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Cavity polycubes: source, data, and verification artifacts for enumeration to size 18

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Zenodo2026-08-15 更新2026-08-20 收录
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Companion archive to the paper "Polycubes with Cavities: Enumeration to Size 18 and Corrections to Published Counts". A polycube has a cavity when its complement in Z^3 is disconnected, i.e. when it completely encloses empty space. This archive contains the exhaustive enumerators, the independent recounting programs, the exhaustive scans underlying the paper's computer-assisted proofs, and the raw per-job outputs of every production run. Included: the production enumerator and the Phase-2 engine; two independent recounters, one of which classifies by canonical form rather than by orbit-stabilizer summation; the minimum-degree scan supporting Proposition 2; the evasion-gate scan; the finite base-case verification for the Shell Connection Lemma; the complete n = 14 cavity-polycube dataset; and per-part outputs for the n = 15 to n = 18 runs under both the production threshold and the unconditionally-exact threshold. REPRODUCE.md gives build instructions, exact command lines, machine specifications, a one-minute worked example reproducing the published counts at n = 13, and an explicit statement of what is not included and why. The work extends OEIS sequences A357083 and A355966, contributes A396101, and corrects two previously published values.

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2026-08-15
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