Theory of Inversive Symmetry: Restrictive Accumulation Dynamics and Multistable Emergence in Record-Biased Cellular Automata

Abstract This paper presents the Theory of Inversive Symmetry, an ontological framework in which Everything (T) and Nothing (∅) are treated as inversive states of a single informational totality, governed by a coherence–readability duality. In this view, ∅ is not a void but a non-manifest state of informational potential, characterized by the logical admissibility constraint of global self-consistency (coherence), while T denotes manifested structure as it is readable from within manifestation. The goal is not to provide a cosmological genesis narrative, but to articulate a coherent conceptual scaffold and extract operational consequences. To connect these definitions to tractable observables, the paper introduces Restrictive Accumulation (RA): a minimal dynamical principle in which accumulated records bias subsequent evolution and restrict the space of compatible future configurations. RA is treated as an operational proxy for the coherence/readability tension, allowing the framework to explore explicit lattice-based implementations without claiming a unique identification with any specific physical microdynamics. Numerical experiments show that RA-like feedback can generate robust, model-internal signatures of emergent structure: in unified 2D RA-Particles (L=41/82), the dynamics can spontaneously produce pronounced structure-factor peaks (Bragg-like ordering) in an intermediate-noise regime; percolation analysis reveals a topological duality: low-noise ordered configurations remain permanently localized (0/5 spanning events), while high-noise regimes achieve full percolation. Preliminary 3D analyses (L=130) confirm seed-dependent coherent regimes; and topological/metric reveal formation of connected effective metric spaces and inhibition of exploration relative to baseline dynamics. Together, these results support the claim that record-constrained evolution induce nontrivial organization and effective irreversibility in simple models, providing a concrete testbed for the broader conceptual program. Technical Summary all experiments are seed-controlled for bit-level reproducibility on CPU. Reading Guide To facilitate different research interests, the paper is structured as follows: Ontology & Theory: Sections I and III. Physics & Numerics: Sections II and III.