Causal Holographic Dynamics: Emergent Gravity and Dimensional Stability from Discrete Spacetime

We present Causal Holographic Dynamics (CHD), an exploratory computational frameworkinvestigating how spacetime geometry and gravitational phenomena might emerge fromdiscrete causal networks subject to information-theoretic constraints. Rather than proposinga complete theory of quantum gravity, CHD serves as a collection of numerical experimentsdemonstrating how established physics can be implemented within a discrete computationalsubstrate.Our comprehensive numerical simulations reveal three key findings: (1) The Benincasa-Dowker action in 2D curved causal sets exhibits anomalous scaling ⟨SBD⟩ ∝ Nγ with γ =1.323±0.002, suggesting a strong geometric aliasing effect at high curvature that serves as acandidate mechanism for dark matter. (2) In 3+1 dimensions, mass induces a causal deficitthat follows a 1/r profile in the weak-field limit, naturally recovering Newtonian gravityfrom purely combinatorial constraints. (3) Myrheim-Meyer dimension analysis confirms astable effective dimension DMM = 4.1 ± 0.1 across scales, demonstrating the dimensionalstability of the emergent spacetime.We emphasize the tentative nature of these results and view CHD as an invitation forfurther investigation into whether aspects of the "dark sector" might be interpretable asemergent phenomena in discrete spacetime.