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, 45 insertions, 0 deletions

diff --git a/artifacts/synth_v1/degeneracy_gate.json b/artifacts/synth_v1/degeneracy_gate.json
new file mode 100644
index 0000000..6a910d0
--- /dev/null
+++ b/artifacts/synth_v1/degeneracy_gate.json
@@ -0,0 +1,45 @@
+{
+  "protocol": "One spectral-start descent per trial, plus one descent started at the truth. A positive gap means the searcher stopped above the truth; zero means it found something the energy cannot distinguish from the truth; negative means the truth is beaten.",
+  "rows": [
+    {
+      "label": "omit-size",
+      "size": 256,
+      "energy_gap_found_minus_truth": 0.43996140951295937,
+      "truth_descends_further_by": 0.0,
+      "blind_accuracy": 0.049479166666666664,
+      "verdict": "truth is DEEPER than what is found -- optimiser failure"
+    },
+    {
+      "label": "noise035",
+      "size": 256,
+      "energy_gap_found_minus_truth": 0.04761915721057547,
+      "truth_descends_further_by": 0.0020415746981433114,
+      "blind_accuracy": 0.88671875,
+      "verdict": "truth is DEEPER than what is found -- optimiser failure"
+    },
+    {
+      "label": "rank8",
+      "size": 256,
+      "energy_gap_found_minus_truth": 0.364986204015837,
+      "truth_descends_further_by": 0.006232799331109179,
+      "blind_accuracy": 0.06510416666666667,
+      "verdict": "truth is DEEPER than what is found -- optimiser failure"
+    },
+    {
+      "label": "synth-full",
+      "size": 256,
+      "energy_gap_found_minus_truth": 0.07695912511043244,
+      "truth_descends_further_by": 0.0005474964148536876,
+      "blind_accuracy": 0.8828125,
+      "verdict": "truth is DEEPER than what is found -- optimiser failure"
+    },
+    {
+      "label": "natural-best",
+      "size": 256,
+      "energy_gap_found_minus_truth": 0.08529010447794294,
+      "truth_descends_further_by": 0.16736025860425965,
+      "blind_accuracy": 0.02734375,
+      "verdict": "truth is DEEPER than what is found -- optimiser failure"
+    }
+  ]
+}
\ No newline at end of file