A kissing configuration of 352192 points in R^32 and A(32,8,8) >= 1712: explicit certificates

Explicit, independently checkable certificate for the new lower bound τ₃₂ ≥ 352192 on the kissing number in dimension 32 (previous best 347584, arXiv:2609.35051), obtained from a new binary constant-weight code showing A(32,8,8) ≥ 1712 (previous best 1676).

The configuration is the Edel–Rains–Sloane three-layer construction: 2¹⁷ vectors from the Cheng–Sloane [32,17,8] code, 128 × 1712 even-sign (±2)⁸ vectors on the 1712 supports, and 1984 vectors (±4,±4,0³⁰). The archive contains the 1712 supports, the generator matrix, and verification programs; a brute-force check of all 6.20×10¹⁰ pairs gives maximum inner product 16 at squared norm 32.