Regime Operator and Confound-Control Matrix for Light-Probe Experiments: A Technical Appendix to Optical Signatures of Structural Failure Regimes in Immiscible Fluids

This technical appendix supports the light-probe protocol proposed in Optical Signatures of Structural Failure Regimes in Immiscible Fluids. The main protocol proposes that independently classified immiscible-fluid failure regimes should produce distinguishable optical profile families when light is used as a probe. This appendix sharpens that prediction without replacing the main experiment. The appendix introduces a local optical admissibility relation: κ_b · χ(γ, μ_b) ≤ τ_b This expression is not presented as a finished optical law. It is a prediction grammar. In plain terms, optical behavior remains smooth when the cost of mismatch is small enough for the local medium to carry. When local fit fails in different ways, the optical profile should fail in different ways. The appendix maps five Structural Flow failure regimes to five distinct local optical changes: Dissolution weakens readability.Shear fragments compatibility.Drift misaligns registration.Echo repeats without settlement.Lock over-retains history. For each regime, the appendix identifies expected optical effects, ordinary confounds, discriminants, falsifiers, and technical notes. It also includes an effective-geometry crosswalk for readers who think in terms of optical paths, wavefronts, and geometry-like constraints, while keeping that crosswalk subordinate to the experiment. The appendix does not report laboratory results. It does not derive photon theory, Maxwell’s equations, quantum electrodynamics, full wave optics, full General Relativity, or numerical thresholds. It does not claim that optical data alone classify a regime. Its narrower burden is to explain what kind of local optical deformation each prior regime classification predicts, what could imitate it, and what would count against it.