A Structural Inaccessibility Statement on the Escape Channel of the P vs NP Problem

Read full text
Authors: Bingchao Zhang
Cited by: 0

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