Open Research Index

Prefix Instructions and Incompressible Flows

OpenAI

OpenAI Mathopenai-math/Prefix-Instructions-and-Incompressible-FlowsSep 27, 2026math.APAI-generatedscore 0

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…

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