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On the Navier–Stokes Millennium Prize Problem

Project documentationPublication date Sep 8, 2026
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Overview

The announcement describes the mathematical/model workflow, later formalization, and concurrent forced-Euler work with a different scope.

Source publication and attributed assessments are distinct from independent OpenMath review.

Passages

The exact passages cited in OpenMath. Each passage identifies how its wording was recorded.

Passage 1 · OpenMath paraphrasePermalink

Our process; concurrent work; Euler and Navier–Stokes scope

The announcement describes the mathematical/model workflow, later formalization, and concurrent forced-Euler work with a different scope.

Passage details

Passage ID: fluid-regularity:entry:announcement:v1

Source item: announcement

Source record: fluid-regularity:source:announcement:v1

Used in

Explicit citations in versioned problem publications. A citation records a use; it does not confer proof or independent verification.

Three-dimensional Euler regularity →

Problem publication v9

Problem context · 3 citations

Research activity

Keep the concurrent forced result distinct

The announcement recognizes Levent Alpöge and Tristan Buckmaster’s separately generated forced-Euler work with an internal Anthropic model.

No theorem of that separate work is republished here without its own exact source and hypotheses.

History

A smooth unforced whole-space construction is released

Credits

Recorded authorship

OpenAI

AI involvement reported by the source

OpenAI reports an internal multi-agent research-model workflow and later GPT-6 Astra formalization. It recognizes Alpöge and Buckmaster’s concurrent forced-Euler work, which is distinct from its unforced Euler result.

Versions

OpenMath source records preserve exact citations. Observation dates order these records; they do not establish the latest upstream paper or proof.

  1. 2026-09-08 · selectedObserved Oct 13, 2026 · used in current publications

    On the Navier–Stokes Millennium Prize Problem

Record details
Source ID
fluid-regularity-announcement
Record ID
fluid-regularity:source:announcement:v1
Recorded title
On the Navier–Stokes Millennium Prize Problem
Revision
2026-09-08
Observed
Oct 13, 2026
Source updated
Not recorded
Content SHA-256
0c79e5644b3aee393f3772268f2ec4b3c624df00e909df3ca65896af334765b6
Update method
Compare the exact source and publish a new immutable curation revision.
Identifier policy
Stable source identity with exact versioned passages.
Check interval
90 days
Rights
metadata-link
License
Original source license and document rights apply.

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.

Source terms ↗