Moon Steady-State Discriminant Formula and Quantitative Research on P/NP Problems

Based on the topological evolution completeness of discrete dynamical systems, finite halting steady-state constraints, and integer base screening criteria, this paper strictly deduces and proves that the unique topological invariant metric of all discrete complex systems with finite-step halting, steady-state convergence and non-chaotic divergence is . Combined with the solution judgment characteristics of P/NP problems and the Collatz conjecture, this paper constructs a complete quantitative discrimination system for system complexity. It realizes the topological transformation and accurate quantitative judgment of the complexity state of P/NP problems, and completes the topological demonstration of the unsolvability of non-stationary chaotic problems represented by the Collatz conjecture. The research results provide a new theoretical support and quantitative basis for the complexity mechanism analysis and intelligent algorithm optimization of discrete dynamical systems.