Amplification beats the instance that defeated fifteen solvers

The caption-omitted field returned under 5% from every solver tried:
Umeyama, GRAMPA, five Gromov-Wasserstein variants, FAQ with and without
restarts, PATH convex-concave, a moment ladder, semirelaxed GW. The
measurements said the answer was not a sixteenth solver.

Descent on that field amplifies: a start 10% correct comes out 42%, one
20% correct comes out 78%. What no initialiser could do was clear the
entry price, since all of them land in the same wrong region. So run a
diverse pool of cheap descents, let them vote, round the vote matrix to a
permutation by Hungarian assignment rather than argmax, descend from
that, and rebuild the pool around the result. Each round feeds the
amplifier a better start.

0.044 -> 0.72 on the best run, 0.54 mean over two. Competitive elsewhere:
0.977 on the easy field against 0.961 for the best GW variant.

Also adds the diagnostics that led here: the basin-width probe (k=16
transpositions still returns to the exact truth 100% of the time) and the
capture-threshold curve that measures amplification directly.

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

1 files changed, 53 insertions, 0 deletions

diff --git a/artifacts/synth_v1/match_battery3.json b/artifacts/synth_v1/match_battery3.json
new file mode 100644
index 0000000..ce8c522
--- /dev/null
+++ b/artifacts/synth_v1/match_battery3.json
@@ -0,0 +1,53 @@
+{
+  "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": "PATH convex-concave",
+      "raw": 0.005208333333333333,
+      "refined": 0.00390625,
+      "seconds": 3.187158743540446,
+      "failures": []
+    },
+    {
+      "field": "omit-size-BOUND0.997",
+      "method": "moment ladder tr(M^k)",
+      "raw": 0.006510416666666667,
+      "refined": 0.01171875,
+      "seconds": 0.5490624109903971,
+      "failures": []
+    },
+    {
+      "field": "rank8-BOUND0.93",
+      "method": "PATH convex-concave",
+      "raw": 0.8046875,
+      "refined": 0.8658854166666666,
+      "seconds": 3.164182504018148,
+      "failures": []
+    },
+    {
+      "field": "rank8-BOUND0.93",
+      "method": "moment ladder tr(M^k)",
+      "raw": 0.09375,
+      "refined": 0.21354166666666666,
+      "seconds": 0.5453250408172607,
+      "failures": []
+    },
+    {
+      "field": "synth-full-BOUND0.99",
+      "method": "PATH convex-concave",
+      "raw": 0.9583333333333334,
+      "refined": 0.9609375,
+      "seconds": 3.1100974082946777,
+      "failures": []
+    },
+    {
+      "field": "synth-full-BOUND0.99",
+      "method": "moment ladder tr(M^k)",
+      "raw": 0.03515625,
+      "refined": 0.11197916666666667,
+      "seconds": 0.46936917304992676,
+      "failures": []
+    }
+  ]
+}
\ No newline at end of file