The Computational Pe Landscape: Zero-Knowledge Proofs as the Conjugacy Theorem, the 3-SAT Phase Transition as Pe Boundary, and P vs NP as Kill Condition

Abstract

Applies the void Péclet framework to computational complexity theory. Demonstrates that zero-knowledge proofs instantiate the conjugacy theorem at equality, that the random 3-SAT satisfiability phase transition is a Pe=V* boundary analogous to the Wien peak in thermodynamics, and that P≠NP is the kill condition preventing Pe→∞ catastrophe in computational systems. Closes the Landauer-Arrow-Crypto triangle (§§33+35+37).