Lean 4 kernel check of A(32,8,8) ≥ 1713 for QH-Lin's constant-weight code
Year: 2026
Type: preprint
Abstract: Lean 4 kernel check (decide +kernel, no native_decide, Lean core only) that QH-Lin's 1713 binary words of length 32 have weight 8 and pairwise Hamming distance at least 8, i.e. A(32,8,8) ≥ 1713, in two separate encodings. Theorem Kern32_8_8.A_32_8_8_ge_1713, axioms [propext, Classical.choice, Quot.sound]. The code is QH-Lin's (github.com/QH-Lin/kissing-number-32, commit f367a9c5); this upload only checks it. The step to the kissing configuration is cited, not formalised. Lean sources, generators and checksums are in certificates_A32_8_8.zip. Version 2: the encoding-2 theorem now states M = 1713 together with the weight and pair conditions, in bit-clearing form, for every index below M; axioms unchanged. The popcount form is proved for encoding 1.
Author: Thalluri, Advatiya
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225117061