P versus NP

Determine whether the complexity classes P and NP are equal by proving or disproving the existence of a polynomial-time algorithm that decides every language in NP, or equivalently by establishing that P = NP or P ≠ NP within the standard Turing machine model of computation.

Background

In Appendix A, the paper reviews foundational aspects of Turing machines and their centrality to computer science theory, noting that major problems in complexity theory are framed in terms of Turing machine computations. Within this context, the author highlights the P vs NP question as a paradigmatic open problem, emphasizing its status and relevance to the theory of computation.

While this open problem is not specific to the simulation framework developed in the main text, its inclusion underscores the broader significance of computability and complexity when reasoning about what universes (and their dynamics) can be simulated or constructed within physical constraints.