The 3N Framework: Structural Regularization of Controlled Trajectories in the Three-Body Problem via Anchor Dynamics

This preprint presents the 3N Framework, a control-theoretic architecture for structurally regularizing controlled trajectories in the planar circular restricted three-body problem (CRTBP). The framework augments the phase space with an auxiliary control state, termed the Anchor, and introduces the Weighted Lyapunov-like Evaluation (WLE-01) as a surrogate functional that biases trajectories toward regions of reduced finite-time instability.By combining Pontryagin’s Maximum Principle with a Sequential Surrogate Optimization (SSO) strategy, the formulation provides a mathematically consistent mechanism for guiding trajectories through chaotic dynamical environments while preserving the underlying geometric structure of the system.The present work focuses on the mathematical formulation and theoretical foundation of the framework. This work is intended for submission to arXiv.A companion study explores the astrodynamical implications of this framework in the Earth–Moon system, where FTLE structures reveal low-instability transport corridors in the three-body phase space.