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 be explored in 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 2D, the dynamics can spontaneously produce pronounced structure-factor peaks (Bragg-like ordering) in an intermediate-noise regime; in 3D, high-resolution scans (L=64, N=200) reveal a strongly seed-dependent region consistent with multistability and competing dynamical attractors for sufficiently strong feedback; and topological and kinetic diagnostics indicate the formation of a connected effective metric space and a marked inhibition of exploration relative to baseline random dynamics. Together, these results support the claim that record-constrained evolution is sufficient to induce nontrivial organization and effective irreversibility in simple models, providing a concrete testbed for the broader conceptual program.

Technical Summary & Reproducibility

• Methodology: Implementation of record-biased stochastic dynamics on 2D and 3D lattices (Restricted Accumulation).

• Key Observables: * 2D structure-factor analysis (emergence of Bragg-like peaks).

  • 3D high-resolution scans (L=64, N=200) identifying a multistable regime for feedback strength $\beta > 1.65$.

  • Topological diagnostics for effective metric emergence and kinetic inhibition.

• Data & Code Availability: The original Python source code and the raw CSV datasets generated during the 3D critical regime sweeps are available upon request to the author.

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.