From a Single Axiom to Four-Dimensional Spacetime: A Readout Mechanism for Discrete Ontology

Abstract

This work establishes a discrete ontological framework whose sole starting point is a single axiom: *zero never stays still*. No manifold, metric, probability, or action is introduced. Words, graphs, divergence identities, zero-sum conservation, and integer multiplicities are all derived structures. We establish a layered index system distinguishing the evolution layer from the historical layer, and give a strict parameter account: one axiom, one free parameter, two named inputs. On this basis we present the main derivation chain: zero-sum constraint $\to$ space of balanced words $\to$ self-identifying coarse-graining partition $\to$ spectral dimension readout. At $n=16$, the participation index of the height-level partition is $q=\sum_b\omega_b^2=0.55777859$, which lies in the interval $(1/2,3/5)$; the functional $F_D=\binom{D}{2}q^D$ then has a unique finite maximum at $D=4$. We explicitly list all open items and conditional boundaries: the necessity of the quantum contextuality threshold is unproven; the partition criterion has been shown non-unique; and $D=4$ holds only for $n\in\{16,20\}$. **Keywords**: discrete ontology; zero-sum constraint; coarse-graining; spacetime dimension; spectral dimension; KCBS inequality ---