Formal Structures of Succession: A Rate-Labeled Order Model for Emergent Geometry

This preprint develops a minimal formal framework for a temporal-rate ontologyin which ordered succession is primitive and geometric structure is treated asrepresentational. The model is based on a partially ordered set of events endowedwith a dimensionless rate labeling. Coordination along ordered chains gives riseto emergent temporal distance, while coordination failure defines horizonswithout reference to spacetime geometry. Under suitable coarse-grainingassumptions, familiar relativistic time-dilation relations are recovered asrepresentational encodings. The framework introduces no new dynamics and makes no empirical claims. Its roleis structural and interpretive, providing a formal scaffold for an ontologicalanalysis developed separately. This paper constitutes a formal continuation ofthe interpretive framework presented in “Geometry as Representation: ATemporal-Rate Ontology for Relativity and Quantum Theory”(https://doi.org/10.5281/zenodo.18341269).