Conservative Motion Theory – PNP IV The Fredholm–Entropy Barrier: Irreducibility of NP Search Under Deterministic Conservation

Kawasaki, Hideyo

Published Nov 20, 2025• 0 citations

Abstract

In addition to the exponential non–conservative mass established in PNP I–III, we showthat NP search problems possess an intrinsic Fredholm–entropy which cannot be reduced byany reflection–positive deterministic operator.For an NP search operator Bn (e.g. for SAT), the normalized singular-value distributionconverges to an entropy-maximizing measure supported on Θ(2n) independent eigenmodes.Deterministic polynomial–time operators Tn preserve entropy and cannot compress thismeasure into the polynomial-rank conservative sector.Thus NP search is irreducible under conservative motion:SearchNP ̸≤CMT P.Combined with the Fredholm Separation Principle of PNP III, this yields the full CMTseparationP ̸= NP and SearchNP cannot be simulated by P.

DOI: 10.5281/zenodo.17658960

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