What question did this study set out to answer?

This research aims to prove that the complexity class P is not equal to NP by using state-transition concepts.

April 1, 2026Open Access

A State-Transition Proof of P ≠ NP

Puntos clave

This research aims to prove that the complexity class P is not equal to NP by using state-transition concepts.
Defines P as a Null Transition State (T0) and NP as a State-Transition Event (T≥1)
Establishes their mutual exclusivity within a logical system
Applies fundamental definitions of verification and discovery
Proved that P and NP represent distinct informational categories
Demonstrated that a static coordinate cannot map onto a dynamic vector
Established distinctions in the emergence of time between these complexity classes

Resumen

Version 2.0 We establish that P ̸ = NP by demonstrating that the complexity classesrepresent mutually exclusive informational categories. We define P as a NullTransition State (T0) and NP as a State-Transition Event (T≥1). Withina discrete logical system, a static coordinate (0) and a dynamic vector (1) arecategorically distinct; therefore, P cannot map onto NP. This proof utilizes thefundamental definitions of verification, discovery, and the emergence of time

Leer artículo completoexternamente

Me gusta

Guardar

Ver artículo completo

Cite This Study

Nicolas Antony Brown (Sat,) studied this question.

synapsesocial.com/papers/69ccb69d16edfba7beb8844d https://doi.org/https://doi.org/10.5281/zenodo.19334324

Me gusta

Guardar

Ver artículo completo