Noise smoothing sharpens a quantitative Aaronson-Ambainis influence bound

Research preprint archive including the manuscript PDF, LaTeX source and document checks. Noise smoothing and classical Bernstein control, composed with Turturean's influence theorem, give max_i Inf_i(f) >= sqrt(45)/(16000 pi^4) Var(f)^(5/2)/d^(11/2) for every bounded real multilinear polynomial on the uniform sign cube. The note includes an explicit average-input query consequence, without a polynomial-runtime claim. This is a quantitative corollary of attributed results; no independent AA proof, peer review, formal certification or established priority is claimed. OpenAI Codex assisted with mathematical derivation, source comparison, drafting and package preparation.