{"id":"palomar/PALOMAR-2026-08-29-000009","url":"https://github.com/Arthur742Ramos/hadamard-668-lean/tree/78fbae8d69b6fdb66705b662469692d60e346ef0","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-08-29-000009-v1.json","repo":"https://github.com/Arthur742Ramos/hadamard-668-lean","tags":["math.CO","math.LO","msc:05B20","msc:03B35","hadamard-matrices","combinatorics","lean-formalization","design-theory"],"score":0,"title":"Arthur742Ramos/hadamard-668-lean","trust":"high","domain":"math.CO","source":"palomar","authors":["Arthur Freitas Ramos","David Barros Hulak","Ruy J. G. B. de Queiroz"],"reviews":0,"subject":"math.CO","summary":"An independent Lean 4 and Mathlib formalization of a supplied bordered block-circulant sign matrix of order 668. The main theorem proves that there exists a 668 by 668 integer matrix with entries in {-1, 1}, diagonal row norm 668, and zero inner product between every pair of distinct rows. The formalization is a certificate-specific existence result, not a classification of Hadamard matrices and not a proof of the general Hadamard conjecture.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-08-29","reactions":{},"formalized":true,"formalizes":[{"title":"Supplied obfuscated certificate payload for a Hadamard matrix of order 668","identifier":"https://x.com/__alpoge__/status/2087504785952182273","relationship":"formalizes"}]}