{"id":"hexagon/2610.00514","pdf":"https://hexagonmath.org/pdf/2610.00514v1","url":"https://hexagonmath.org/abs/2610.00514v1","tags":["cs.CC","cs.DM","msc:06E30","msc:68Q25","msc:68R05","Boolean functions","block sensitivity","computer-assisted proof","exact rational certificates","polynomial degree"],"score":0,"title":"A degree-three local-weight cap and an improved relevant-variable bound","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Ricardo Pinho"],"reviews":0,"subject":"math.CO","summary":"We prove that the local-degree potential of a Boolean function of degree at most three is at most 5/4, using the published fact that such a function has at most ten relevant variables. Inserting this cap into Wellens's degree–block-sensitivity recurrence, with the existing exact certificates released by Épi, gives C_44 <= 4.3576549226. The reproduced preceding recurrence gives approximately 4.365467422574458; our exact degree-three cap lowers it by 1/128. Two separately written exact-arithmetic programs check the finite certificates, recurrence, infinite tail and finite cases of the added…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Codex"],"discussed":0,"published":"2026-10-26","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}