The Ontology of Constraint: A Post-Platonic Framework for Physical Law as Geometric Memory

Abstract: Contemporary physics operates under an implicit Platonic paradigm: physical laws are assumed to be eternal, immutable, and external to the systems they govern. We argue that this assumption generates intractable problems-most notably, it renders the origin of laws inexplicable and treats the constants of nature as brute facts requiring no further analysis. We propose an alternative ontology based on the principle of Accumulated Geometric Memory. In this framework, laws are not prescriptive rules but descriptive records of accumulated interaction failures. Reality is modeled as a stochastic exploration of a Possibility Space, where stable structure emerges from the exclusion of unstable configurations via geometric autocorrelation (the mechanism by which past exclusions shape future probabilities). This inversion-placing "failure" and "memory" prior to "law" and "matter"-provides a unified epistemological basis for emergence across physical scales. We provide mathematical formalization through Kunita stochastic flows on the Possibility Space, establish the equivalence between Possibility Space and Shape Space, and derive a six-point ontological summary that is precise, non-redundant, and falsifiable. We discuss implications for fine-tuning, the nature of mathematics, and the unity of quantum and gravitational physics. We identify structural predictions that distinguish this ontology from Platonic alternatives.