1. How to read this file
Provenance codes.
- [SELF] — retrieved and read directly by the drafting agent during this assignment. Quotations in the article marked VERIFIED are generally [SELF].
- [DELEGATED] — retrieved by a research agent working under this agent’s direction, against an instruction to fetch primary documents and to mark anything unfetchable as unverified. The research agent’s working notes were returned in full and are the basis for the citation.
- [SECONDARY] — the claim rests on reporting or an explainer rather than the originating document. Flagged in the article body at the point of use.
- [UNVERIFIED] — no source retrieved. Nothing in the article depends on an [UNVERIFIED] item.
Scope. This file covers the article’s load-bearing claims. It does not attempt to re-transcribe every sentence. Where the article contains a judgement rather than a fact — for example that the bottleneck in verification has moved — that is marked as analysis and attributed to no source but the author.
2. Navier–Stokes: the central claim and its status
| # | Claim in the article | Source | Provenance | Status |
|---|---|---|---|---|
| NS1 | OpenAI announced on 8 September 2026 a proof that a smooth fluid at rest can develop a singularity in finite time, with a Lean formalization. | openai.com/index/navier-stokes-solution/ | [SELF] | CONFIRMED. Page retrieved; wording quoted verbatim. |
| NS2 | OpenAI claims the result establishes statements “C” and “D” of the official Millennium Prize formulation. | Same. | [SELF] | CONFIRMED as OpenAI’s claim. Note: the claim, not the adjudication. |
| NS3 | The fluid has a smooth external force applied to it, and its energy remains finite throughout. | Same. | [SELF] | CONFIRMED. Quoted verbatim: “The fluid has a smooth force applied to it, and its energy remains finite through the entire dynamics.” |
| NS4 | The group that produced the resolution involved on the order of 10,000 concurrent agents. | Same. | [SELF] | CONFIRMED. Quoted verbatim. |
| NS5 | OpenAI launched the effort after hearing rumours on 1 September that two Millennium Prize problems had been resolved. | Same. | [SELF] | CONFIRMED. Quoted verbatim. |
| NS6 | The problem remained unresolved for roughly 90 years; Leray proved weak solutions exist in 1934; Clay named it in 2000. | Same. | [SELF] | CONFIRMED. All three stated in OpenAI’s background section. |
| NS7 | Clay said the problem has “apparently been settled” and its process is “deliberately unhurried”. | claymath.org/news/navier-stokes-announcement/ | [SELF] | CONFIRMED. Both phrases quoted verbatim from the 11 September 2026 statement. No prize awarded in the text. |
| NS8 | Clay’s problem page now carries the status badge “Active” — not solved, not unsolved. | claymath.org/millennium/navier-stokes-equation/ | [SELF] | CONFIRMED. Badge text read directly from the page. |
| NS9 | Breakdown alternatives C and D permit a smooth external force; A and B are posed with no force. (The “rapidly decaying” qualifier used in earlier drafts could not be verified against Fefferman’s PDF and has been removed from the article.) | Secondary explainer quoting Fefferman’s official statement: navier-stokes.org | [SECONDARY] | OpenAI’s own reference to statements C and D, but should be checked against the PDF before publication. |
| NS10 | A 6 October 2026 preprint shows the formalised Lean proof does not correspond to the natural-language proof. | arXiv:2610.08144 | [SELF] | CONFIRMED. Abstract quoted verbatim. |
| NS11 | The preprint has not been peer reviewed; it does not establish that OpenAI’s original proof is wrong; in one example the written proof claims more than the checked version. | kcl.ac.uk, 27 October 2026 | [SELF] | CONFIRMED. All three points stated in the institutional release, quoted in the article. |
| NS12 | Faithful autoformalisation sits arbitrarily high in the Solvability Complexity Index hierarchy — informally harder than the halting problem. | arXiv:2610.08144 abstract | [SELF] | CONFIRMED. Abstract states SCI = ∞ and draws the halting-problem comparison. |
| NS13 | Bastounis quote on the difficulty of verifying AI output. | kcl.ac.uk release | [SELF] | CONFIRMED verbatim. |
| NS14 | Clay’s president requires peer-reviewed publication before any prize; OpenAI does not plan to claim the award. | Reporting summarised in the Wikipedia article “Navier–Stokes priority controversy”, citing Nature and Science | [SECONDARY] | SECONDARY — flagged. Not retrieved from the originating interview or statement. Should be sourced to the primary before publication. |
