C=2A: Unifying Quantum Measurement, Gravitational Collapse, and Consciousness

Problem: Quantum measurement, gravity-driven reduction, and the definiteness of conscious experience are usually treated as separate puzzles. We lack an exact, parameter-free mechanism that simultaneously explains Born weights in measurement, the onset of collapse in gravity-related proposals, and the conditions under which experience becomes definite. A successful account should be local, predictive, and falsifiable, with a single threshold that governs all three.

Bridge: We propose and substantiate an exact identity C = 2A between a recognition path action C, derived from a unique convex cost 1/2 (x + 1/x) - 1, and a residual (gravitational) rate action A computed along two-branch geodesics. This identity fixes probabilities via e^(-C) = e^(-2A), determines the amplitude modulus |A| = e^(-C/2) = e^(-A), and eliminates free parameters. The construction is local and admits formal verification.

Triple unification: Three phenomena emerge as facets of one process regulated by the same threshold. (i) Quantum measurement: Born weights obey P = e^(-C) = e^(-2A). (ii) Gravitational collapse: reduction occurs when A ≥ 1. (iii) Consciousness: definite experience arises when C ≥ 1 and A ≥ 1, i.e., when a Consciousness Hamiltonian reaches a local minimum at the shared boundary. Thus, measurement, gravity, and consciousness coincide at C = 2A.

Predictions: The framework yields parameter-free mesoscopic scaling: coherence is lost when τ_m |Φ_12| ~ 1 (nanogram-second regime), implying A ~ 1 and C ~ 2. It predicts modest observer-dependent modulation of decoherence via mutual information between agent and environment, testable with randomized, double-blind attention protocols. Strong falsifiers include threshold mismatches between C and A, absence of the expected mass scaling, and null observer-coupling effects. These near-term tests can decisively support or refute the C = 2A bridge.