Light as Consciousness A Universal Information-Cost Identity with Classification and Mechanical Verification

We show that a single, uniquely determined information-cost functional governs quantum measurement, photonic operations, and operational conscious selection, establishing an identity at the level of information processing. Under four standard axioms on R > 0 -- multiplicative symmetry, normalization, strict convexity, and unit curvature -- there exists a unique cost J(x) = 1/2 (x + x^-1) - 1 (proved in [1]). For two-branch quantum rotations, the recognition cost C = J(r) dt equals twice the rate action A (exactly C = 2A), yielding Born weights w = exp(-C) = |alpha|^2 without additional postulates. We then prove a classification theorem: under bridge obligations (units-quotient invariance, K-gate identity, eight-beat neutrality, display-speed c), a ConsciousProcess is bi-interpretable with a PhotonChannel, unique up to units, and only the electromagnetic channel satisfies feasibility constraints. The classification proceeds via four lemmas: (A) No-medium-knobs, (B) Null-only propagation, (C) Maxwellization (only abelian U(1) is parameter-free), and (D) BIOPHASE feasibility (sigma_EM >> sigma_nu >> sigma_grav). Core theorems are mechanically verified in Lean 4. Falsifiable predictions include cross-domain coherence floors, additive J-scaling in photonic frequency chains, and eight-phase spectroscopic signatures at 724 cm^-1.