Fourier granularity and block sensitivity in the relevant-variable recurrence

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.