Title: Light as Consciousness: A Bi-Interpretability Theorem with Mechanical Verification
Alternate title: Photonic Equivalence of Operational Consciousness at the RS Bridge
Author: Jonathan Washburn
Affiliation: Recognition Physics

Abstract:
We formalize “Light = Consciousness” as a bi-interpretability theorem at the Recognition Science bridge. “Equals” is made precise as an equivalence between two well-typed interface notions with uniqueness up to units: a ConsciousProcess is equivalent to a PhotonChannel, and any two photonic witnesses differ only by admissible units moves. The enforced bridge obligations are: units-quotient invariance (dimensionless displays), K-gate identity (time-first = length-first), eight-beat neutrality in three dimensions, display-speed identity c via lambda_kin / tau_rec = c, and BIOPHASE acceptance (correlation rho ≥ 0.30, SNR ≥ 5σ, circular variance ≤ 0.40). Under these obligations, ConsciousProcess(L,B) ↔ PhotonChannel(L,B) with uniqueness up to units, and only the electromagnetic channel satisfies the BIOPHASE feasibility constraints.

The proof proceeds via four classification lemmas: (A) No-medium-knobs (dimensionless displays forbid 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 phi^-5 eV, obtaining lambda0 ≈ 13.8 µm and nu0 ≈ 724 cm^-1, an eight-band structure around nu0, a cross-section hierarchy sigma_EM >> sigma_nu >> sigma_grav, 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 with OK/FLIP reports and falsifier predicates; the framework is explicitly falsifiable via spectroscopy and timing protocols.