From 22acd2899958def0d103f11da49c2c4a499be773 Mon Sep 17 00:00:00 2001 From: YurenHao0426 Date: Sat, 1 Aug 2026 21:37:55 -0500 Subject: 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 --- .../eval_impure_anchors.log | 60 ++++++++++++++++++++++ 1 file changed, 60 insertions(+) create mode 100644 artifacts/spectral_frontier_probe/eval_impure_anchors.log (limited to 'artifacts/spectral_frontier_probe/eval_impure_anchors.log') diff --git a/artifacts/spectral_frontier_probe/eval_impure_anchors.log b/artifacts/spectral_frontier_probe/eval_impure_anchors.log new file mode 100644 index 0000000..a4b957a --- /dev/null +++ b/artifacts/spectral_frontier_probe/eval_impure_anchors.log @@ -0,0 +1,60 @@ +=== (a) PURE random anchors: reproduce the published curve === + K= 12 pure accuracy 0.589 +- 0.055 + K= 25 pure accuracy 0.860 +- 0.058 + K= 40 pure accuracy 0.926 +- 0.032 + K= 50 pure accuracy 0.949 +- 0.026 + K= 64 pure accuracy 0.971 +- 0.017 + K= 128 pure accuracy 0.996 +- 0.005 + +=== (b) IMPURE random anchors: c correct, K-c wrong (wrong = derangement among selected) === + K= 12 prec=1.00 (12/12 right) accuracy 0.620 +- 0.093 + K= 12 prec=0.92 (10/12 right) accuracy 0.390 +- 0.101 + K= 12 prec=0.88 (10/12 right) accuracy 0.399 +- 0.109 + K= 12 prec=0.84 (10/12 right) accuracy 0.330 +- 0.098 + K= 12 prec=0.80 (10/12 right) accuracy 0.408 +- 0.120 + K= 12 prec=0.72 (9/12 right) accuracy 0.264 +- 0.068 + K= 12 prec=0.60 (7/12 right) accuracy 0.135 +- 0.064 + + K= 25 prec=1.00 (25/25 right) accuracy 0.852 +- 0.049 + K= 25 prec=0.92 (23/25 right) accuracy 0.766 +- 0.073 + K= 25 prec=0.88 (22/25 right) accuracy 0.746 +- 0.071 + K= 25 prec=0.84 (21/25 right) accuracy 0.704 +- 0.079 + K= 25 prec=0.80 (20/25 right) accuracy 0.677 +- 0.070 + K= 25 prec=0.72 (18/25 right) accuracy 0.527 +- 0.103 + K= 25 prec=0.60 (15/25 right) accuracy 0.371 +- 0.091 + + K= 40 prec=1.00 (40/40 right) accuracy 0.933 +- 0.032 + K= 40 prec=0.92 (37/40 right) accuracy 0.902 +- 0.038 + K= 40 prec=0.88 (35/40 right) accuracy 0.859 +- 0.037 + K= 40 prec=0.84 (34/40 right) accuracy 0.835 +- 0.038 + K= 40 prec=0.80 (32/40 right) accuracy 0.812 +- 0.047 + K= 40 prec=0.72 (29/40 right) accuracy 0.742 +- 0.085 + K= 40 prec=0.60 (24/40 right) accuracy 0.574 +- 0.081 + + K= 50 prec=1.00 (50/50 right) accuracy 0.950 +- 0.024 + K= 50 prec=0.92 (46/50 right) accuracy 0.920 +- 0.026 + K= 50 prec=0.88 (44/50 right) accuracy 0.893 +- 0.033 + K= 50 prec=0.84 (42/50 right) accuracy 0.877 +- 0.033 + K= 50 prec=0.80 (40/50 right) accuracy 0.855 +- 0.031 + K= 50 prec=0.72 (36/50 right) accuracy 0.783 +- 0.055 + K= 50 prec=0.60 (30/50 right) accuracy 0.629 +- 0.102 + + K= 100 prec=1.00 (100/100 right) accuracy 0.992 +- 0.009 + K= 100 prec=0.92 (92/100 right) accuracy 0.953 +- 0.014 + K= 100 prec=0.88 (88/100 right) accuracy 0.933 +- 0.016 + K= 100 prec=0.84 (84/100 right) accuracy 0.915 +- 0.018 + K= 100 prec=0.80 (80/100 right) accuracy 0.895 +- 0.012 + K= 100 prec=0.72 (72/100 right) accuracy 0.852 +- 0.020 + K= 100 prec=0.60 (60/100 right) accuracy 0.787 +- 0.021 + +=== (c) IMPURE with wrong partners drawn from OUTSIDE the anchor set === + K= 25 prec=1.00 accuracy 0.866 +- 0.040 + K= 25 prec=0.88 accuracy 0.729 +- 0.064 + K= 25 prec=0.84 accuracy 0.689 +- 0.070 + K= 25 prec=0.80 accuracy 0.603 +- 0.079 + K= 25 prec=0.72 accuracy 0.501 +- 0.094 + K= 50 prec=1.00 accuracy 0.945 +- 0.025 + K= 50 prec=0.88 accuracy 0.832 +- 0.031 + K= 50 prec=0.84 accuracy 0.808 +- 0.020 + K= 50 prec=0.80 accuracy 0.775 +- 0.031 + K= 50 prec=0.72 accuracy 0.689 +- 0.043 -- cgit v1.2.3