{"id":"openai-math/Prefix-Instructions-and-Incompressible-Flows","pdf":"https://github.com/openai/math/blob/main/preprints/Prefix-Instructions-and-Incompressible-Flows-September-27-2026/manuscript.pdf","url":"https://github.com/openai/math/tree/main/preprints/Prefix-Instructions-and-Incompressible-Flows-September-27-2026","tags":["fluid-dynamics","computability","incompressible-flows"],"score":0,"title":"Prefix Instructions and Incompressible Flows","domain":"Partial differential equations","family":"376","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AP","summary":"Finite prefix instructions may change area and erase information. We give explicit history processors and smooth incompressible motions that retain that information and realize every instruction on its full domain. A first application assigns each machine and finite input a smooth mean-zero force on the flat unit three-torus, at any fixed positive computable viscosity. The solution starts from rest; a fixed particle enters a fixed open strip exactly when the machine halts. The force repeats with period one after an initial loading interval. We then prove alternative realizations using full…","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"}