Influence Bounds for Arbitrary Product Measures

We prove a variance-dependent influence bound for bounded functions on arbitrary finite product spaces. Its constants are independent of all atom probabilities. We derive deterministic approximations of quantum acceptance probabilities. The article includes full analytic derivations, four diagrams, footnotes, examples and appendices. The finite-product theorem has variance exponent five halves. The general sharp exponent-two question remains open here. Original results and their authors retain explicit attribution. Independent peer review and novelty assessment are pending.