This repository contains the preprint “Emergent Geometry from a Discrete Capacity Substrate”, which presents a speculative but internally constrained derivation of classical spacetime geometry from a discrete, capacity-bounded informational substrate. The work is formulated within the Space Register Metric – Planck Pixel Asymmetry (SRM–PPA) framework. In this ontology, the fundamental degrees of freedom are discrete registers with finite adjacency, causal partial order, and locally conserved information capacity. No background manifold, metric, or quantum field theory on curved spacetime is assumed at the fundamental level. The main result of the preprint is a derivation in which: Coarse-grained transport of conserved capacity defines an effective inverse spacetime metric. Capacity congruences obey a Raychaudhuri-like focusing equation. The Einstein field equations arise as an integrability condition ensuring consistency of capacity focusing across all congruences and coarse-grainings, rather than as fundamental dynamical postulates. Geometry and gravitation are thus interpreted as emergent bookkeeping structures for constrained capacity transport, rather than as primitive entities. The construction is structurally analogous to thermodynamic and information-theoretic approaches to gravity, but differs in that it begins from a fully discrete substrate without assuming continuum spacetime or horizon thermodynamics. The paper is deliberately limited in scope. Quantum theory, gauge interactions, and particle content are not assumed and are left for future work. Nevertheless, the framework yields qualitative phenomenological consequences, including modifications to gravitational-wave transport and a characteristic stochastic background spectrum potentially testable by pulsar timing arrays and future space-based interferometers. This preprint is archived on Zenodo to ensure open accessibility, timestamping, and long-term preservation. The framework is explicitly speculative and is presented to invite technical scrutiny, comparison with related approaches (e.g. thermodynamic gravity, causal set theory, and emergent spacetime models), and critical evaluation. No claim of empirical verification or correctness is made.
Dauren Sarsenov (Sun,) studied this question.