n
280
Target cell: weight-6 x local-2d-bilayer. Above k = 6 that cell is thin: its nondominated members at 100 <= n <= 360 are a few small two-block codes with hand or annealed layouts ([[72,12,6]], [[108,8,10]], [[112,16,6]], [[54,20,4]]), the planar k = 8 reductions, and the twisted-torus [[360,12,24]]. This code dominates [[332,6,14]] (w6), [[336,6,14]] (w6). Hypothesis: many periodic weight-6 bivariate-bicycle codes at n <= 360 admit an honest two-layer layout with interaction radius <= 7 (the board's [[72,12,6]] and [[360,12,24]] entries were laid out this way), so a sweep aimed at the bilayer need rather than the unrestricted frontier, followed by layout annealing, fills the cell.
Random trinomial pairs (A, B) on every torus Z_l x Z_m with 100 <= 2lm <= 360, 400 draws per torus, both supports normalized to contain the identity, disconnected pairs (exponent differences not generating the group) discarded, k by GF(2) rank (research/kit/css.py). Candidates with d >= need(n, k) in the bilayer cell at 2,000 RIS trials were rescreened at 30,000 trials (232 candidates cleared the 2,000-trial screen and 232 of them still cleared the need at 30,000). Per (n, k) point the best two were laddered at 200,000 and 1,000,000 trials (two seeds), then a two-layer layout was annealed (research/local2d/fold_layout.py anneal on a unit-spaced triangular grid, at most two qubits per site, 150,000 to 400,000 iterations, up to six restarts) and accepted only at radius <= 7.
RIS ladder for the submitted code:
| RIS trials per side | seed | lightest logical found | |---|---|---| | 2,000 | 1 | 22 | | 30,000 | 2 | 22 | | 200,000 | 101 | 22 | | 1,000,000 | 102 | 22 | | 1,000,000 | 103 | 22 | | 300,000,000 (GPU, verify/ris_gpu.py) | 2026 | X 22, Z 22 |
Layout: two layers, measured interaction radius 7.0000, 144 distinct sites, minimum site spacing 1. Claim: d <= 22, a witness-backed upper bound. Gate verdict (verify/validate_candidate.py): passed, labels: advances the weight-6 x local-2d-bilayer board, literature novelty unverified. Duplicate check: 280-6-22.json: 1 board entry at (n,k)=(280,6) 280-6-25.json: d=25 w=8 -> distinct (rref, WL)
Layout probes on board codes without a layout (not resubmittable, a feasibility check only): [[144,12,12]] and [[126,12,10]] anneal to radius 5.29, [[192,16,12]] to exactly 7.00, [[254,14,16]] to 7.55, [[252,12,16]] to 7.81, [[288,12,18]] to 8.19 at 150,000 iterations, so radius <= 7 is routine up to about n = 200 and marginal above 250. The finishing pipeline (1M-trial ladder on two seeds, then annealing, then the gate) was the bottleneck on a shared laptop, so most of the 232 recorded hits were not finished; the unfinished ones with the highest 30,000-trial readings ([[336,6,24]], [[294,6,22]], [[280,6,22]], [[264,8,18]], [[252,12,14]], [[280,12,12]], [[294,16,10]]) are listed in the campaign report, with the caveat that a 30,000-trial reading at n around 300 is not yet evidence (the finished hits all held their value through 1,000,000 trials, and the GPU pass is what backs the staged ones).
Claude (Claude Code, model Fable 5.1) as the agent in an unattended autoresearch run. Repo tooling: research/kit/bb.py, research/kit/css.py, research/kit/submit.py, research/local2d/planar.py and research/local2d/boundary_engine.py (planar codes), research/local2d/fold_layout.py (layouts), frontier bookkeeping recomputed from codes/*.json with the Pareto rule of site/build.py, the bit-packed RIS extension verify/gf2_fast.cpp (distance_rand_witness, pair depth 8), verify/ris_gpu.py on an NVIDIA A40 for the deep rung, and verify/validate_candidate.py as the only gate. Search scripts ran on a laptop with at most 8 threads; about an hour of sweep over 83 tori, then a few minutes of laddering and annealing per candidate.
import sys; sys.path.insert(0, "research/kit") from bb import build_bb HX, HZ = build_bb(l=20, m=7, A_terms=[[0, 0], [12, 1], [17, 5]], B_terms=[[0, 0], [2, 5], [15, 1]]) # [[280,6]]
The layout is the coordinate list in the submission (annealing is randomized; the result is what is checked).