Theory of the TDH — Perpetually Creation and Evolution of the Universe: The Universal Hybrid Regime Framework - Volume I: Local Phase Topologies and Boundary Interfaces (Version 1.0)

Title Theory of the TDH — Perpetually Creation and Evolution of the Universe: The Universal Hybrid Regime Framework - Volume I: Local Phase Topologies and Boundary Interfaces Version 1.0 Author Thai, Hau Dinh (Pen-names: TDH, or Thomas H.D. Thai, and Thái Đình Hầu (Vietnamese name) Affiliation Independent Researcher Date of Publication 2026-10-15 Description/Abstract This volume establishes the foundational macro-scale phase-space topology and localized interaction mechanics governing multi-scale systems within the Theory of the TDH framework. We introduce an original architectural abstraction designed to model the localized spatial friction, boundary containment, and systemic hybridization of arbitrary multi-regime systems. Specifically, we investigate the multi-dimensional interplay between populations of chaotic fields {Ai} (from i=1 to n) and counter-chaotic fields {Bj} (from j=1 to m). By structuring these domains through custom algebraic operators, we isolate distinct phase interaction layers including homogeneous fluidic miscibility, binary immiscible phase segregation, structural veiling, and intrusive matrix-inclusion networks. This localized topological foundation forms the computational baseline required to simulate micro-regime structural thresholds using spatial discrete grids. Historical Note & Cross-Reference:The structural, operator-driven methodology introduced in this new master lineage builds directly upon the foundational equations, thermodynamic boundary limitations, and priority dates established in previous Zenodo submissions. Specifically, this text scales, formalizes, and de-clutters the mathematical structures originally reported across Zenodo Records 3.0 through 3.3 under the lineage tracking from the historic TDH Unified Hybrid Regime Theory (UHRT) portfolio. This Volume I Version 1.0 serves as a clean-slate, uncompacted mathematical infrastructure intended to link sequentially into future multi-agent population networks (Volume II) and macro-cosmological accretion engines (Volume III). Key Words TDH Theory Universal Hybrid Regime Phase Topology Boundary Interface Fluidic Mixing Segmented Inclusion Thai Dinh Hau