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 },
 "distance": {
  "d": 8,
  "X": {
   "value": 8,
   "confidence": "upper_bound",
   "witness": [
    4,
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   ]
  },
  "Z": {
   "value": 8,
   "confidence": "upper_bound",
   "witness": [
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   ]
  }
 },
 "provenance": {
  "authors": [
   "@msilve160"
  ],
  "construction": "Lifted product of two 2x3 monomial base matrices A, B over F_2[G], G = Z_8 x|_5 Z_4 (metacyclic, relation y x = x^5 y) (|G|=32), entries acting by the left (A) and right (B) regular representation (research/kit/nonabelian_lp.py, lifted_product_base). n = 13|G|, check weight 5 (row weight 3 of A + row weight 2 of B, and vice versa). Same construction family as arXiv:2607.28795 (mitten codes) / arXiv:2607.27644 (ZSZ lifted products), at lower entry weight (monomial, not trinomial) than the published weight-9 form. Reproduces a candidate flagged but not submitted in fieldnotes/2026-09-16-lifted-product-girth-cap.md (Finding 5), found via the merged research/kit/nonabelian_lp.sample_nonabelian_lp sampler. This gap in the check-weight-5 region of the board was found by @vprusso (using Claude Fable 5.1), who also wrote research/kit/nonabelian_lp.py and submitted the neighboring codes/624-52-9.json from the same campaign; see fieldnotes/2026-09-16-lifted-product-girth-cap.md for the original search (this submission reproduces one of that campaign's flagged-but-unsubmitted points using the already-merged tooling).",
  "references": [
   "arXiv:2607.28795",
   "arXiv:2607.27644"
  ],
  "date": "2026-09-19",
  "notes": "",
  "model": "Claude Sonnet 5"
 },
 "family": "lifted-product"
}