Systematics-Orthogonality via Controlled Invariance

T76 establishes a controlled-invariance framework for distinguishing candidate Q5 interferometric signals from ordinary experimental systematics. The theorem begins from the observed residual decomposition\[εobs(φ)=∑_s ε_s(φ)+εQ5(φ),\]and corrects the earlier assumption that Q5 signals could be isolated through function-space orthogonality. Since both ordinary systematics and Q5-consistent residuals generically occupy the same first-harmonic subspace\[span\{cosφ,sinφ\},\]Orthogonality in function space is not an operational discriminator. T76 replaces this with a behavioural criterion based on invariance under controlled experimental transformations. The theorem defines a five-part Q5-consistency protocol. A valid candidate signal must exhibit: first-harmonic confinement, coefficient stability under repeated scans, absence of systematic tracking with controllable nuisance parameters, compliance with the \( Z_4\) phase-cycling rotation law\[vₖ₊₁=Jv_k,\]and persistence after calibration subtraction. Among these conditions, the phase-cycling rotation law inherited from T73 is identified as the strongest discriminator because it tests the specific quarter-turn transport structure predicted by the Q5 framework rather than merely the presence of a harmonic residual. The theorem, therefore, shifts the experimental logic from amplitude fitting to transformation-law verification. T76 is structurally important because it completes the experimental falsification arc initiated in T72-T75. Earlier theorems established the signal form, structural discriminator, statistical detectability threshold, and predicted magnitude scale. T76 adds the final layer: a concrete nuisance-rejection protocol capable of separating Q5-consistent behaviour from conventional interferometric artifacts. The theorem does not claim that unknown systematics cannot mimic the full five-criterion structure, nor does it claim that any existing experiment has observed a Q5 signal. It establishes only the operational framework required for a credible detection claim. Status: solid for the controlled-invariance framework and for the identification of behavioural invariance as the correct replacement for function-space orthogonality; solid for the formulation of the five experimental consistency criteria; conditional on the practical ability to test the \( Z_4\) phase-cycling law and nuisance-parameter independence at sufficient precision; not a claim of positive Q5 detection or uniqueness against all conceivable unknown systematics.