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\begin{document}
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\title{On the P Versus NP Problem}



\author[1]{Frank Vega}%
\affil[1]{Information Physics Institute}%


\vspace{-1em}



  
  \date{April 25, 2026}


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\begin{abstract}
The P versus NP problem is a cornerstone of theoretical computer
science, asking whether problems that are easy to check are also easy to
solve. ``Easy'' here means solvable in polynomial time, where the
computation time grows proportionally to the input size. While this
problem's origins can be traced to John Nash's 1955 letter, its
formalization is credited to Stephen Cook and Leonid Levin. Despite
decades of research, a definitive answer remains elusive. Central to
this question is the concept of NP-completeness. If even one NP-complete
problem could be solved efficiently, it would imply that all problems in
NP could be solved efficiently, proving P equals NP. This research
proposes that a notoriously difficult NP-complete problem can be solved
efficiently, thereby potentially establishing the equivalence of P and
NP.%
\end{abstract}%



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