{"id":"openai-math/Finite-Instructions-and-Solenoidal-Shear-Flows","pdf":"https://github.com/openai/math/blob/main/preprints/Finite-Instructions-and-Solenoidal-Shear-Flows-September-27-2026/manuscript.pdf","url":"https://github.com/openai/math/tree/main/preprints/Finite-Instructions-and-Solenoidal-Shear-Flows-September-27-2026","tags":["fluid-dynamics","computability","incompressible-flows"],"score":0,"title":"Finite Instructions and Solenoidal Shear Flows","domain":"Partial differential equations","family":"376","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AP","summary":"We realize finite reciprocal affine instruction maps by smooth incompressible shear flows on a flat three-torus. Applied to a reversible one-head recorder with a finite transition table, this gives a complete machine-to-fluid construction: a fixed particle enters a fixed open strip exactly when a given machine halts, with zero initial velocity, zero pressure, and a solenoidal mean-zero force that is periodic after initialization. The construction acts on full closed rectangles and controls every intermediate trajectory. Separate heights resolve overlap between sources and targets, and an…","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"}