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 "name": "[[84,34,6]] pair-partition CPM CSS code (weight-12)",
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 "provenance": {
  "authors": [
   "Okada, Koki",
   "Kasai, Kenta"
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  "origin": "baseline",
  "construction": "Cyclic all-one pair-partition CPM CSS construction (arXiv:2607.14091), small-p frontier instance qc_84_34_6 (internal id j4_l12_p7_small_frontier_s5): lift size p=7, (J,L)=(4,12), n=12*7=84, 4*7=28 checks per side, column weight 4, row weight 12. CPM exponent arrays (rows = the four CPM block-rows per side, columns = the 12 block-columns): E_X = [[0, 4, 0, 4, 5, 6, 2, 4, 5, 0, 4, 6], [5, 1, 6, 3, 5, 1, 3, 1, 6, 3, 0, 3], [3, 0, 5, 0, 2, 6, 3, 1, 6, 6, 3, 6], [4, 3, 2, 4, 1, 4, 2, 1, 6, 1, 2, 1]], E_Z = [[4, 0, 1, 6, 5, 5, 6, 0, 6, 2, 4, 5], [1, 6, 0, 4, 2, 0, 2, 5, 0, 4, 5, 6], [1, 3, 5, 0, 6, 1, 5, 5, 6, 6, 6, 4], [4, 4, 5, 6, 5, 2, 2, 2, 2, 3, 6, 6]]. Lift convention per the authors' expand_and_verify_cpm_matrices.py (github.com/kasaikenta/pair-partition-cpm-css-codes @ 9c2a6f2): check a of block-row b on side S has support {12*((a - E_S[b][t]) mod 7) + t : t=0..11}. Source: https://kasai.ict.eng.isct.ac.jp/pair_partition_cpm_css_codes_data/certificate_bundles_20260805/qc_84_34_6/certificate_bundle.tar.gz, artifacts/fixed_input/candidate.cpm (sha256 abb5eeef2c2d99f4be5395fafad4aa3d4c8fb309980a28fd4fda6630d86a781d), expanded with the authors' own script.",
  "date": "2026",
  "references": [
   "arXiv:2607.14091"
  ],
  "novelty": "known_parameters",
  "notes": "Literature baseline, seeded 2026-08-14. Published in the certificate-bundle set of the Okada-Kasai pair-partition CPM catalogue (arXiv:2607.14091; certificate_bundles_20260805, directory qc_84_34_6, status exact_distance_machine_verified in master_manifest.json). The authors' bundle gives complete lower-bound exclusion through weight 5 on both sides plus explicit weight-6 logicals, certifying d=6 exactly; the witnesses here are the bundle's published upper_logical_vectors.json entries, re-verified in this repo (kernel membership, row-space non-membership). Marked exact on the strength of that public machine-verified bundle (complete lower-bound exclusion through weight 5 on both sides, SHA-256-pinned artifacts, independent-verifier record included). Per board policy the entry still displays as an upper bound until this repo's own certification. Reproduction was validated end to end: the bundle's fixed-input .cpm expanded with the authors' own script gives a CSS-orthogonal (4,12)-regular pair with GF(2) ranks 25/25 (k=34)."
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}