Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 376-07. Velocity-Field Detection of Computation in Forced Navier–Stokes Flows
Manuscript map · lines 9595–9604
OpenAI@2026-10-07#rem:oai-p-376-07
Authors: OpenAI. Family 376.
Title: Velocity-Field Detection of Computation in Forced Navier–Stokes Flows.
Abstract: We construct smooth forces for three-dimensional incompressible Navier–Stokes flow, from rest at any fixed positive computable viscosity, whose velocity field detects whether a prescribed machine halts. On the unit flat torus, a pointwise test of the third velocity component uses successively shorter stirring intervals in a fixed spatial region. On ${}mathbb R{}2{}times{}mathbb T$, an integral test uses an expanding array of translation regions and a force with globally bounded mixed derivatives. The vertical velocity solves an advection–diffusion equation: short bursts control its pointwise error in the first construction, and a moving cutoff controls the total escaped mass in the second.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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