Causal Priority Theory Part-11 On the Non-Automaticity of Continuous Derived Time from Continuous State Descriptions

This paper investigates the relation between continuous state descriptions and derived time within the framework of Causal Priority Theory (CPT). In CPT, time is treated as a history-dependent quantity constructed from causally ordered quantum state updates quantified by quantum relative entropy. Key contributions: • Structural non-automaticity: The paper shows that the existence of a continuous state description does not by itself guarantee a canonically assigned continuous derived time. • Two levels of non-automaticity: • Existence level: Continuity does not ensure finite or convergent partition-sum derived time. • Asymptotic-assignment level: The leading asymptotic time scale is not determined by the state image alone in general, as shown by an explicit same-image counterexample. • Conditional existence: The paper formulates conditions under which continuous derived-time candidates exist, while showing that such candidates remain description-dependent. This part (Part-11) provides the continuous-description layer of the broader CPT program and prepares the transition to the subsequent structural analysis of breakdown regimes and non-comparability.