Information-Dynamic Theory of Stable Actualization Regimes: Conceptual Overview and Mathematical Foundations

This repository contains Version 3.3 (Unified Canonical Edition) of the Information-Dynamic Theory (IDT) Mathematical Core, integrating the audited mathematical core (Part I) with the Actualization-Bound & Clock-Cost Module (Part II) into a single canonical reference. IDT is a mathematical framework in which physical systems are described through admissibility geometry, actualization dynamics, Fisher information geometry, generalized eigenvalue spectra, and structural inertia. The theory provides a unified mathematical description of actualization processes, emergent physical time, and information-driven structural evolution. Version 3.3 consolidates the complete audited mathematical canon, including: • Zero Actualization Principle (A3)• Information Potential and the H-Theorem• Fisher Information Geometry and Natural Gradient Dynamics• Generalized Eigenvalue Problem (GEP) Formulation• Structural Inertia M(ω)• Emergent Physical Time (P7)• Structural Demarcation between IDT and Fisher Geometry• β-GEP Theorem• T0 Dimensional Selection Framework• Dimensional Stability Window (2 < d < 4)• Actualization Budget Formalism• Actualization-Bound & Clock-Cost Theory• Effective Clock Cost (Meff) Framework• Universal Actualization Bound (UAB)• Expected Clock Cost Lemma (ECCL)• Unified Priority Map and Open Research Programme Version 3.3 incorporates all audit-accepted corrections from previous releases, resolves internal consistency issues identified during the v3.0 audit process, and introduces a unified canonical presentation with explicit theorem-status classification (CANON, THEOREM, OBSERVATIONAL, INTERPRETATION, HYPOTHESIS, POSTULATE, and RETRACTED). This document serves as the current canonical mathematical reference for the IDT programme and supersedes all previous Mathematical Core editions where explicitly stated. The repository is intended as a research reference and mathematical foundation for ongoing work on structural actualization, emergent physical time, admissibility geometry, generalized spectral dynamics, and information-dynamic approaches to fundamental physics. Status: Unified Canonical Mathematical Core (v3.3) — STRONG EVIDENCE, not DISCOVERY.