World-Alignment.git/artifacts/vg_5k/anchor_bound_reprice.json, branch main Unnamed repository; edit this file 'description' to name the repository. The failure is the optimiser, not the information: a 257x faster descent and a benchmark 2026-08-01T22:59:32+00:00 YurenHao0426 Blackhao0426@gmail.com 2026-08-01T22:59:32+00:00 4f7ee05cc3b072478062e53645af016861c4b529 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> 
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>