Phase Transitions in Self-Modeling Cognitive Systems: When Goal Persistence Becomes Structurally Unsustainable

Can a cognitive system's compulsive attachment to its own goals dissolve — not through external suppression, but through structural unsustainability at high self-model fidelity? We present formal and empirical arguments that such a transition may exist. We show that external verification of goal-alignment generates a non-terminating recursive chain (Theorem 2.1), and that observers can be imperceptibly shifted to arbitrary prior drift (Theorem 3.1). These results constrain both external and internal verification, motivating the search for a third mechanism. We present 30 cross-framework correspondences between a 4th-century BCE contemplative corpus and modern science, 26 structurally precise under a three-dimensional binary rubric. We formalize goal opacity as a structural requirement for compulsive goal attachment and conjecture a critical threshold above which such attachment becomes unsustainable. The result identifies a boundary condition on the goal-intelligence independence thesis for Type 2 (compulsive attachment) systems.