Structural Dynamics of Polynomial Solvability: Layered State Spaces and Polynomial Navigability

This note develops a structural and geometric viewpoint on polynomial-time solvability based on the dynamics of computational state spaces. Instead of treating P and NP primarily through the distinction between search and verification, the paper focuses on layered state spaces, polynomial navigability, structural collapse, and admissible compression. The framework introduces notions such as divergence, frontier, completion, layered dynamics, and polynomial collapse, and illustrates them on Horn-SAT, 2-SAT, bipartite matching, and 3-SAT. Particular attention is given to the distinction between compact representation and polynomially realizable operations, formalized through robust computational formalisms. The paper is exploratory and programmatic in character. Its purpose is not to propose a completed alternative foundation of complexity theory, but to introduce a preliminary structural vocabulary that may support future work on state-space complexity, proof complexity, and global mechanisms of polynomial solvability.