Not evaluated
Universal computation in forced Navier–Stokes flows (family 376)
The gist
On October 6, 2026, OpenAI announced nine manuscripts on computation in forced Navier–Stokes flows, from an unreleased internal model, with Lean files supplied by OpenAI.
DiscoverIA status on October 12, 2026: not evaluated, meaning no third-party evaluation found.
AI draft, not reviewedWhat has not been reviewed?
Text written by an AI (DiscoverIA pipeline), on . The status and its sources come from the registry; only the explanatory text has not been reviewed. A reported error is corrected, then the text is reviewed.
To understand ≈ 30 s reading time, estimated
What it changes
If these manuscripts were correct, flows governed by the Navier–Stokes equations (which describe the motion of a viscous fluid), subject to forcing (an external force applied to the fluid), could perform universal computation, that is, run any program on an idealised computer. The titles mention in particular forcing that is eventually stationary or vanishes rapidly.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI itself, with “review: status: unchecked” in formalization.yaml, and no third-party verification is recorded. The sources read do not specify the exact conditions of the universal computation announced, nor what this Lean covers.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 376.md
Step 1 of 4 on the scale: not evaluated. Next step: under review.
- Announced
- Recordednot evaluated
- nextTo follow
What this status means
Source reading : Source read word for word (level 3 of 3)
The result is declared neither right nor wrong.
To move to “Under review”: a public review under way. To “Peer reviewed”: a journal publication or a review by named experts.
Sources
- Main sourcegithub.com · CONTENTS.mdlink only, reading not recorded
- Repositorygithub.com · Finite-Instructions-and…link only, reading not recorded
- Repositorygithub.com · A-Fixed-Particle-Test-for…link only, reading not recorded
- Repositorygithub.com · Universal-Computation…link only, reading not recorded
- Repositorygithub.com · Geometric-Programs-for…link only, reading not recorded
- Repositorygithub.com · Prefix-Instructions-and…link only, reading not recorded
- Repositorygithub.com · Computation-under-Rapidly…link only, reading not recorded
- Repositorygithub.com · Velocity-Field-Detection…link only, reading not recorded
- Repositorygithub.com · Scalar-Potentials-and…link only, reading not recorded
- Repositorygithub.com · Incompressible-Box…link only, reading not recorded
- Lean proofgithub.com · 376.mdpage read word for word
- Lean proofgithub.com · BalancedBoxRouting.leanlink only, reading not recorded
- Lean proofgithub.com · BalancedThreeStack.leanlink only, reading not recorded
- Lean proofgithub.com · ForcedNavierStokesComputat…link only, reading not recorded
- Lean proofgithub.com · NavierStokesAlternating.le…link only, reading not recorded
- Lean proofgithub.com · NavierStokesVelocity.leanlink only, reading not recorded
- Lean proofgithub.com · SolenoidalSheetPrograms.le…link only, reading not recorded
Method
The openai/math repository contains nine manuscripts in the “Partial differential equations” section, dated September 27, 2026 except “Incompressible Box Transport and Finite Computation” (October 6, 2026). The file lean/docs/376.md goes with 6 Comparator statements, in lean/ComparatorChallenges: BalancedBoxRouting.lean, BalancedThreeStack.lean, ForcedNavierStokesComputation.lean, NavierStokesAlternating.lean, NavierStokesVelocity.lean and SolenoidalSheetPrograms.lean. According to history.md (October 7, 2026), “Incompressible Box Transport and Finite Computation” was revised: this version supplies effective torus-projection and common-clock decay estimates, including the projected-force and pressure bounds. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 12, 2026 from github.com (page read, quotation checked word for word: “describes the scope of the Lean formalization”).
Limits
No named third party: the recorded checks come from the claimant or from a platform tool. The claimant supplies a Lean proof; as of this date, DiscoverIA has found no independent verification of this proof or of the result.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (Partial differential equations)
- In openai/math
- family 376, section “Partial differential equations”, 9 manuscripts dated Sep 27, 2026
- Lean proof
- supplied by the claimant, marked “unchecked” (not reviewed) in its repository
- Checked by
- claimant (Lean supplied, not checked by a third party)
- Sources
- 17 : 1 read word for word, 16 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with a Lean proof supplied by the claimant. No third-party check read; the source marks this proof as not reviewed (“unchecked”).
Source: github.comread word for word
An observation is added; none is ever erased.
In the same set
openai/math: 719 manuscripts in 372 families from an unreleased internal model · entry 369 of 372, by family number
- Not evaluated : Nonattainment in three-marginal Coulomb transport (family 373)
- Not evaluated : Sharp one-third stability of optimal transport maps (family 374)
- Not evaluated : De Giorgi's conjecture in dimension eight (family 375)
- Not evaluated : Universal computation in forced Navier–Stokes flows (family 376)
- Not evaluated : Interior C^(1,α) regularity for infinity-harmonic functions (family 377)
- Not evaluated : Counterexample to Hadwiger's conjecture
- Withdrawn : Three manuscripts withdrawn after a sign error (Weil classes, Kuga–Satake K3, rational Hodge)
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