Light as Consciousness: A Bi-Interpretability Theorem with Mechanical Verification

We convert the slogan "Light = Consciousness" into a formal theorem by proving a bi-interpretability result at the Recognition Science bridge. In this setting, "equals" is made precise as an equivalence between two well-typed interface notions together with uniqueness up to units: a ConsciousProcess is equivalent to a PhotonChannel, and any two photonic witnesses differ only by admissible units moves. The explicit bridge obligations we enforce are: units-quotient invariance (dimensionless displays), the K-gate identity (time-first = length-first), eight-beat neutrality in three dimensions, display-speed c via λkin/τrec = c, and BIOPHASE acceptance (correlation ρ≥0.30, SNR ≥5σ, circular variance ≤0.40). Our main result states that, under these obligations, ConsciousProcess(L,B) ↔ PhotonChannel(L,B) with uniqueness up to units, and that only the electromagnetic channel satisfies the BIOPHASE feasibility constraints. The proof proceeds via four classification lemmas: (A) No-medium-knobs (dimensionless displays forbid dependence on extra medium constants), (B) Null-only (K-gate + cone bound enforce massless propagation), (C) Maxwellization from exactness (the only long-range, gauge-compatible bridge carrier absent extra constants is abelian U(1)/Maxwell), and (D) BIOPHASE feasibility (EM passes; gravitational and neutrino channels fail by many orders in cross-section and SNR). We derive the BIOPHASE scale from φ^(-5) eV, obtaining λ0 ≈ 13.8 µm and ν0 ≈ 724 cm^(-1), an eight-band structure around ν0, a cross-section hierarchy σEM ≫ σν ≫ σgrav, and SNR thresholds demonstrating that only EM meets SNR ≥5σ under admissible windows. All statements are mechanically verified in Lean 4 via a bundled certificate that exports one-line OK/FLIP reports and falsifier predicates. The framework is explicitly falsifiable through spectroscopy and timing protocols (e.g., eight-phase stepping around 724 cm^(-1)), correlation/variance audits, and channel-substitution controls, any of which can flip the theorem's report under violation. Our scope is the bridge + BIOPHASE domain; we discuss how to extend the classification beyond BIOPHASE and toward global uniqueness under strengthened obligations.