Towards a Unified Physics: The Mathematical Foundation of the Discrete Gravitational Ontology (DGO)

This paper presents the mathematical foundation of the Discrete Gravitational Ontology (DGO)
— a unified framework linking quantum mechanics, general relativity, and the arrow of time
through a discrete relational substrate. Building on three prior works (Asplind, 2025a–c), this
paper formalizes DGO using coarse-graining, Gamma-convergence, and renormalization group
(RG) flow, deriving Einstein’s equations and quantum behavior as emergent limits.
Key insights:
• Gravity is not a field in spacetime; it is the substrate of spacetime.
• Spacetime, matter, and quantum behavior emerge from discrete gravitational relations.
• Gamma-convergence demonstrates that general relativity is a macroscopic limit.
• Probabilistic updates reproduce quantum interference and entanglement.
• The effective Newton constant Geff(L) evolves with scale, yielding testable predictions.

Testability: DGO predicts observable deviations from Newton’s law at sub-millimeter
scales, potential gravitational wave anomalies, and cosmological implications from the running
of Geff(L).