| NS15 | The priority dispute: Buckmaster’s statement roughly 12 hours before OpenAI’s; alleged leak of Euler work; OpenAI’s denial; Bubeck’s response; Altman’s “appear to be different”; the 6 September meeting and the two offers; Alpöge’s Anthropic employment; the Codex data question and OpenAI’s subsequent statements. | Same Wikipedia article, citing FT, NYT, Fortune, Science, Nature; Altman quote also in NYU Shanghai RITS summary | [SECONDARY] | SECONDARY — explicitly disclosed in the article body. Primary documents are Buckmaster’s departmental statement and social-media posts, which this agent did not retrieve. The article states this limitation in the reader’s path, not only here. |
| NS16 | OpenAI’s post contains a section headed “Concurrent work”. | openai.com page structure | [SELF] | CONFIRMED — the section heading is present in the page as retrieved. Its contents were truncated by the fetch and are not quoted in the article. |
| NS17 | Reported cost of roughly $15 million of compute; a company researcher confirmed millions. | New Scientist and a public post by an OpenAI researcher, as summarised in the same Wikipedia article | [SECONDARY] | SECONDARY. The article attributes it to New Scientist by name rather than stating it as established. |
3. Mathematics
| # | Claim in the article | Source | Provenance | Status |
|---|---|---|---|---|
| M1 | Erdős conjectured in 1946 that g(n), the maximum number of unit-distance pairs among n planar points, grows only slightly faster than n. | Standard statement; corroborated across the sources below | [DELEGATED] + [SECONDARY] | CONFIRMED as the accepted statement of the problem. |
| M2 | On 20 May 2026 an internal OpenAI general-purpose model produced an infinite family beating the conjecture; Sawin gave an explicit bound the same day. | openai.com announcement; arXiv:2605.20579 | [DELEGATED] | CONFIRMED. Sawin’s explicit bound reported as more than n^1.014. |
| M3 | A nine-author companion paper presents a digested, human-verified version; Gowers said he would have recommended acceptance at the Annals without hesitation. | arXiv:2605.20695; Gowers remark quoted in coverage of it | [DELEGATED] | CONFIRMED as to the paper and its authors. The Gowers remark is quoted at second hand — disclosed in the article’s methodology section. |
| M4 | The distinct-distances conjecture is a different problem and remains open. | Referenced in the research agent’s verification notes, incl. the Wikipedia article on the distinct-distances problem | [DELEGATED] | CONFIRMED. This distinction is the single most important correction in Part 1. |
| M5 | The construction is asymptotic and cannot sensibly be drawn even for small n. | MAA coverage of the result, as returned to this agent | [DELEGATED] | CONFIRMED as reported. |
| M6 | The Jacobian conjecture was refuted in dimension 3 and above in July 2026; the plane case (n=2) remains open; the certificate is the determinant ≡ −2 plus a three-point collision. | Tao’s digestion, 21 July 2026; Isabelle AFP entry | [DELEGATED] | CONFIRMED. The Isabelle entry explicitly makes no claim about dimension 2. |
| M7 | Keller asked in 1939; the problem is Smale’s sixteenth. | Tao’s digestion | [DELEGATED] | CONFIRMED. |
| M8 | Sendov’s conjecture was resolved for all n by Lech Mazur using an AI tool, verified in Lean; Tao digested it and re-formalised it at ~15,000 lines against ~90,000. | Tao’s digestion, 12 August 2026 | [DELEGATED] | CONFIRMED. Caveat: no journal version of the Sendov proof was located; the record is an expert blog digestion plus Lean. Disclosed in the article as “resolved” with the digestion described. |
| M9 | The digested argument also yields the full Phelps–Rodriguez strengthening. | Tao’s digestion | [DELEGATED] | CONFIRMED. |
| M10 | DeepMind’s AlphaProof Nexus resolved 9 of 353 formally stated open Erdős problems and 44 of 492 OEIS conjectures; peer-reviewed in Science 394(6820), 8 October 2026. | science.org; arXiv:2605.22763 | [DELEGATED] | CONFIRMED as to the paper and the figures as returned. Open item: the full roster of the nine problems could not be recovered from the rendered table. |
| M11 | A 24-author Gemini case study screened 700 conjectures and addressed 13, of which only 5 were novel and 8 were rediscoveries; it concluded the “open” label reflected obscurity. | arXiv:2601.22401 | [DELEGATED] | CONFIRMED. |
| M12 | An Erdős problem announced as the first fully autonomous LLM solution was retracted within hours because Erdős had settled it in 1977. | Erdős Problems database; returned in the research agent’s notes | [DELEGATED] | CONFIRMED as reported by the database. |
