Theory of the TDH — Perpetually Creation and Evolution of the Universe: The Universal Hybrid Regime Framework - Volume III: Spacetime Kinetic Singularities and Autonomous Localized Cosmic Loops (Version 3.0)

Title Theory of the TDH — Perpetually Creation and Evolution of the Universe: The Universal Hybrid Regime Framework - Volume III: Spacetime Kinetic Singularities and Autonomous Localized Cosmic Loops (Version 3.0) Version 3.0 Date of Publication 2026-10-17 Authors Thai, Hau Dinh (TDH) (Pen-names: TDH, or H.D Thai, or Thomas H. D. Thai, or Thomas Thai, and Thái Đình Hầu (Vietnamese name)) Affiliation Independent Researcher (Scientifically Theoretical Researcher/Architect) Description/Abstract This volume formalizes the high-energy boundary mechanics and non-linear metric transformations that govern the transition from localized spacetime singularities into outward cosmological expansions. By introducing the Gravitational Transgression Operator (Γ), we provide a geometric proof showing how static geodesics morph into accelerating kinetic loops under extreme field compression profiles. To prevent standard mathematical infinity states, we introduce the Radiative Runaway Operator (⇝R) to model continuous energy venting through closed spatial boundary horizons. Finally, we derive the Metric Expansion Ignition Equation to isolate the absolute mathematical threshold under which accumulated kinetic loops violently invert into a macroscopic expansion cascade, establishing an independent, expanding cosmic offspring lineage (R_Offspring). Historical Note & Cross-Reference:This text forms an essential consecutive link in the fresh master lineage tracking of the Theory of the TDH portfolio. It builds directly upon the multi-agent field interventions, non-linear coupled differential networks, and global continuum stability limits verified in Volume II: Multi-Agent Populations and Assimilation Networks (Version 2.0). The mathematical transformations and thermodynamic boundaries derived herein directly succeed, patch, and complete the fundamental cosmic life cycles historically filed across Zenodo Records 3.0 through 3.3 under the legacy tracking metrics of the TDH-UHR.roi system. Keywords TDH Theory Universal Hybrid Regime Gravitational Transgression Radiative Runaway Volumetric Ignition Spacetime Singularities Cosmic Loops (Autonomous Localized Cosmic Loops) Thai Dinh Hau