We construct a minimal formal universe U = (D, E, C) from three primitives: countable distinctions D, a generative relation E, and a consistency predicate C. Five axioms constrain C to produce a causal partial order from which proper time, spatial hypersurfaces, and spacetime volume emerge as derived objects without additional postulates. We execute a sequence of four computational simulation experiments, implementing candidate consistency predicates C1 through C4 and measuring emergent spacetime dimension via the interval-volume scaling law |I (x, y) | proportional to tauᵈ, calibrated against Minkowski sprinklings of known dimension. The central result is the Locality-Dimension Theorem: consistency predicates satisfying Axiom 2 (local evaluation, finite radius r) are bounded by emergent dimension d approximately 2. 4, robust across all tested parameters. Non-local predicates recover dimension cleanly across d = 1 through 5. The corollary is precise: Axiom 2 is incompatible with four-dimensional Lorentzian geometry. A universe with d = 4 requires a consistency predicate encoding global causal structure. The question of why spacetime is four-dimensional translates, within this framework, into a precise mathematical problem about the global form of the consistency predicate C. This is the first formal system deriving spacetime from ontological primitives more elementary than events or causal relations, and the first computational demonstration of a dimensional ceiling for local generative predicates. This work was conducted under the Sciencedelic discipline at the Pleroma Philosophical Research Society, powered by Claude AI Simulation Experiment (Anthropic).
Eliam Raell (Tue,) studied this question.