OpenAI pushed a batch of 722 mathematics manuscripts to a public GitHub repository on October 6, 2026, crediting the work to an internal frontier model the company has not released or named. The number did not hold for long: OpenAI withdrew three of those manuscripts on October 7, 2026, after a sign error invalidated one argument and the two further papers that depended on it, and separately revised 14 more to fix smaller issues, as Retraction Watch and other outlets reported. The repository, hosted at openai/math, has held at 719 manuscripts across 372 families of related results since that correction, and still ships under an Apache-2.0 license, according to OpenAI’s own announcement post and coverage from The Verge. It remains one of the largest single dumps of AI-generated mathematical research ever made public, and it lands at a moment when OpenAI’s math credibility is already under scrutiny.
The release does not arrive in a vacuum. Two months earlier, OpenAI said a swarm of its agents had made progress on the Navier-Stokes existence and smoothness problem, one of the six unsolved Clay Mathematics Institute Millennium Prize Problems, each worth $1 million. That earlier claim drew both excitement and a very public rebuke from parts of the mathematics community over how the work was conducted and credited. The October 6 manuscript drop reads, in part, as OpenAI’s attempt to answer that criticism with scale and transparency, while critics argue it mostly repeats the same pattern on a larger canvas.
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What OpenAI Actually Released on October 6
According to OpenAI’s community post, the company is “releasing a broad range of new mathematical results produced by an internal frontier model,” and the public openai/math repository “currently contains 722 manuscripts organized into 372 related result families.” That framing, taken directly from the announcement, was the most precise description OpenAI gave of the release’s scope at launch. It lasted one day: on October 7, OpenAI withdrew three manuscripts after discovering the sign error and revised 14 others, which is why the live catalog has shown 719 manuscripts since. The model itself remains unnamed and unreleased, described only as an internal frontier system still undergoing safety work before any public rollout.
Each manuscript in the collection corresponds to a specific mathematical problem the model was set loose on. OpenAI says the system was posed roughly 4,000 problems in total, and it originally judged 722 of those attempts worth publishing, a figure revised down to 719 after the October 7 withdrawal. Either way, that is roughly an 18 percent yield rate from problem to publishable manuscript, though OpenAI has not characterized it that way itself. The subjects span number theory, combinatorics, theoretical computer science, and mathematical physics, according to a detailed breakdown published by FourWeekMBA.
Only ten of the 719 manuscripts ship with an abridged summary of the model’s reasoning process, a detail multiple outlets flagged as a transparency gap. Readers can see the final proof text and, in many cases, a formal verification, but not the chain of reasoning that produced all but a handful of the results. That matters for a release billed partly as a transparency fix, since the Advisory Group on Mathematics and AI had specifically asked labs to publish reasoning summaries for every released result, not just a sample.
The October 7 Withdrawal and Revisions
The correction came fast enough that it barely reads as a separate news cycle from the release itself. OpenAI pulled three manuscripts from the openai/math repository on October 7, 2026, after a sign error was found to invalidate one argument outright and undermine two further papers built on top of it. Fourteen additional manuscripts were revised in place rather than withdrawn, meaning their core results survived but needed correction to specific steps, figures, or citations. OpenAI has not published a detailed changelog explaining what each of the 14 revisions fixed, leaving outside reviewers to spot the differences between the original and corrected versions themselves. For a release already facing criticism over its lack of published reasoning summaries, a same-week retraction is not a reassuring signal, even though catching and fixing the error quickly is, on its own, a reasonable thing for a research team to do.
Inside the openai/math Repository: The Numbers
The repository structure itself tells part of the story. A preprints directory holds PDFs, source files, and citation instructions for each manuscript, while a separate Lean library tracks which results have a machine-checkable formal proof attached. The table below summarizes the headline figures OpenAI and independent reporting have attached to the release, updated to reflect the October 14, 2026 catalog count.
| Metric | Figure | Source |
|---|---|---|
| Manuscripts in catalog (as of Oct. 14, 2026) | 719 | openai/math repository |
| Manuscripts originally published (Oct. 6, 2026) | 722 | OpenAI community post |
| Manuscripts withdrawn (Oct. 7, 2026) | 3 | Retraction Watch, Online-Tech-Tips |
| Manuscripts revised in place (Oct. 7, 2026) | 14 | Retraction Watch, Online-Tech-Tips |
| Result families | 372 | OpenAI community post |
| Problems posed to the model | ~4,000 | FourWeekMBA / OpenAI README |
| Average compute per accepted result | ~3 hours of ChatGPT Pro-equivalent thinking | OpenAI README, via FourWeekMBA |
| Manuscripts with abridged reasoning summaries | 10 | Unite.AI, FourWeekMBA |
| Manuscripts with a Lean formalization (as of Oct. 14, 2026) | 300 of 719 (~42%) | openai/math repository |
| Repository license | Apache-2.0 | openai/math GitHub repository |
| Release date | October 6, 2026 | OpenAI community post |
Formal verification in Lean means a computer has independently checked the logical steps of a proof, removing the need to trust the model’s own account of its reasoning. The gap between the total catalog and what has actually been machine-checked is still the detail most mathematicians focus on first. OpenAI’s own README reportedly states that “some of the unformalized results could have issues,” a caution that undercuts any reading of the drop as a set of fully settled theorems, and one the October 7 withdrawal did nothing to dispel.
