n
150
Target: the unrestricted x weight-8 cell at n in 111..220 with check weight 7. Only board entries with check weight <= 7 can dominate a weight-7 code; at the time of the search no such entry had n' <= 150, k' >= 33 and d' >= 6, so d = 6 was enough here. The gate's novelty check reports that it advances the frontier (k, n, w); board-relative novelty from verify/validate_candidate.py, literature novelty unverified.
Hypothesis: a lifted product of two one-row bases over a non-abelian group, A = [a1, a2] and B = [b1, b2] with entries of weight 2 and 3, has n = 5|G| and k >= |G|; because left and right supports need not commute, the weight-2 entries need not create the short cycles an abelian group forces, so d can reach 6 at rate above 1/5. Mixing a weight-3 entry into one base lifts the check weight to 7 and buys extra k over the weight-6 shape.
Lifted products of two 1x2 base matrices with entries of weight 2 or 3 (check weight 6..8) over non-abelian groups of order 23..44, n = 5|G|, 1,500 random bases per group. Funnel for this job: 85497 candidates built, 81800 connected with k >= 8 screened at 400 gf2_fast RIS trials, 1 promoted to 20,000 trials, 1 survived it, 1 survived 200,000 trials and 1 survived 2,000,000 trials with the reading still at or above the needed d (a reading below the needed d is final, since the search returns an upper bound).
Witness-backed upper bound d <= 6: the lightest logical operators found are embedded in the submission (distance.X / distance.Z witnesses) and are checked by the verifier. Confirmation ladder on the box (gf2_fast, research/kit/surrogate.distance_rand_witness, 20 threads):
| trials per side | lightest logical found | |---|---| | 400 / 20,000 / 200,000 / 2,000,000 funnel readings | 6 | | 4,000,000 fast RIS trials per side, fresh seed (62868) | 6 (X) | | 4,000,000 fast RIS trials per side, fresh seed (70787) | 6 (X) | | 4,000,000 fast RIS trials per side, fresh seed (78706) | 6 (X) |
Ladder verdict: corroborated (minimum over fresh seeds = 6, claimed 6). The claim is an upper bound; no exactness is asserted.
non-abelian groups of order 28..44: 229,579 bases, 201,685 connected codes; best readings [[160,36,6]] (a board tie), [[200,44,6]] and [[180,40,5]], all dominated by the board's [[160,36,6]] and [[186,64,6]]. No reading reached d = 7 at any k >= 32.
[[150,33,6]] cell three times and nothing better; near misses [[120,25,5]] and [[210,47,5]].
weight 7, far below the weight-7 frontier there (d >= 9 needed).
Model: Claude Opus 5.5 (Claude Code agent, campaign agent A04). Brev n2d-highcpu-64 box, gf2_fast RIS (make fast) with 58 threads; research/kit modules nonabelian_lp / group_algebra / search / surrogate / submit / prescreen; gate = verify/validate_candidate.py via research/kit/coordination.gate_and_record. Approximate compute: 3 box minutes for the sweep plus the ladder above.
The code is the lifted product over the group G = metacyclic(15,2,11)[0] of order 30 (research/kit/nonabelian_lp.lifted_product_base: entries of A act by the left regular representation, entries of B by the right one).
import sys; sys.path[:0] = ['research/kit', 'verify'] from group_algebra import metacyclic, cyclic_product from nonabelian_lp import group_from_name from nonabelian_lp import lifted_product_base mul = metacyclic(15,2,11)[0] HX, HZ = lifted_product_base(mul, [[[0, 23], [0, 2, 16]]], [[[0, 5], [0, 13]]])
Witness search: research/kit/surrogate.lightest_logical (1,500 NumPy trials) tightened by gf2_fast RIS at the funnel depth; the ladder seeds are listed in the table above.