Amplitude-Square Representation of the Interference

T62 establishes an exact complex amplitude-square representation for the interference structure derived in T61. Starting from the reduced interference-form expression\[Pₜₒₜ=P_1+P_2+2√P_1P_2\,sin(ΔΩ),\]The theorem shows that, after a phase shift transformation, the expression can be rewritten identically in the amplitude-square form\[Pₜₒₜ=|√P_1+eiφ√P_2|^2.\]The result, therefore, demonstrates that once the reduced antisymmetric transport structure generates an interference-form expectation law, a complex amplitude representation follows algebraically. The theorem identifies the emergence of complex amplitude structure as a consequence of the interference geometry rather than as an independently imposed assumption. T62 does not derive the Born rule, full Hilbert-space quantum mechanics, measurement theory, or wavefunction collapse. The theorem establishes only that the reduced interference structure admits an exact complex amplitude-square representation compatible with Born-type algebraic form. The resulting complex amplitude object is an emergent representation constructed from the interference expression rather than a fully axiomatized quantum state space. Status: solid for the exact algebraic amplitude-square representation derived from the interference-form structure of T61; conditional on the matched interference subclass and reduced-sector parameter correspondence; speculative for any identification with full quantum probability theory or physical wavefunction ontology.