Phase-Referenced Interference Test for Structured Phase-Dependent Deviations

This note proposes a simple, falsifiable interferometric test for structured deviations from standard two-path interference. In conventional interference, the observed intensity is described by a single effective phase parameter: \ I () = P₁ + P₂ + 2P₁ P₂, \ and deviations are typically attributed to visibility loss or phase offset. The present protocol tests for a different class of behaviour: phase-locked deviations that depend on the internal structure of the phase profile applied to one arm of the interferometer. A controlled phase modulation of the form ϕ (x) =n⋅f (x) (x) = n f (x) ϕ (x) =n⋅f (x) is introduced in one arm, where nn n indexes the complexity of the imposed phase structure. The resulting interference signal is measured as a function of the global phase and decomposed into quadrature components: \ Iₙ () = Cₙ + Vₙ\![Aₙ + Bₙ. \] A deviation metric is defined relative to the baseline (flat-phase) case: \ ₙ = (Aₙ - A₀) ² + (Bₙ - B₀) ². \ The testable prediction is that, if structured phase-dependent effects are present, then: the baseline satisfies Δ0≈0₀ 0 Δ0≈0; the deviation Δnₙ Δn increases systematically with the imposed phase structure, and the deviation remains phase-locked in the quadrature basis and cannot be absorbed into a simple phase offset. The protocol includes explicit control conditions to distinguish such behaviour from conventional effects: symmetric modulation of both arms should eliminate the deviation; random phase noise should reduce visibility but not produce systematic scaling in Δnₙ Δn; and phase referencing is required to resolve the quadrature structure. The outcome is binary. If no structured deviation is observed, the hypothesis is falsified. If a phase-locked, structure-dependent deviation is observed, then the standard interference model is incomplete under these conditions. This proposal is intentionally model-independent. While motivated by broader work on structured phase transport in discrete systems, the experimental test does not rely on that framework and can be evaluated directly.