Temporal Membranes: Non-Markovian Dependence and Selective Temporal Inheritance

Recent arguments treat the Markovian character of fundamental laws as evidence for presentism and foundational non-Markovianity as pressure toward eternalism. This article argues that both inferences outrun the evidence. Law-level Markovianity, reduced-state non-Markovianity, Markovian embedding, and metaphysical screening-off are distinct. Even a complete state that screens off earlier conditions specifies dependence without settling which times exist; non-Markovian dynamics likewise calls for explanation without requiring past events to coexist with present ones. The neglected issue is selective temporal inheritance: how historically generated differences remain efficacious at a specified boundary and scale. The article develops temporal membranes as a process-relational schema for this issue. A membrane is the organized carrier through which some historical differences constrain later processes while others are filtered, delayed, transformed, or erased. Quantum process tensors supply the principal formal correspondence, and hysteresis offers a controlled non-quantum comparison. Temporal membranes constitute no fourth temporal ontology. Presentists, eternalists, and growing-block theorists may adopt the schema, but each must explain how its existence claims relate to selective inheritance. A limited process interpretation of local settlement is then developed, leaving objective passage as a further question.