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

Information-Dynamic Theory of Stable Actualization Regimes (IDT) This record contains the current canonical mathematical core of the Information-Dynamic Theory (IDT) as of Version 2.6. IDT is a pre-geometric theoretical framework in which physical reality is described in terms of admissible informational structures, their stability properties, and their dynamics on an information-geometric manifold. Within the theory, space, time, mass, and physical laws emerge as stable regimes of actualization rather than being assumed as fundamental primitives. The present version consolidates the core mathematical results of the programme, including: • The admissibility framework S(ω), w(x|ω), Z(ω), Φ(ω), and the normalized density ρ(x|ω).• Fisher information geometry and the canonical natural-gradient flow.• Structural inertia M(ω) and its relation to information geometry.• The H-Theorem for IDT, establishing the information potential Φ as a Lyapunov function.• The theorem M ≤ κ and the canonical information-curvature formulation.• The C29 lower-bound theorem M(ω) ≥ 1.• The three-time formalism (τ_int, τ_phys, τ_obs).• The Fisher–IDT demarcation theorem, specifying the conditions under which IDT reduces to ordinary Fisher information geometry.• Current canonical definitions, derivations, conjectures, and open problems. This document is intended to serve as the primary mathematical reference for the current IDT programme and as the reconstruction source for subsequent theoretical developments. Related foundational record:DOI: 10.5281/zenodo.18296688