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. In this model, spacetime curvature is not treated as fundamental, but as the macroscopic response of a deeper redistribution substrate. Einsteinian gravity is therefore interpreted as an infrared closure of underlying microstructure rather than as the deepest gravitational ontology. 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 effective energy–momentum conservation, while permitting regime-dependent departures from General Relativity in strong-field or partially resolved environments. Core Mechanism The gravitational sector is built from three linked structural elements: • a redistribution microstructure correlation scale governing the granularity of the underlying substrate • stabilisation gating that selects admissible persistent curvature responses • a renormalisation-style resolution flow connecting microscopic redistribution dynamics to macroscopic gravitational behaviour Within this structure, discrete curvature behaviour appears through stabilised response modes associated with partially resolved redistribution microstructure rather than through a fundamental graviton field. Gravity is thus treated as an emergent curvature regime of the substrate, not as an irreducible gauge interaction. Weak/Strong Gravity Regime Structure The framework is explicitly regime-structured. • In the weak-gravity regime, redistribution microstructure is sufficiently suppressed by coarse-graining that the effective curvature response approaches the Einstein field equations. • In the strong-gravity regime, routing activity, boundary-locking, occupancy structure, and unresolved redistribution support become dynamically relevant, so departures from the simplest Einsteinian closure are expected. Strong gravity is therefore not treated as an external complication or pathological limit, but as a physically meaningful regime in which the deeper redistribution architecture becomes more directly exposed. Projection Limits and External Form Recoveries Under specific coarse-graining and boundary 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. The model therefore treats standard gravitational descriptions as effective readouts of a deeper substrate process rather than as primitive starting points. Dark-Sector Interpretation The framework also provides a unified substrate-level interpretation of dark-sector phenomenology. • dark matter-like behaviour is interpreted as stabilised, gravitationally active redistribution support not exhausted by luminous matter • dark energy-like behaviour is interpreted as a diffuse long-wavelength redistribution-pressure sector On this view, gravity, excess gravitating support, and large-scale acceleration are not treated as disconnected theoretical inputs, but as distinct effective regimes of the same underlying redistribution architecture. Observationally Testable Predictions The ψ₀–OCM generates falsifiable predictions tied to redistribution microstructure and resolution scale: • mode-dependent black hole ringdown deviations associated with near-horizon 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 A central point of the framework is that these deviations are not arbitrary. They are tied to the suppression window and must vanish in the infrared limit, ensuring compatibility with precision tests of General Relativity in sufficiently coarse-grained regimes. Distinction from Existing Approaches The ψ₀–OCM differs from existing approaches in both mechanism and ontological scope. • Unlike graviton-based approaches, it does not begin by assuming gravity is fundamentally quantised. • Unlike effective field-theory extensions, it does not treat departures from General Relativity as merely local higher-curvature corrections. • Unlike equilibrium entropic-gravity models, it allows non-equilibrium regimes, discrete curvature spectra, and environment-dependent gravitational responses tied to redistribution microstructure. The framework instead proposes that gravitational behaviour is the coarse-grained curvature response of a redistribution substrate, with different observational regimes emerging as different levels of microstructure exposure. Scope and Interpretation This work is concerned with emergent gravity, infrared General Relativity recovery, strong/weak regime structure, and dark-sector interpretation within the ψ₀–OCM. It does not attempt a complete ultraviolet completion of gravity, nor does it require particle dark matter as a primitive assumption. Apparent dark gravitational responses arising in projection limits are interpreted as effective manifestations of redistribution structure rather than as immediate evidence for new particle species. Scientific Contribution By linking substrate-level redistribution dynamics to measurable gravitational deviations, the ψ₀–OCM provides a mechanistic pathway from primordial structure to observational constraint in strong-field gravity, galactic phenomenology, and cosmology. The work positions General Relativity as an infrared limit of a deeper redistribution framework and offers a regime-structured alternative to graviton-based quantisation, local effective field-theory correction models, and purely thermodynamic emergent-gravity accounts. This release presents the emergent-gravity architecture of the ψ₀–OCM together with its reduction logic, regime structure, and principal observational discriminants.