Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 376-04. Geometric Programs for Solenoidal Forcing
Manuscript map · lines 9565–9574
OpenAI@2026-10-07#rem:oai-p-376-04
Authors: OpenAI. Family 376.
Title: Geometric Programs for Solenoidal Forcing.
Abstract: We construct smooth solenoidal mean-zero forces, periodic from time zero, for which a fixed particle on a flat three-torus reaches a fixed open strip exactly when a given machine halts. The initial fluid velocity and the pressure are zero. We also realize positive diagonal maps on coding sheets by incompressible shears, with explicit normal compensation for changes of planar area, and reciprocal maps on whole boxes of positive thickness. Complete local inverses, initialization rules, and intermediate trajectory bounds connect these geometric constructions to finite computations.
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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