The Structural Impossibility of P = NP

In this work, it is shown that the P vs NP problem is not merely unsolved, but structurally ill-posed in its classical formulation. Starting from a systemic comparison between prime number recognition and NP-completeness, a common principle becomes visible: global structures that emerge cannot be reconstructed by local procedures. The central thesis is: every previous attempt to solve NP problems using deterministic algorithms of class P implicitly employs the same structural projection that must, in fact, be overcome. What becomes visible is therefore not merely a technical failure, but an ontological boundary: P = NP is not only unlikely – it is structurally impossible. This insight is not obtained through algorithmic construction, but through analysis of the underlying forms of order.The result is a structural proof of P ≠ NP that returns the question to its origin: How does structure arise – and where does it collapse in representation? Related theoretical foundation:Heinz, K. J., The Irreducible Structure of the Prime Distribution, Zenodo, 2025.DOI: 10.13140/RG.2.2.17117.47846https://zenodo.org/records/17649211 Reference implementation of the constructive prime generator:https://github.com/syntaris/primes4everybody