Discreteness as ontology: A hodon-based approach to dark matter

Abstract

This work proposes a geometric-statistical reinterpretation of the dark sector, grounded in a discrete spacetime framework composed of non-material spatial units termed hodons. Unlike particle-based dark matter models, hodons are kinematically inert and possess ultra-light effective mass derived from vacuum energy density and holographic volume bounds. We introduce a covariant scalar field $\mathcal{N}(x^\mu)$ representing local hodon density and derive an entropy-driven evolution equation consistent with causal structure and general relativity. The resulting stress-energy contribution from hodon fluctuations yields gravitational clumpiness without invoking new particles or modified gravity. A virial-based toy model demonstrates that baryonic matter surrounded by hodons forms stable, cored halo profiles, consistent with galactic rotation curves and low-mass halo observations. The framework naturally suppresses small-scale structure via spatial uncertainty relations, aligning with constraints from the Lyman-$\alpha$ forest and weak lensing. By integrating Bousso's covariant entropy bound and distinguishing between strong and weak holography, we situate the model within a broader epistemological context. These results suggest that dark sector phenomenology may emerge from the statistical geometry of space itself, offering a falsifiable alternative to particle dark matter.