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

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.