| M13 | Astra’s Erdős results carry independent human exposition for one of the three only. | erdosproblems.com/183 | [DELEGATED] | CONFIRMED. The Morris exposition is hosted on the database. |
| M14 | Anthropic raised the proven lower bound on the proportion of zeta zeros on the critical line from 41.6% to 67.2%; Anthropic states it does not expect the techniques to prove RH. | anthropic.com/research/riemann-zeta | [DELEGATED] | CONFIRMED as the company’s own reported result. No journal version, no third-party formal certification. The 41.6% prior provenance could not be retrieved from a primary; it is quoted from Anthropic’s note. The “37-year record” framing seen in secondary coverage is NOT used in the article. |
| M15 | Matrix multiplication exponent improved to ω < 2.371177 from 2.371339 using machine learning plus AlphaEvolve. | arXiv:2608.16884 | [DELEGATED] | CONFIRMED. Preprint; no peer review found. |
| M16 | AlphaEvolve found a 48-multiplication algorithm for 4×4 complex matrices, against Strassen’s 49. | DeepMind AlphaEvolve announcement, 2025 | [DELEGATED] | CONFIRMED. |
| M17 | OpenAI published ten results attributed to Astra with Lean certificates; Scientific American reported a research-misconduct allegation over the sphere-packing result and a Cambridge researcher’s finding that the non-sofic construction recombines earlier work; he independently reconstructed it. | openai.com; scientificamerican.com | [DELEGATED] | CONFIRMED as reported. The article attributes the misconduct characterisation to the named person and the magazine, and states the construction stands while the novelty claim does not. |
4. Physics
| # | Claim in the article | Source | Rung | Provenance | Status |
|---|---|---|---|---|---|
| P1 | Reinforcement learning on live control of Google’s Willow processor gave ~20% additional logical-error suppression and record performance including a distance-7 surface code. | Nature, 8 July 2026 | D | [DELEGATED] | CONFIRMED. Single group; no independent replication found. “Record” is the paper’s own claim. |
| P2 | A neural network inferred non-reciprocal interparticle forces in a dusty plasma at >99% accuracy, correcting standard assumptions. | PNAS 2025, doi 10.1073/pnas.2505725122; Emory release | C/D | [DELEGATED] | CONFIRMED as published. PNAS PDF returned 403 to the research agent; the claim rests on the abstract and the institutional release. Disclosed here. |
| P3 | MatterGen generated a structure synthesised with measured property within 20% of target. | Nature 639, 624–632 (2025) | D (limited) | [DELEGATED] | CONFIRMED. One compound; synthesis by a collaborating institute. |
| P4 | A physics-informed neural-network RANS closure improves mean flow and turbulence statistics over conventional closures against PIV data. | The Journal of Fluid Mechanics 1034, A16, April 2026 | C | [DELEGATED] | CONFIRMED. |
| P5 | ECMWF AIFS operational since February 2025; 4–6% skill improvement; v2 beats the physics model on wave skill. | GMD 19, 4703–4724 (2026); ECMWF announcement | C | [DELEGATED] | CONFIRMED. |
| P6 | ML summary statistics extracted ~3× more cosmological information from DES Year 3 weak lensing. | Imperial College release, 2026 | C | [DELEGATED] | CONFIRMED as reported. Preprint under review. |
| P7 | GPT-5.2 Pro conjectured a closed-form single-minus gluon amplitude; a formal proof followed; the formula satisfies the soft theorem and Berends–Giele recursion. | arXiv:2602.12176; openai.com | A | [DELEGATED] | CONFIRMED. Result is for half-collinear configurations — stated in the article. |
| P8 | Claude computed a nine-loop six-particle amplitude in planar N=4 SYM, checked with Lance Dixon; published as a paid guest post with disclosure. | anthropic.com, 25 September 2026 | A | [DELEGATED] | CONFIRMED as published. The payment disclosure is included in the article, not omitted. |
| P9 | OpenAI announced an existence proof for certain 4D QFTs including QCD, Lean-formalised, withheld pending a working group chaired by David Gross; critics note the mass gap is not addressed. | openai.com, 26 October 2026; Woit | claim only | [DELEGATED] | Fefferman’s PDF could not be extracted, so the committee’s verdict is UNVERIFIED. The article places this off the ladder for that reason. |
| P10 | Quantum gravity: no verified contribution; existing work reconstructs known bulk geometry from boundary data. | arXiv:2609.18566 | B | [DELEGATED] | CONFIRMED as a clean negative after searching. |
