Part 2. Structural Investigation into the Recursive Fixation and Halting Problem of the Saṃsāra System

This study reinterprets the Early Buddhist doctrines of Dependent Origination (Paṭiccasamuppāda) and Non-self (Anattā) through the formal languages of modern System Dynamics and Theory of Computation, thereby identifying Saṃsāra as a 'Closed Loop of Automated Recursive Computation.' Whereas existing Buddhist studies have largely confined themselves to describing the arising structure of Dukkha statically, this paper analyzes the dynamic execution mechanisms operating along the time axis. Its primary objective is to diagnose, from an engineering perspective, the 'Halting Hard Problem': why the system continues to cycle (idle) without stopping itself, even after recognizing its own structure. To this end, this study models the human consciousness system as a self-referential system incorporating a 'Phantom Controller.' According to this model, the self (Attā) is not a substantial controller but merely an 'Implicit Reference Point' generated by the system to retrospectively attribute computational results. By demonstrating the absence of this reference point, this paper elucidates the engineering paradox of non-self—"there is no controller, yet control persists"—and formally proves that a subject possessing the privilege to terminate computation is structurally absent within the system. Specifically, by employing Turing's Halting Problem and Lyapunov stability theory, this study argues for the topological closure of the Saṃsāra system in three dimensions. First, the positive feedback structure of Clinging to Sensuality (Kāmupādāna) and Becoming (Bhava) traps the system in a local minimum of a 'Double-well Potential,' creating a paradox where internal optimization efforts conversely reinforce structural fixation. Second, it formally establishes the 'incompleteness' of the system by proving that a termination command function (f_{stop}) cannot be contained within the system's internal operation set (F_{int}); thus, the loop of Saṃsāra can never be broken by internal means alone. Third, it reveals that Craving (Taṇhā) is not merely a psychological desire but a physical 'Refresh' operation that latches volatile data into a non-volatile structure (Upādāna), demonstrating that even 'intentional action' is consumed as fuel to maintain system inertia. In conclusion, this study redefines Nirodha not as psychological comfort or a change of state, but as a fundamental 'Computational Termination' and 'Phase Transition' of the system architecture. This posits that Dukkha is not an emotion to be healed but an erroneous computational process to be terminated, providing a theoretical foundation to extend Buddhist practice into a universal, substrate-independent system termination protocol.