What question did this study set out to answer?

The central aim is to prove that the complexity classes P and NP are mutually exclusive.

April 1, 20260 citationsOpen Access

Version 3.0 A State-Transition Proof of P ≠ NP

Key Points

The central aim is to prove that the complexity classes P and NP are mutually exclusive.
Define P as a Null-Transition State and NP as a State-Transition Event.
Utilize a discrete logical system to analyze the distinctions between static and dynamic states.
Employ fundamental definitions of verification and discovery in the proof.
Demonstrated that P cannot map onto NP due to their categorical distinctness.
Clarified the implications of static coordinates versus dynamic vectors in complexity theory.

Abstract

Version 3.0 We establish that P ̸ = NP by demonstrating that the complexity classes represent mutually exclusive informational categories. Building on the foundational workof Cook 1, we define P as a Null-Transition State (T0) and NP as a StateTransition Event (T≥1). Within a discrete logical system, a static coordinate (0)and a dynamic vector (1) are categorically distinct; therefore, P cannot map ontoNP. This proof utilizes the fundamental definitions of verification, discovery, andthe emergence of time

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Cite This Study

Nicolas Antony Brown (Sat,) studied this question.

synapsesocial.com/papers/69ccb74216edfba7beb89223 https://doi.org/https://doi.org/10.5281/zenodo.19339897