A Structural Inaccessibility Statement on the Escape Channel of the P vs NP Problem
Abstract
This note isolates the unique structural condition under which the equality P = NP could possibly hold. Rather than proposing algorithms or complexity bounds, we identify the sole logical escape channel: the existence of a uniform, polynomially verifiable structural compression capable of representing exponentially many candidate witnesses without loss of information. We argue that the simultaneous requirements of global applicability, polynomial verifiability, information preservation, and instance independence place this hypothetical structure under irreconcilable structural tension. As a result, the escape channel admits no coherent realization. This work does not constitute a proof of P \neq NP. Instead, it precisely localizes the point at which any such proof must operate and asserts that no alternative structural route remains available. Any future resolution of the problem must therefore confront this inaccessibility directly.
Fields of Study & Subjects
Complexity and Algorithms in Graphs
Cryptography and Data Security
DNA and Biological Computing
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 3 January 2026
- Document type
- Preprint