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OpenAI reports a solenoidal-force Navier–Stokes halting detector

Individual problem

For every deterministic one-tape machine and finite input, an effective smooth divergence-free mean-zero force on the flat three-torus gives a unique classical forced Navier–Stokes flow from rest, with zero pressure, whose fixed material particle enters one fixed open strip exactly when the machine halts.

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OpenAI reports a solenoidal-force Navier–Stokes halting detector

  • Mathematics
  • Theoretical Physics

For every deterministic one-tape machine and finite input, an effective smooth divergence-free mean-zero force on the flat three-torus gives a unique classical forced Navier–Stokes flow from rest, with zero pressure, whose fixed material particle enters one fixed open strip exactly when the machine halts. The force and velocity have bounded mixed derivatives and become one-periodic after initialization.

AI involvementAI-led
ImportanceNotable
Technical verificationReported
Human understandingFew

Understanding the problem

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For every deterministic one-tape machine and finite input, an effective smooth divergence-free mean-zero force on the flat three-torus gives a unique classical forced Navier–Stokes flow from rest, with zero pressure, whose fixed material particle enters one fixed open strip exactly when the machine halts. The force and velocity have bounded mixed derivatives and become one-periodic after initialization.

Why it matters

If correct, gives an effective machine-to-fluid reachability construction with a fixed observer and incompressible forcing.

What counts as progress

Can a forced flat-torus Navier–Stokes flow from rest encode halting in one fixed particle trajectory?

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