n
30
For issue #1155, target a connected code on the unrestricted, weight-8 frontier with an (n,k) pair absent from the entire leaderboard. This submission recovers a previously constructed literature-derived candidate; it is not a claim of a newly discovered construction. At upstream commit 6995fc4f72a33fcbea27a244da230fcfc370e108, all 663 code documents were checked and none had (n,k) = (30,6).
Screened existing candidate documents for absent pairs, n <= 1000, maximum check weight <= 8, and claimed d <= 40. Fourteen documents met these preliminary filters, including repeated pairs. Three small candidates were evaluated with the trusted candidate gate: (30,6,5), (64,14,8), and (126,8,10). No new random construction sweep was run, and earlier witness-search budgets are unknown.
For submission, the repository CLI regenerated and saved weight-5 witnesses using 20,000 RIS trials per side with seed 0. A 2,000,000-trial optional accelerator budget was requested, but the accelerator was unavailable and that pass did not run. A fresh verifier run on the generated submission found no lighter logical in 3700 RIS trials with seed 132198931.
The trusted candidate gate returned passed: true and board_advancing: true for unrestricted / weight-8. Neither exact-duplicate nor WL-equivalence screening found a match. Its refutation pass found no lighter logical in 3700 RIS trials with seed 839506834. Both stored logical witnesses have weight 5.
The repository's scipy/HiGHS MILP certifier, with a 10-second limit per logical-generator solve, returned exact: true on both sides and d_exact: true: no logical of weight below 5 exists on either side. This is local exact-certifier evidence, not a published maintainer certificate. The submitted JSON deliberately retains upper_bound confidence on both sides pending the maintainer certification workflow.
The combined check-incidence graph reaches all 30 qubits. Maximum check weight is 8 and kd^2/n = 5. The candidate is non-dominated in its target cell; this is not a claim to beat the cell's best efficiency. The trusted validator files were not modified.
(64,14,8) passed validation but was dominated by (64,18,8), weight 8. (126,8,10) passed validation but was dominated by (90,8,10), (108,8,10), (120,8,12), and (126,12,10), all weight 6. Passing validation alone did not make either candidate board-advancing.
Union Alpha 1.0, via the Zed coding-agent harness, assisted with candidate selection, verification, reproduction checks, and submission. The candidate predates this audit; model credit is for this work, not original invention. Tooling: the repository submission CLI, trusted candidate validator, RIS witness search, and scipy/HiGHS MILP certifier. Computation was local CPU work; no paid remote compute was used. Exact elapsed compute for the earlier audit was not recorded.
The inherited provenance cites arXiv:2408.10001v6. That attribution is preserved, but the paper attribution was not independently verified during this audit. Literature novelty remains unverified.
Work over GF(2) with 15-by-15 circulant blocks. Define P by P[i,j] = 1 precisely when j = i+1 modulo 15. Set A = I + P + P^3 + P^4 and B = I + P + P^3 + P^7. Then H_X = [A | B] and H_Z = [B^T | A^T], with left-block qubits 0 through 14 and right-block qubits 15 through 29. Each side has 15 checks. This recipe was compared entry-for-entry against all submitted X and Z supports and matched.
Equivalently, identify t in Z_15 with (t mod 3, t mod 5). The supports on Z_3 x Z_5 are A = [(0,0),(1,1),(0,3),(1,4)] and B = [(0,0),(1,1),(0,3),(1,2)].
The durable matrices and logical witnesses are in codes/30-6-5.json. Re-run structural and witness validation with uv run python verify/qldpc_verify.py codes/30-6-5.json. Re-run the local exact-distance check with uv run python verify/certify.py codes/30-6-5.json --tlim 10.