Conservative Motion Theory – PNP III The Fredholm Separation Principle: A Non–Conservative Rank Barrier for Deterministic Computation

Kawasaki, Hideyo

Published Nov 20, 2025• 0 citations

Abstract

Within the Conservative Motion Theory (CMT), deterministic polynomial–time computationscorrespond to reflection–positive Fredholm contractions T satisfying ∥T∥op ≤ 1 andpossessing finite conservative rank. Nondeterministic computations correspond to maximallynon–conservative branching operators B whose Fredholm mass grows exponentially withinput size n.We prove the Fredholm Separation Principle: no reflection–positive contraction T cansimulate a maximally non–conservative branching operator B of an NP–complete computation.Equivalently, the conservative rank of T is strictly sub–exponential while that of B is Θ(2n).Thus P and NP correspond to two disjoint components in Fredholm–operator space,yielding a structural proof of P ̸= NP within CMT.

DOI: 10.5281/zenodo.17658937

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