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

Abstract

We formalize “Light = Consciousness” as a bi‑interpretability theorem at the Recognition Science bridge: a ConsciousProcess is equivalent to a PhotonChannel, with uniqueness up to admissible units moves. The bridge obligations include units‑quotient invariance (dimensionless displays), the K‑gate identity (time‑first = length‑first), eight‑beat neutrality in three dimensions, the display‑speed identity (λ_kin/τ_rec = c), and BIOPHASE acceptance thresholds (ρ ≥ 0.30, SNR ≥ 5σ, circular variance ≤ 0.40). Under these obligations, ConsciousProcess(L,B) ⇔ PhotonChannel(L,B), and only the electromagnetic channel satisfies BIOPHASE feasibility. Proof proceeds via four classification lemmas (no‑medium‑knobs, null‑only, Maxwellization, BIOPHASE feasibility) and is mechanically verified in Lean 4 with bundled OK/FLIP reports and falsifiers.