Dissipative Numeral System, Paper VI: Autonomous Structural Geometry — A Hybrid Dynamical Theory of Self-Executing Mathematical Objects and Historical Geometric Freezing

This paper establishes the theoretical foundation for autonomous structural geometry within the Dissipative Numeral System (DNS). Classical mathematics treats structural points as passive nodes awaiting external operators. We challenge this assumption by introducing the Autonomous Structural Point: P = (C, B, H; Θ) where (C, B, H) are state terms (cost, base/institution, history) and Θ is the intrinsic law — the mathematical answer to "how this structural point exists." We introduce the State-Transfer Operator Φ_Θ := Eval(Θ, P, Γ) and formulate the system as a Hybrid Dynamical System with continuous cost evolution and discrete suit-carrying phase transitions. We prove the Structural Self-Execution Theorem: under contract, resource, and topological continuity conditions, the point autonomously evolves along a well-defined local trajectory without any external operator. We extend to multi-body systems via a coarse-grained field-theoretic framework with explicit dynamics for both state and rule fields, identifying three global dynamical regimes and defining the DNS structural stress field as the measure of contract incompatibility that triggers Reset Dynamics. Finally, we introduce the DIT (Dynamic Information Topology) Persistence Filter, which selects historical trajectories based on structural persistence. We prove the Conditional Geometric Freezing Theorem: under DIT convergence conditions, the feature space converges to a limiting metric space that admits a structure-preserving embedding into a static DNS geometric manifold. The central thesis is stated as: Structure is frozen history.