The Geodesic Principle of Inference: Finite Accessibility, Operational Geometry, and Structural Constraints

Arc V — Gravity & Quantum Theory Paper 1 Title The Geodesic Principle of Inference: Finite Accessibility, Operational Geometry, and Structural Constraints Zenodo DOI 10.5281/zenodo.18225935 Description This paper establishes a non-geometric framework in which spacetime geometry and geodesic motion arise as optimal inference structures under finite accessibility. Rather than assuming a metric or gravitational dynamics a priori, the work derives structural constraints on any accessibility-based theory capable of reproducing classical gravity. Using operational distinguishability (via Fisher information), finite signal speed, and minimal inference cost, the paper shows how Lorentzian structure, geodesic motion, and curvature emerge as effective descriptions. A central result is a no-go theorem (“the scalar trap”) demonstrating that scalar accessibility fields cannot reproduce vacuum gravitational phenomena such as Weyl curvature or light bending, thereby proving the necessity of tensorial accessibility for any viable gravity theory. The paper further invokes Lovelock’s uniqueness theorem to show that, once a metric description is adopted, admissibility requirements uniquely select Einstein-form dynamics. Importantly, the work is explicitly a framework paper: it establishes structural necessities and no-go results while deferring all constitutive relations (how matter deforms accessibility) to subsequent work. This paper initiates the Gravity & Quantum Theory arc by cleanly separating structural requirements from constitutive completion and setting the stage for strong-field gravity, accessibility thermodynamics, and post-geometric quantum theory. Keywords emergent gravity; geodesic principle; finite accessibility; inference geometry; Lovelock theorem; scalar no-go theorem; foundations of general relativity Notes Arc V — Gravity & Quantum Theory (framework paper) Establishes structural constraints only Constitutive laws deferred to Papers V.2–V.4 Conceptual bridge from intersubjective geometry to gravity