{"id":"palomar/PALOMAR-2026-11-03-000024","url":"https://github.com/L-iet/HadamardBound/tree/4b8a125af5c8c94e183df8ddc1a4e9f262f9abbe","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-11-03-000024-v1.json","repo":"https://github.com/L-iet/HadamardBound","tags":["math.CO","math.NT","msc:05B20","msc:11J25","msc:68V20"],"score":0,"title":"Sparse multi-base representations and asymptotic Hadamard existence","trust":"high","domain":"math.CO","source":"palomar","authors":["Joshua Mark"],"reviews":0,"subject":"math.CO","summary":"Lean formalization of sparse multi-base representations and unconditional asymptotic Hadamard existence, gap, flatness and conditioning bounds. The required logarithm-ratio separation is proved independently from mathlib.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-11-03","reactions":{},"formalized":true,"formalizes":[{"title":"Sparse Multi-Base Representations and Asymptotic Existence of Hadamard Matrices","identifier":"","relationship":"formalizes"}]}