{"id":"openai-math/Incompressible-Box-Transport-and-Finite-Computation","pdf":"https://github.com/openai/math/blob/main/preprints/Incompressible-Box-Transport-and-Finite-Computation-October-6-2026/manuscript.pdf","url":"https://github.com/openai/math/tree/main/preprints/Incompressible-Box-Transport-and-Finite-Computation-October-6-2026","tags":["fluid-dynamics","navier-stokes","computability"],"score":0,"title":"Incompressible Box Transport and Finite Computation","domain":"Partial differential equations","family":"376","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AP","summary":"We realize finite positive diagonal affine maps of determinant one by effective smooth incompressible flows on neighborhoods of entire closed rational solid boxes. The source and target families are each disjoint, but may overlap each other. The construction uses localized curls, evacuation to storage and obstacle detours. A balanced three-stack recorder then assigns every machine and finite input a smooth Navier–Stokes force with one compact spatial support, periodic after a loading interval, at any fixed positive computable viscosity. The fluid starts at rest, and one fixed particle enters…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-06","reactions":{},"formalized":false,"family_title":"Universal computation in forced Navier–Stokes flows"}