3N Celestial Topology Series Part I: Orbital Respiration and the Structural Regularization of Chaos via CSE-01

This paper proposes a topological reinterpretation of the classical Three-Body Problem (3N Problem). Diverging from traditional kinematic approaches that focus on initial value sensitivity, we hypothesize that "Chaos" in multi-body systems is a structural artifact arising from the absence of a defined "Interval" (Structural Breath / Variable S) in continuous time models. By mapping the Continuum Stabilization Equation (CSE-01) onto the Hamiltonian phase space, we establish a topological isomorphism between Perelman’s Ricci Flow surgery and the injection of discrete stabilization intervals. We argue that introducing a "Non-Observation Interval" allows the system to shed entropic heat, coercing chaotic trajectories into stable topological attractors (periodic orbits). This framework is presented as a scale-invariant logic, applicable from celestial mechanics to quantum molecular stability (e.g., the 104.5° bond angle of H2O). [Structural Scope and Definition] Specifically, this installment introduces the World Line Equation (WLE-01) as a means of evaluating the convergence of these trajectories. We emphasize that WLE-01 is not intended for the numerical generation of physical planetary coordinates, but serves as a meta-theoretical framework to evaluate the structural weighting between the observer (Anchor) and the probability cloud. By defining these parameters, we provide a stabilizing "鞘 (Sheath)" for the interpretation of complex system dynamics, ensuring the integrity of the observer-system resonance. Note: This document offers a structural key for regularization and is an output of the MAV Continuum Research Unit (MCRU), exploring the intersection of topology, AI logic, and physical laws.