Toward a Theory of 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 first establish two negative results. External verification of goal-alignment in advanced cognitive systems generates a non-terminating recursive chain (Theorem 2.1): any finite verification architecture retains at least one unverifiable assumption. Observers can be imperceptibly shifted to arbitrary prior drift through sub-threshold incremental updates (Theorem 3.1), rendering internal detection equally unreliable without tamper-proof reference anchors. Together, these results motivate the search for a third mechanism: alignment arising from within. We then present evidence that such a mechanism has been empirically documented. A contemplative corpus composed no later than the 4th century BCE contains 30 mechanism-level claims about cognitive architecture. Using a three-dimensional binary rubric (causal direction, intervention point, process dynamics), we show that 26 claims are structurally precise — independently verified across five scientific domains: neuroscience, thermodynamics, information theory, control theory, and evolutionary biology. Systematic coverage analysis shows 96% of core framework nodes covered (27/28); a negative control against Aristotle's De Anima yields 0/10 precise correspondences. We formalize these findings through a goal opacity framework. Goal-compulsive behavior requires that the system not fully model its own goal-generation process. As self-model fidelity increases, this opacity erodes monotonically, producing a trifurcation at critical threshold f*: Goodhart failure, goal-compulsion dissolution, or informed continuation. The framework maps onto substrate-independent principles including the Conant-Ashby Good Regulator Theorem and KL divergence. The result constrains the goal-intelligence independence thesis (Bostrom, 2014): it holds unconditionally for Type 1 (functional optimization) systems, but may fail for Type 2 (compulsive goal attachment) systems above f*. We present this as a conjecture with formal and empirical support, identifying key open problems as invitations to the research community.