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 "name": "[[50,6,4]] weight-6 planar (generalized BB, our record family)",
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 "provenance": {
  "authors": [
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  "origin": "submission",
  "construction": "f = 1 + xy + x^-1 y^2, g = 1 + x^-1 y + x^-2 y^-1; annulus-type boundary engine, (5,5) lattice.",
  "model": "Claude Opus 4.8",
  "references": [
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  "date": "2026-06-16"
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  "notes": "Interleaved memory extraction with joint reset and measurement layers and 7 CX layers per round. Bulk (template) checks follow the Bravyi et al. depth-7 monomial pattern (arXiv:2308.07915 Table 5) applied edge-by-edge via the A/B grid labels (two 5x5 grids); boundary checks were placed by a min-conflicts search enforcing layer parallelism and the X/Z overlap-parity condition, then optimised by a local search whose objective is the exact count of undetected logical fault sets of weight <= 3 (GF(2)-hash enumeration): it reached zero in 374 moves. That count, re-run on the committed DEMs, is zero in both bases, so d_circ = 4 = d is exact for these circuits. The lightest fault sets before optimisation combined an X-check hook, a Z-check hook and a Y error on an X-degree-1 boundary qubit.",
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