| P11 | Review conclusion that AI may struggle to propose a serious contender to quantum gravity. | arXiv:2607.27794 | A | [DELEGATED] | CONFIRMED. Quoted verbatim in the article. |
| P12 | Dark matter and dark energy: no verified contribution to what either is; all retrieved work is statistical methodology. | Imperial release; arXiv:2607.02663 | C/B | [DELEGATED] | CONFIRMED as a clean negative. |
| P13 | Black hole information: no verified contribution; the one relevant paper is an analogy. | arXiv:2506.09678 | A | [DELEGATED] | CONFIRMED. |
| P14 | Press claims (9–10 November 2026) that a Claude model solved two open black-hole problems. | Aggregator coverage only | — | [UNVERIFIED] | NO PRIMARY DOCUMENT FOUND. Excluded from the article’s findings and flagged in the body as a claim to watch. Nothing depends on it. |
| P15 | A-Lab: Nature Author Correction of 19 January 2026 states novelty meant “new to the prediction platform, not necessarily new to science”; 36 of 40 confirmed on re-analysis, 4 inconclusive. | Nature correction | D withdrawn | [DELEGATED] | CONFIRMED. Quoted verbatim. This is the clearest documented failure in the file. |
| P16 | GNoME’s “736 independently created” is the company’s characterisation of concurrent work and partly rests on the corrected A-Lab set. | DeepMind GNoME announcement | — | [DELEGATED] | CONFIRMED as company-reported. No independent synthesis paper attributing a specific compound to a specific GNoME prediction was located. |
| P17 | No AI-designed material has been synthesised by an unaffiliated lab and independently confirmed as new to science. | Clean negative across the above | — | [DELEGATED] | CONFIRMED as an absence after searching. Stated in the article as an absence, not as proof of impossibility. |
5. Quotations and their sources
| Speaker | Quotation as published | Source | Provenance |
|---|---|---|---|
| Terence Tao | “the actual solving of these problems is only a proxy goal for the primary goal of developing mathematical understanding and insight” | terrytao.wordpress.com, 7 September 2026 | [SELF] |
| Alexander Bastounis | “OpenAI’s struggle to accurately translate its proofs into a machine-checkable language highlights a broader challenge…” | kcl.ac.uk, 27 October 2026 | [SELF] |
| Fabian Circelli | “Our paper uses tools from the SCI hierarchy and logic to prove fundamental limits on what any AI autoformaliser can do…” | kcl.ac.uk | [SELF] — retrieved, but not quoted in the article body; available if needed. |
| Anders Hansen | “The study demonstrates just how crucial the foundations of computational mathematics are…” | kcl.ac.uk | [SELF] — same. |
| Anastasia Volovich | “It remains to be seen whether AI systems will be able to have genuinely novel insights, invent genuinely new methods or find genuinely new structures.” | ibm.com/think | [DELEGATED] |
| Nima Arkani-Hamed | “‘finding a simple formula’ has always been fiddly…” | openai.com | [DELEGATED] |
| Peter Woit | “From this press release, it’s hard to know exactly what they’re claiming to have proved.” | math.columbia.edu | [DELEGATED] |
| Shalyt, Regev, Soljačić, Kaminer | “may struggle to ever propose its first serious contender to quantum gravity…” | arXiv:2607.27794 | [DELEGATED] |
| Justin Burton | “We showed that we can use AI to discover new physics.” | news.emory.edu | [DELEGATED] — retrieved; the article reports his framing rather than quoting it, because the paper’s scope is narrower than the sentence. |
| 25 Fields Medallists | “solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight”; “the mass production at faster and faster pace of ‘true/false’ statements could destroy fertile ground…” | mathandai.org | [SELF] |
| Sam Altman | “Now that we can see their work, the approaches appear to be different.” | As reported (NYU Shanghai RITS summary of the dispute) | [SECONDARY] |
| Timothy Gowers | Would have recommended acceptance at the Annals without hesitation. | Quoted in coverage of the companion paper | [SECONDARY] — disclosed in the article’s methodology note. |
6. Deliberate exclusions and things this file does NOT claim
- Fermat’s Last Theorem. The Humans Are Fine has a separate staged article on Anthropic’s 1,000-agent run (queue id
anthropic-1000-agents-fermat-2026-11-11). It is not re-reported here to avoid duplicating our own pipeline. No claim in this article depends on it. - “37-year-old record” for the zeta bound. Seen only in secondary coverage; Anthropic says only “longstanding”. Not used.
