Deterministic Structural Barriers in NP: A Band–Admissibility and Spectral Framework

We present a deterministic, arithmetic-first framework for understanding com-putational intractability in NP. Building on the Standing/Sitting Band Frame-work (SSBF) and the Band–Amplitude Admissibility Principle (BAAP),we demonstrate that admissible spectral modes of combinatorial problems are scale-invariant and structurally rigid. By mapping the configuration space of NP-completeproblems into logarithmic bands, we construct a Hamiltonian whose spectrum en-forces global arithmetic balance. This produces a deterministic, combinatorial “ex-plosive combinatrix”, showing that polynomial-time traversal of all admissible con-figurations is structurally impossible, providing a logically rigorous foundation sup-porting P̸ = N P . Classical NP examples, including Travelling Salesman andKnapsack, are explicitly analyzed.