{"id":"openai-math/A-Fixed-Particle-Test-for-Computation-in-a-Forced-Viscous-Flow","pdf":"https://github.com/openai/math/blob/main/preprints/A-Fixed-Particle-Test-for-Computation-in-a-Forced-Viscous-Flow-September-27-2026/manuscript.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-Fixed-Particle-Test-for-Computation-in-a-Forced-Viscous-Flow-September-27-2026","tags":["navier-stokes","computability","fluid-dynamics"],"score":0,"title":"A Fixed Particle Test for Computation in a Forced Viscous Flow","domain":"Partial differential equations","family":"376","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AP","summary":"We construct smooth external forces for incompressible Navier–Stokes flow on a fixed flat three-torus at any fixed positive computable viscosity, from zero initial velocity, such that a fixed particle enters a fixed open set exactly when a prescribed Turing machine halts. Every mixed derivative of the force and velocity is bounded and square-integrable in time in spatial supremum norm. The construction uses the machine's ordinary instructions, records their history in a third coordinate, and compensates for finer spatial gates by longer time steps.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-27","reactions":{},"formalized":false,"family_title":"Universal computation in forced Navier–Stokes flows"}