Distinguishability Geometry as a Universal Foundation for Physical Dynamics

<title>Abstract</title> <p> We take physical distinguishability as the sole primitive of physics: two states are distinct if and only if some measurement can tell them apart. From this single principle, a geometry emerges on the space of all physical states. Its universal threshold — the point where the rate of change of distinguishability saturates — is simultaneously the quantum speed limit, the event horizon of a black hole, and the critical point of a thermodynamic phase transition. Quantum mechanics, general relativity, and thermodynamics are three expressions of the same geometric threshold on different state spaces; the constants ℏ, <italic>c</italic> , and <italic>k</italic> _B are conversion factors between them. Within this structure, we identify a parameter-free geometric mechanism that yields the Schrödinger equation; the Einstein field equations, exactly on the horizon and in the bulk to corrections below 10⁻³² for stationary configurations (the fully dynamical case is not established here); the Lorentzian signature of spacetime; and a structural mechanism that reduces the standard 10¹²³ discrepancy of the cosmological constant problem to order unity, conditional on two framework-internal postulates (Section 13.8). Applying this, the framework evaluates a vacuum length scale of ~88 μm and energy ~2.25 meV from the observed dark-energy density, placing the dominant source in the lightest neutrino sector. The framework further suggests that macroscopic quantum coherence suppresses geodesic distinguishability — the Bose–Einstein condensate (BEC) analogue of the Meissner effect — with a predicted breathing-mode shift of ~1.5 mHz in ⁸⁷Rb. IBM Quantum experiments on three independent 156-qubit Heron processors show excitation probabilities differing by a factor of ≈3.7 across protocols with identical control parameters but different geometric paths, consistent with the prediction that endpoint distinguishability governs the outcome. Cross-backend transfer errors remain below 1%. Physical reality is what is distinguishable. The laws of nature are the geometry of distinguishability. </p>