Emergent Gravity from Redistribution Microstructure: A ψ₀–OCM Coarse-Grained Mechanism for the Infrared Recovery of General Relativity without a Fundamental Graviton

This work develops the ψ₀–OCM (Osborne Cosmological Model) as a mechanism-level framework in which gravitational behaviour emerges from redistribution dynamics within a primordial substrate field ψ₀. Spacetime curvature is interpreted as the macroscopic response of this redistribution substrate, with discrete curvature modes arising from stabilisation of partially resolved microstructure. A parent action is constructed whose coarse-grained variation reduces to the Einstein field equations in the infrared limit while allowing resolution-dependent corrections governed by a suppression window W(Λres). The framework preserves locality, causality, and energy–momentum conservation while allowing regime-dependent deviations in strong-field or partially resolved environments. Core Mechanism The model constructs a resolution-dependent curvature response based on three structural elements: • a microstructure correlation length governing redistribution granularity• stabilisation gating that selects admissible persistent curvature modes• a renormalisation-style resolution flow linking microstructure dynamics to macroscopic gravitational behaviour Within this structure, quantised curvature behaviour arises as a constraint-driven regime associated with partially resolved redistribution microstructure rather than as a fundamental property of spacetime geometry. Projection Limits and External Form Recoveries Under specific coarse-graining conditions the framework reproduces known gravitational descriptions as effective projection limits: • Einstein gravity in the infrared coarse-grained regime• entropic-gravity form as a near-equilibrium boundary projection• Verlinde-type galaxy scaling as an optional phenomenological interface in a de Sitter–screen limit These correspondences arise as projection limits of the parent redistribution dynamics rather than as foundational assumptions. Observationally Testable Predictions The ψ₀–OCM generates falsifiable predictions tied to redistribution microstructure scales: • mode-dependent black hole ringdown deviations associated with horizon-scale microstructure• scale-dependent effective gravitational coupling flowing toward Newton’s constant under coarse-graining• discrete curvature resonance scales in extreme-density regimes where stabilisation selects isolated modes• regime-localised cosmological non-Gaussianity linked to incomplete coarse-graining during early-universe structure formation All deviations vanish in the infrared limit, ensuring compatibility with precision tests of General Relativity. Distinction from Existing Approaches Unlike effective field theory extensions of gravity, which introduce local higher-curvature corrections, the ψ₀–OCM predicts deviations governed by resolution scale and redistribution microstructure. Unlike equilibrium entropic-gravity models, the framework allows non-equilibrium regimes, discrete curvature spectra, and environment-dependent gravitational responses. Scope and Interpretation The framework does not posit particle dark matter. Apparent “dark” gravitational responses arising in projection limits are interpreted as effective parameterisations of coarse-grained horizon entropy sectors rather than evidence for new particle species. Scientific Contribution By linking microstructure scales to measurable gravitational deviations, the ψ₀–OCM provides a mechanistic pathway from substrate dynamics to observational constraints in strong-field gravity and cosmology. The framework offers a regime-structured alternative to graviton-based quantisation, effective field-theory corrections, and purely thermodynamic emergent-gravity models.