -0,0 +1,70 @@
+{
+  "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": "baseline-keep8",
+      "correlation": 0.6558829559111277,
+      "probe_scenes": 128,
+      "chance": 0.0078125,
+      "nearest_neighbour": 0.1296875,
+      "anchor_bound": 0.1953125
+    },
+    {
+      "label": "base-6seg",
+      "correlation": 0.7309253746041517,
+      "probe_scenes": 128,
+      "chance": 0.0078125,
+      "nearest_neighbour": 0.1671875,
+      "anchor_bound": 0.290625
+    },
+    {
+      "label": "large-6seg",
+      "correlation": 0.7089623334444304,
+      "probe_scenes": 128,
+      "chance": 0.0078125,
+      "nearest_neighbour": 0.1609375,
+      "anchor_bound": 0.284375
+    },
+    {
+      "label": "base-16seg",
+      "correlation": 0.6794444345566255,
+      "probe_scenes": 128,
+      "chance": 0.0078125,
+      "nearest_neighbour": 0.15625,
+      "anchor_bound": 0.24375
+    },
+    {
+      "label": "oracle-boxes",
+      "correlation": 0.7027488907202334,
+      "probe_scenes": 128,
+      "chance": 0.0078125,
+      "nearest_neighbour": 0.165625,
+      "anchor_bound": 0.2734375
+    },
+    {
+      "label": "structured-phrase",
+      "correlation": 0.7252267991153302,
+      "probe_scenes": 128,
+      "chance": 0.0078125,
+      "nearest_neighbour": 0.19375,
+      "anchor_bound": 0.321875
+    },
+    {
+      "label": "third-order",
+      "correlation": 0.7171326909156865,
+      "probe_scenes": 128,
+      "chance": 0.0078125,
+      "nearest_neighbour": 0.196875,
+      "anchor_bound": 0.325
+    },
+    {
+      "label": "bow-text",
+      "correlation": 0.4699873859667931,
+      "probe_scenes": 128,
+      "chance": 0.0078125,
+      "nearest_neighbour": 0.14375,
+      "anchor_bound": 0.3296875
+    }
+  ],
+  "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