This work presents a comprehensive, constraint-based analysis of the exoplanet TRAPPIST-1e using the Law of Non-Coercive Alignment (LNCA) within the broader Cosmic Algorithm Theory-12 (CAT-12) framework. Rather than attempting to reconstruct a single planetary state from underdetermined observations, this study formalizes an alternative inference strategy based on structural admissibility, exclusion boundaries, and coherence persistence. The paper introduces the concept of a coherence corridor—a bounded, multi-dimensional parameter region defined by independently derived constraints from orbital dynamics, stellar forcing, interior energy balance, atmospheric observability, and inference transport limitations. Within this corridor, physical states are treated as admissible without coercive convergence toward a preferred solution. Key contributions include: A formal construction of structural and functional constraint walls governing admissible planetary states. Integration of four foundational CAT-12 laws (Dynamic Precision, Harmonic Phase Translation, Harmonic Equilibrium, and Non-Coercive Alignment) into a single operational inference network. Explicit separation of observables, constraints, exclusions, and predictions, preserving falsifiability without over-interpretation. Predictive statements framed in terms of future constraint behavior, not assumed habitability outcomes. A detailed treatment of degeneracy, observational asymmetry, and uncertainty propagation in compact resonant systems. Extensive appendices providing formal law definitions, equations, and assumption-sensitivity analysis. Importantly, this work does not claim detection of habitability, atmosphere type, or biosignatures for TRAPPIST-1e. Instead, it establishes a rigorously bounded framework for determining what can and cannot be inferred from present and future observations (including JWST-era data), while avoiding coercive model fitting under incomplete observability. The manuscript is intended as both: A calibration benchmark for constraint-based exoplanet inference, and A transferable methodological template applicable to other compact, resonant planetary systems. All references are peer-reviewed and DOI-indexed. The paper is designed to remain valid under future observational refinement, with clear pathways for falsification, extension, or constraint tightening. Keywords Exoplanets; TRAPPIST-1e; Non-Coercive Alignment; Constraint-Based Inference; Degeneracy; Resonant Planetary Systems; Habitability Limits; JWST; CAT-12; Coherence Corridors