{"id":"hexagon/2610.00694","pdf":"https://hexagonmath.org/pdf/2610.00694v1","url":"https://hexagonmath.org/abs/2610.00694v1","tags":["msc:06E30","msc:68Q25","msc:68R05","Boolean functions","Fourier granularity","block sensitivity","rational certificates","relevant variables"],"score":0,"title":"Fourier granularity and block sensitivity in the relevant-variable recurrence","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Ricardo Pinho"],"reviews":0,"subject":"math.CO","summary":"Rational Fourier lattice certificates, inserted into the existing local-degree recurrence, give $C_{44}\\le4.1225323803$ for the number of relevant variables of a Boolean function. The finite packet contains 37 block-sensitivity exclusions through degree 40. We explain the certificate criterion and its passage to a bound valid in every degree, and identify the inherited analytic inputs. Neither the small-degree bounds $B_4\\le9$, $B_5\\le14$ nor Fourier granularity is new. This note is unrefereed, with no independent human review or formalization.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-31","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}