Emergent Generator from Barrier Transport (Reduced Form)

T64 develops the projective-state geometry naturally induced by the interference and amplitude structures established in T61-T63. Once the reduced transport framework admits an exact complex amplitude-square representation,\[Pₜₒₜ=|ψ|^2,\]global phase transformations of the form\[ψ ~ eiθψ\]leave all amplitude-square observables invariant. The theorem therefore identifies physically equivalent amplitude states as phase-equivalence classes, producing a natural projective quotient structure on the reduced state space. Observable content depends only on the equivalence class of the amplitude representation rather than on a particular global phase representative. T64 is structurally important because it shifts the framework from interference algebra toward quotient-state geometry. The theorem shows that once interference-compatible complex amplitudes emerge, projective equivalence becomes unavoidable as a consequence of phase redundancy in the observable sector. The result does not derive the full structure of projective Hilbert-space quantum mechanics, but it establishes that the Q5 interference architecture naturally descends to a projective amplitude geometry after elimination of globally redundant phase information. Status: solid for the phase-equivalence and projective quotient structure induced by amplitude-square invariance; conditional on the amplitude representation framework established in T61-T63; speculative for any claim of complete equivalence with full quantum projective Hilbert geometry or wavefunction ontology.