Information Manifold Model – Volume III: Operators, State Transitions, and Invariant Structure

Volume III advances the Information Manifold Model (IMM) from conceptual structure into formal mechanics. Building on entropy-driven curvature and constraint geometry, this volume introduces operators, transition rules, and invariant conditions governing motion across information manifolds. System evolution is modeled as discrete and continuous state transitions constrained by topology, entropy gradients, and persistence conditions. Rather than optimizing outcomes or predicting trajectories, the framework defines when transitions are structurally permitted, forbidden, or invariant under transformation. Key developments in this volume include: Definition of state-transition operators on information manifolds Invariant structures preserved across transitions Entropy-weighted transition constraints Discrete versus continuous evolution regimes Persistence criteria as a structural stability condition Market systems are treated as one applied domain among many, illustrating how price dynamics emerge from invariant transition rules rather than stochastic prediction. The formal structure presented here is designed to be domain-agnostic, supporting later specialization into markets, physical systems, or computational models. This volume establishes the mechanical core of IMM, providing a foundation for simulation, implementation, and further mathematical formalization.