Causal Structure, Indistinguishability, and Coherent Filtrations in Polynomial-Time Computation

This paper develops a causal theory of deterministic polynomial-time computation based on indistinguishability of internal states. Building on earlier work that characterized polynomial-time computation via informational filtrations, it introduces graphs of causal dependence describing how the compatibility of literals propagates through execution. It proves that such graphs cannot contain long directed cycles without violating polynomial state bounds, yielding the Causal Indistinguishability Theorem. As a consequence, every deterministic polynomial-time computation induces a computationally coherent filtration of its compatibility complex, forbidding the creation of high-dimensional global dependencies in a single step. This framework provides a dynamic foundation for earlier informational and topological obstructions and reduces the P versus NP problem to the existence of irreducible global dependencies incompatible with coherent filtrations.