GCFT-0433: Constructive BF Kernel — A Peter-Weyl Candidate for the SM-G02 Weak-Angle Endpoint

This paper proposes a constructive S³ heat-damped BF kernel that analytically generates the first Peter-Weyl coefficient, defines the electroweak projection, and produces a candidate weak mixing angle within the previously established GCFT-0427 tolerance. The work explicitly distinguishes this constructive source object from earlier archival material and retains open precision electroweak scheme corrections and remaining Standard Model validation gates. The publication presents a candidate SM-G02 closure while not claiming complete Standard Model derivation.