What does this research mean for the field?

There exists a rigorous isomorphism between the discrete state space of a Turing Machine and a continuous Hilbert Space spanned by the prime numbers, providing a physical obstruction to polynomial inversion. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to establish a relationship between Turing dynamics and kinematics involving prime numbers.

February 19, 2026Open Access

On the Isomorphism Between Turing Dynamics and Prime-Basis Kinematics

Key Points

The aim is to establish a relationship between Turing dynamics and kinematics involving prime numbers.
Developed a mathematical framework for the isomorphism between Turing Machines and Hilbert Spaces.
Analyzed lower bounds of complexity using the new model instead of traditional combinatorial approaches.
Identified a continuous metric for analyzing complexity lower bounds.
Provided evidence of a physical obstruction to polynomial inversion regardless of logical basis choice.

Abstract

Traditional approaches to the P vs N P problem rely on combinatorial models of complexity, whichlack a natural continuous metric for analyzing lower bounds. In this paper, we propose a rigorous iso-morphism between the discrete state space of a Turing Machine and a continuous Hilbert Space spannedby the prime numbers (HP ). The framework developed provides a physical obstruction to polynomialinversion, independent of the choice of logical basis.

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