The Combinatorial Hidden Space as an Informational Limit

We propose an information-theoretic obstruction to polynomial-time computation, motivated by the question of whether P = NP. Our approach models a class of decision problems as combinatorial lock systems, in which the input induces a large, implicitly defined combinatorial space of candidate structures. The decision depends on the existence or absence of an exact configuration within this space. We argue that, in such systems, the negative instance requires exclusion over the entire combinatorial structure, while the positive instance admits a local witness. This asymmetry leads to a lock-like behavior: any exact decision procedure must preserve all. decision-relevant combinatorial distinctions. Consequently, any algorithm capable of solving the problem exactly must, explicitly or implicitly, encode information equivalent to the full combinatorial structure. Since this structure is not polynomially reducible, we obtain a structural obstruction to polynomial-time computation. This perspective suggests that certain problems cannot admit polynomial-time solutions, not due to lack of algorithmic ingenuity, but due to intrinsic informational constraints.