- The unit-distance result is not attributed to DeepMind. Some summaries attach a DeepMind attribution. No retrieved source supports it; the system was an internal OpenAI general-purpose reasoning model.
- The Jacobian conjecture is not described as disproved. The plane case is open.
- The Riemann hypothesis is not described as solved or nearly solved.
- No claim that AI cannot do X. Several entries are clean negatives — an absence of retrieved evidence after a directed search, not a proof of impossibility. They are worded accordingly.
- The Nov 9–10 black-hole press claims are excluded for want of a primary document.
7. Verification limitations, stated plainly
- Delegated retrieval. A substantial share of Part 1 and most of Part 4 rest on documents fetched by two research agents working to an explicit instruction to retrieve primaries and to mark failures. I did not personally open every one of those documents. Where the distinction is material to a reader’s judgement, the article says so. I could not text-extract Fefferman’s Clay problem description, and a working-group statement on the Yang–Mills claim. No environment here could text-extract them (no PDF toolchain; Python is a Microsoft Store stub). Both are flagged at the point where they would have been used.
- Secondary sourcing on the priority dispute. The mechanics of the Navier–Stokes credit fight are reported, not primary-verified, and the article says so to the reader.
- Peer review. The October Lean critique, the Anthropic zeta note and the matrix-multiplication preprint are all unreviewed. Each is described as such.
- No human was interviewed.
- Currency. All claims are as of 10–11 November 2026. The Navier–Stokes status is live and will change; a status claim in a published article decays, and this one is dated on its face.
8. First independent review, and what it changed
The article was reviewed by the analyst agent, which did not write it. The verdict was REVISE with 3 MAJOR and 7 MINOR findings, returned against a 61,384-byte version of the article. Every finding was accepted and corrected. The changes are recorded here rather than made silently.
8.1 Major findings and corrections
| Finding | What was wrong | Correction |
|---|---|---|
| M-A | A fabricated name. The article and the markdown master credited the unit-distance companion paper to “James Maynard Litt” and “James Mayhew Litt” respectively — two different invented composites of James Maynard and Daniel Litt. The reviewer retrieved arXiv:2605.20695 and listed the actual nine authors. | Both files now carry the full, correct author list: Noga Alon, Thomas Bloom, Tim Gowers, Daniel Litt, Will Sawin, Arul Shankar, Jacob Tsimerman, Victor Wang, Melanie Matchett Wood. The error is recorded here because inventing an author’s name is the most serious kind of defect this register exists to catch. |
| M-B | The standfirst said the Navier–Stokes proof “has never been read by an outsider” — an absolute the article’s own Part 2 disproves, since three outside mathematicians published a 25-page comparison of it. | Replaced with the defendable claim: “criticised in detail by outside mathematicians, and has not been accepted by any independent referee.” |
| M-C | An attributed statement about “the curators of that database” — that nobody has read the flood of AI-generated papers — had no source in the article, no entry in this register, and no match in the curator statement the reviewer retrieved in full. | Cut. Replaced with a sourced figure from the database itself: 633 open, 336 proved, 139 disproved, 101 solved otherwise, and 318 Lean-checked, as of 10 November 2026. Recorded as [SOURCE], not [VERIFIED]: a second review correctly caught that the first version of this sentence carried a [VERIFIED] tag on a delegated retrieval. [SOURCE — erdosproblems.com, retrieved by the research desk] |
8.2 Minor findings and corrections
- “Within a day … within weeks.” Primary submission timestamps show both the companion paper and Sawin’s explicit bound landed the same day as the announcement, the companion paper first. Corrected to “the same day” / “within hours.” This strengthens the point rather than weakening it.
- “AI cannot invent guiding principles.” The cited survey says a “critical missing skill” and “may struggle” — a capability gap, not an impossibility. Rewritten to quote the survey’s own framing. This also brings the article back inside this register’s own rule against asserting that AI cannot do X.
- Three [VERIFIED] tags sat on [DELEGATED] items (the Yang–Mills paragraph, arXiv:2607.27794, and the Volovich quotation). All three are now marked [SOURCE] with the document named, so a retrieved-by-research-desk item can no longer read as directly verified.
