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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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The Conjugacy Barrier: An Information-Theoretic Impossibility Theorem for P = NP

Authors: Eckert, Anthony;

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

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.

Part of the Void Framework research project (Moreright DAO).

Keywords

impossibility theorem, conjugacy theorem, computational complexity, complexity barriers, natural proofs, Shannon entropy, NP certificate, witness hiding, algebrization, communication complexity, relativization, millennium prize, P vs NP, information theory

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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