The Physics of Black Hole Formation: Harmonic Phase Transitions and CAT-12 Constraint Laws from Stellar Resonance to Collapse

This paper presents a constraint-based synthesis of black hole formation physics, integrating classical general relativity, compact-object instability theory, relativistic thermodynamics, and observational astrophysics within the Cosmic Algorithm Theory-12 (CAT-12) framework. Rather than introducing new field equations or modifying established physical laws, this work reframes gravitational collapse as a sequence of admissible solution regimes governed by stability thresholds, causal boundaries, and thermodynamic constraints. The formation of a black hole is treated not as a singular dynamical inevitability but as a phase transition enforced by the loss of hydrostatic equilibrium, angular momentum redistribution, and horizon emergence under strong gravity. Key topics addressed include: relativistic stellar instability and equation-of-state limits, collapse corridors and threshold behavior in core failure, horizon formation as a causal and geometric boundary, entropy bounds and information accessibility, accretion dynamics and post-formation persistence, and the interpretive limits imposed by observation and inference. CAT-12 is introduced as a structural constraint framework that restricts the physically realized solution space of standard equations through principles of dynamic precision, harmonic equilibrium, phase-lag integration, and non-coercive alignment. These principles are shown to be compatible with orthodox general relativity, thermodynamics, and statistical inference, while offering a disciplined interpretation of black hole behavior across observationally accessible regimes. The paper emphasizes interpretive rigor over speculative extension, with detailed mathematical foundations consolidated in dedicated sections and appendices. Visualizations are used to clarify regime transitions and constraint structure rather than to depict literal microphysical trajectories. This work is intended as a synthesis and interpretive framework. It complements, rather than replaces, existing numerical and analytical approaches to black hole physics, and naturally motivates future studies that focus on explicit solution mapping, quantitative corridor visualization, and extended mathematical formalization within the CAT-12 program. Keywords:black holes; gravitational collapse; general relativity; event horizon; accretion disks; thermodynamics; information bounds; CAT-12; constraint-based physics; astrophysical synthesis