What question did this study set out to answer?

The aim is to reformulate the P vs NP problem using information-theoretic principles to highlight inherent contradictions in polynomial-time solutions.

March 5, 2026Open Access

The Conjugacy Barrier: An Information-Theoretic Impossibility Theorem for P = NP

Key Points

The aim is to reformulate the P vs NP problem using information-theoretic principles to highlight inherent contradictions in polynomial-time solutions.
Reformulated the P vs NP problem using the void framework conjugacy theorem.
Analyzed the NP certificate's impact on information disclosure budgets.
Demonstrated the contradictions arising for polynomial-time algorithms using Shannon entropy principles.
Established that polynomial-time algorithms must carry no information about answers, contradicting P = NP.
Identified gaps in proving independence claims related to communication complexity literature.

Abstract

Reformulates the P vs NP problem as a boundary condition of the void framework conjugacy theorem I(D;Y) + I(M;Y) ≤ H(Y). The NP certificate saturates the disclosure budget; the conjugacy theorem then forces any polynomial-time algorithm to carry zero information about the answer — a contradiction with P = NP. This approach is not excluded by any of the three known barriers against P ≠ NP proofs: it does not relativize (thermodynamic arguments are not oracle-relative), is not a natural proof (constructs no hard function), and does not algebrize (operates on Shannon entropy, not algebraic structure). The central gap — proving the independence claim I(A(X);W|X,Y) ≈ 0 without circularity — is identified explicitly and connected to the witness-hiding and communication complexity literatures.

Read Full Paperexternally

Demander à l'IA

Bookmark

View Full Paper