Formal proof and numerical validation that QPE dispersive photon counting, beamsplitter-mediated Fock-state entanglement, and bosonic stimulated emission compose without operator conflict, yielding a unified scan-rate equation R = RQPE (0) × N² × (m+1) ². Extends and corrects the Axion Hunter 1. 0 XPRIZE submission (DOI: 10. 5281/zenodo. 18806641). All results independently reproducible via three companion Python scripts.
Christopher Head (Sun,) studied this question.