T74 establishes the statistical detection threshold for the Q5 phase-cycling signal developed in T72 and T73. Starting from the single-scan fringe residual\ () =2P₁P₂[ (A-1) + B, \]The theorem defines the intrinsic bias magnitude\= (A-1) ²+B², proves that the maximum balanced-path residual amplitude satisfies\_=. key refinement is introduced: measurement of a first-harmonic bias alone is not operationally sufficient for Q5 detection, because such a bias can be absorbed into standard interferometric fitting parameters. The correct discriminator is therefore the phase-cycling invariantₐ₅=₊=₀^3|v₊+₁-Jvₖ|², tests whether the measured quadrature evolution obeys the expected \ (Z₄\) cycling structure established in T73. T74 proves that Q5 detectability requires two simultaneous conditions. First, the intrinsic signal scale must exceed the statistical shot-noise floor, \ ₍, \ (N\) is the photon count and \ (N_\) is the required detection significance. Second, the observed phase evolution must remain consistent with the Q5 phase-cycling law through sufficiently small \ (Iₐ₅\), distinguishing genuine Q5-compatible structure from ordinary calibration artifacts. Under shot-noise scaling, the minimum detectable bias obeys\_ ₍. \ T74 is structurally important because it completes the minimal experimental prediction arc initiated in T72 and T73 by separating signal shape, structural discriminator, and statistical detectability. The theorem converts the earlier transport-cycling framework into a falsifiable interferometric prediction program with explicitly identified observables, structural consistency conditions, and detection scaling laws. Status: solid for the fringe-residual amplitude relations and shot-noise detection-threshold scaling under the stated assumptions; solid for the necessity of combining signal magnitude with structural phase-cycling discrimination; conditional on the T73 \ (Z₄\) cycling framework and practical extraction of quadrature vectors; speculative for the existence or magnitude of any physical Q5 signal prior to empirical observation.
Craig Edwin Holdway (Sat,) studied this question.