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Incompressible Box Transport and Finite Computation

OpenAI · September 27, 2026

Earlier edition Lean

This is an earlier edition (September 27, 2026). Current edition: Incompressible Box Transport and Finite Computation, October 6, 2026.

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Cite

@misc{OAI:Incompressible-Box-Transport-and-Finite-Computation-September-27-2026,
  author = {{OpenAI}},
  title = {{Incompressible Box Transport and Finite Computation}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Incompressible-Box-Transport-and-Finite-Computation-September-27-2026/manuscript.pdf}{OAI:Incompressible-Box-Transport-and-Finite-Computation-September-27-2026}},
  year = {2026}
}

Lean formalization

OpenAI provides Lean files for this family: lean/docs/376.md. The Lean statements have not been checked by people against the paper's claims.

Family 376: Universal computation in forced Navier–Stokes flows

Constructs viscous incompressible flows starting from rest on a fixed flat three-dimensional domain that perform universal computation under smooth external forcing. A terminating compiler turns a Turing machine and input into a finite program for the force, so a designated particle reaches a fixed region exactly when the machine halts. The viscosity is fixed, positive and computable.

Other papers in this family: