Irreducible Global Dependencies, Informational Monotonicity, and a Structural Obstruction to Deterministic Polynomial-Time Computation

This paper develops an informational framework for analyzing the limits of deterministic polynomial-time computation based on irreducible global dependencies. Building on earlier work that constructed explicit DGNL families and isolated structural exposure principles, it introduces the notion of inconsistency flow, measuring the capacity of a computation to eliminate globally coherent configurations. It proves that polynomial-time algorithms admit only polynomial flow, while DGNL families require exponential flow. To formalize this obstruction, the paper introduces Informational Monotonicity, expressing the impossibility of destroying algorithmic information without explicit representation. Under this principle, it derives a general impossibility theorem for deciding DGNL families. The framework reduces the P versus NP problem to the compatibility between irreducible dependencies and informational constraints of deterministic computation.