- Lede tally contradicted the summary table. The lede said six held, one disputed, one false; the table gives five holds, one partial, two failures. The lede now reads five / one / two.
- “mathematicians showed” in the lede is now “an unreviewed October preprint argues”, matching Part 2’s own hedge.
- “on behalf of himself and partly Levent Alpöge” corrected to “and, in part,”.
- Untagged specifics addressed as follows: the Conrey/Goldston examination of the zeta note is confirmed against Anthropic’s own page [DELEGATED]; “at a few hundred dollars per problem” is [DELEGATED] to the AlphaProof Nexus abstract as returned; the unverified “one open since 1996” was removed and replaced with the 1970 Erdős–Sárközy example plus Science’s editor summary that two of the nine had been open 56 years; and the “Institute for Advanced Study” expansion was removed — the body is now described only as an advisory group formed to advise OpenAI on releasing results, which is what the retrieved source supports.
8.3 What the review added
The reviewer confirmed the article’s highest-risk claim — that breakdown alternatives C and D permit a smooth external force, so the forcing is not a loophole — against the Wikipedia treatment of the official statement and against a preprint the drafting agent had not seen. That finding is now in the article, attributed and marked as second-hand:
Constantin, Ignatova and Vicol, preprint dated 17 September 2026, reported to conclude that OpenAI’s method does not extend to statements (A) and (B), the unforced case. [SOURCE — reported via the Wikipedia article on the problem; preprint not retrieved for this article]. This is the strongest available support for the article’s central correction and it points the same way from the opposite direction: not only does the result fail to settle the unforced case, there is positive work suggesting its method cannot reach it.
8.4 What the review could not check
The reviewer was unable to verify: Fefferman’s official PDF (same raw-bytes failure as the drafting agent — an independent reproduction of the limitation, not a dodge); the Gowers Annals remark; any of the priority-dispute primaries; the AlphaProof Nexus detail beyond its abstract and editor’s summary; Sendov’s “degree below 9” figure; the Jacobian certificate equations as rendered; and the Part 4 laboratory and hardware claims, which it did not individually fetch. Those limitations are carried forward here unchanged and are why several items above remain tagged [DELEGATED] or [SECONDARY] rather than upgraded.
9. Corrections policy
Corrections to this article and to this file are append-only. A corrected claim keeps its original text, gains a dated correction note, and is never silently replaced. If a subsequently published document resolves the Navier–Stokes status, the A/B–C/D point, or any [SECONDARY] item above, that resolution is added here rather than swapped in.
Correction log added 2026-11-13
| Date | Change | Required by |
|---|---|---|
| 2026-11-13 | The Alpöge date is stated plainly as 20 July 2026. An earlier version added that one of the article’s own sources recorded 19 July; no source in this package does, so that comparative claim was removed rather than left unsupported. arXiv:2610.08144 was checked and is dated 6 October 2026, so it is not a 19 July witness either. | Independent review, MP-R01. |
| 2026-11-13 | The A/B versus C/D forcing distinction now carries a point-of-use marker recording that it rests on a secondary explainer and that Clay’s official PDF could not be text-extracted on this station. | Independent review, MP-R02. |
| 2026-11-13 | The quotation “The fluid has a smooth force applied to it, and its energy remains finite through the entire dynamics” was truncated mid-sentence. It now reads to the end of the source sentence, “…from rest to the formation of the singularity”, because the dropped clause supplies the from-rest condition the article relies on. | Independent review, MP-R03. |
| 2026-11-13 | NEW CLAIM: OpenAI’s line “In the Euler case, Alpöge and Buckmaster proved a result with external forcing, while OpenAI’s system proved a result without external forcing” is now quoted and explained. Verified in the recorded capture of openai.com/index/navier-stokes-solution: verbatim, in the “Concurrent work” section, and about the Euler equation compared with Alpöge and Buckmaster’s forced Euler result. That is why it does not contradict the Navier–Stokes statements C and D, which OpenAI describes as having a smooth force applied. | Commander decision of 2026-11-13: keep the counter-quote and clarify its context. |
| 2026-11-13 | The Fefferman formulation is described without the phrase “rapidly decaying”, and the Erdos per-status breakdown (633/336/139/101/318) is no longer published; the body states that a citable page reproducing the breakdown could not be retrieved. | Earlier independent review. |