Calibration-Invariant Q5 Signature

T78 establishes the first calibration-invariant experimental signature proposed for Q5-consistent interferometric residuals. Earlier theorems showed that a raw first-harmonic residual of the form\[ε(φ)=αcosφ+βsinφ\]is not diagnostically meaningful on its own because it can be absorbed into ordinary fitted fringe parameters such as visibility and phase offset. The theorem further demonstrates that simple scalar constructions, including alternating quarter-phase sums, also fail identically for generic first-harmonic signals. T78 therefore shifts the experimental focus away from scalar residual magnitude and toward transformation structure in quadrature space. The central construction is the quadrature-vector formulation. For each controlled quarter-phase offset, the residual is decomposed into quadrature coefficients\[v_k=(α_k,β_k),\]and the theorem proves that quarter-phase stepping induces the rotation law\[vₖ₊₁=Jv_k,\]where\[J={pmatrix}0&-1\\1&0{pmatrix}\]is the \(90^∘\) rotation operator. Iteration produces the characteristic four-step cycle\[(α,β)→(-β,α)→(-α,-β)→(β,-α)→(α,β).\]The associated Q5 cycling defect\[ IQ5=∑ₖ₌₀³|vₖ₊₁-Jv_k|^2\]vanishes for an ideal quadrature-locked signal and serves as the operational invariant tested experimentally. T78 reframes the interferometric search strategy developed in T72-T77. The relevant question is no longer simply whether a small fringe residual exists, but whether the residual transforms as a \( Z_4\)-structured quadrature object under controlled quarter-phase cycling. Generic uncontrolled systematics may generate first-harmonic residuals, but they do not generally preserve stable quarter-turn quadrature transport behaviour across repeated phase cycling. The theorem, therefore, identifies quadrature-cycling structure, rather than raw fringe bias alone, as the first genuinely nontrivial falsifiable signature in the Q5 interferometric program. Status: solid for the derivation of the quarter-phase rotation law from first-harmonic quadrature transport and for the definition of the cycling defect invariant \( IQ5\); solid that ideal quadrature-locked cycling implies \( IQ5=0\); conditional as an experimental discriminator because sufficiently engineered systematics could in principle mimic the same cycling behavior; not a claim that observation of \( IQ5≈0\) alone would establish Q5 transport physics.