The φ-locked framework describes the emergence of stable physical laws via inflationary selection on a direct-sum Hilbert space of incompatible Hamiltonian sectors. While the framework includes a decoherence formalism, ensemble flow, and a gradient flow for couplings, the fundamental collision event — the transition from two parent sectors to a daughter sector — has lacked an explicit operator. This paper supplies that missing operator formalism. We define an inter-sector coupling Hamiltonian H₂₎₋₋ that directly couples distinct sectors when their worldvolumes overlap, with coupling strength derived from the known decoherence rate. We promote the gradient flow's incompatibility term to an operator C₈₉ = (gᵢ - gⱼ) ² and build a Fock space over the direct-sum Hilbert space, interpreting aᵢ^ as creating a new disconnected causal patch. The collision amplitude is written as a time-ordered matrix element, and the form factor is identified from the influence functional's decoherence weight. The complete collision operator recovers the gradient flow in the semi-classical limit. Unitarity is proved. A worked example demonstrates the formalism. Geometric embedding of the overlap state is deferred to future work.
Robert Clark (Sat,) studied this question.