Causal Priority Theory part-2 Derivation of the Page Curve — Proof of Zero Additional Free Parameters

This paper derives the Page curve within the framework of Causal Priority Theory (CPT) without any additional free parameters beyond standard semi-classical inputs. By employing the causal conservation law of CPT, the purification condition S_BH + S_rad = const is shown to follow directly from the theory's axioms. Key Results: 1.Page Time Prediction: The Page time is derived as t_Page ≈ 0.646 * t_evap. 2.Structural Difference: CPT incorporates information conservation from the outset as 'causal kinematics', leading to a distinct Page time compared to the island formula. 3.prediction is in principle distinguishable from the island formula result and verifiable in analog gravity systems. This work provides an independent derivation of the Page curve consistent with unitarity, addressing the information paradox through the foundational structure of CPT.