Lean Formalization Coverage Since Launch
The catalog’s Lean coverage improved in the week after release. As of October 14, 2026, 300 of the 719 manuscripts in the repository — about 42 percent — carry a Lean formalization, after six new formalizations were added following the October 6 launch. That leaves roughly 58 percent of the catalog resting on the model’s own written proof without an independent, machine-checked verification. Six new formalizations in a week is a meaningful but modest clip against a catalog this size, suggesting that closing the remaining gap will be a slow, incremental process rather than a single dramatic verification push. Mathematicians already skeptical of treating the release as a block of settled results have a straightforward number to point to: most of the catalog still has not cleared the one verification bar that does not depend on trusting OpenAI’s account of its own model.
The Navier-Stokes Precedent That Set Up This Release
To understand why October 6 landed with this much baggage, it helps to rewind to September 8, 2026. OpenAI announced that a large swarm of its agents, reported at around 10,000 agents working roughly 88 hours and exchanging close to 5 million messages, had produced a proof that a singularity exists in the three-dimensional Navier-Stokes equations under idealized, frictionless conditions, according to Quanta Magazine. Navier-Stokes existence and smoothness is one of the seven original Millennium Prize Problems the Clay Mathematics Institute set in 2000, each carrying a $1 million prize; six remain formally unsolved by the institute’s own accounting.
Who Actually Gets Credit
Quanta’s reporting on the episode is notable for how little credit it assigns to the AI system itself. Princeton’s Charles Fefferman, a Fields Medal winner, pointed to human mathematicians Diego Córdoba and Luis Martínez-Zoroa as the actual source of the key mathematical insight, rather than the AI agents that eventually formalized a version of the result. Mathematician Tristan Buckmaster, separately, described an early AI-generated proof draft he reviewed as badly written and difficult to parse, a far cry from a clean, citable paper. The picture that emerges from named mathematicians who reviewed the work is one of AI accelerating formalization of a result humans had already largely worked out, not of a machine discovering a Millennium Prize solution unaided.
NPR’s coverage of the same episode carried a headline that captured the mathematics community’s ambivalence: the AI had produced a result, but humanity had reportedly learned comparatively little from it, because the proof’s reasoning was not published in a form other mathematicians could study and build on. That is the exact complaint OpenAI’s October 6 release tries, at least partially, to address by including Lean formalizations and a handful of reasoning summaries alongside the manuscripts.
The Advisory Group’s September Rebuke
The Navier-Stokes episode triggered a formal response from the mathematics establishment. The Advisory Group on Mathematics and Artificial Intelligence, after collecting more than 600 replies from working mathematicians, published a set of responsible-release recommendations on September 29, 2026. The group’s core complaint was that frontier labs were testing advanced mathematics problems on proprietary models inaccessible to the broader research community, then publicizing selective results as marketing moments. “We do not endorse this practice, and we ask them to stop,” the group wrote, according to reporting that circulated the statement widely in the days after publication.
The recommendations were specific: deposit results in a scholarly repository no AI lab controls, attach persistent citable identifiers, disclose the model name, the exact prompts used, a reasoning summary, the time spent, and the estimated computing cost for every single result, and formalize proofs wherever possible rather than relying on the model’s own narrative account. Measured against that checklist, OpenAI’s October 6 release is a partial compliance story at best. The repository is hosted on GitHub under OpenAI’s own account rather than an independent academic archive, the model remains unnamed, prompts are not published, and only 10 of 719 manuscripts carry a reasoning summary. The Lean formalization effort now covers 300 of the 719 manuscripts, which is real progress against the group’s ask, but it leaves most of the collection resting on the model’s unverified word.
Why Mathematicians Remain Divided
Reaction to the October 6 drop has split along a predictable line. Researchers who work directly with AI-assisted proof systems have pointed to the scale of the release, 372 distinct families spanning several branches of pure mathematics, as evidence that frontier models are now capable of generating publishable-quality results far faster than any human research group. Skeptics counter that publishable is not the same as peer-reviewed, and that releasing claims directly to GitHub sidesteps the verification infrastructure mathematics has relied on for centuries. The October 7 withdrawal of three manuscripts gave skeptics a concrete example to point to only a day after launch, rather than a hypothetical one.
The Claims Facing the Heaviest Scrutiny
The presence of specific claimed results, including progress on long-standing problems such as the Mahler conjecture and a reported counterexample related to Kaplansky’s zero-divisor conjecture, according to FourWeekMBA’s reading of the repository, has drawn particular attention because those are the kinds of claims that normally take a research community months or years to verify, not days. Neither claim is among the three manuscripts OpenAI withdrew on October 7, based on the public description of the sign-error correction, but both remain in the roughly 58 percent of the catalog without a Lean formalization, meaning their verification currently rests on the same unformalized, model-written proof standard that already failed once in this release.
That skepticism is not coming from nowhere. OpenAI’s math credibility had already taken a hit before this year’s releases, and the company’s own safety and research staffing has been turbulent; OpenAI fired three safety researchers over a leak claim in a separate incident that fed a broader narrative of an organization moving fast and managing internal dissent aggressively. Against that backdrop, a 719-manuscript GitHub catalog from a model nobody outside OpenAI can test independently was always going to invite scrutiny rather than uncomplicated applause.
Expert and Industry Reactions
OpenAI’s own framing of the release, in its community announcement, is that the company is “releasing a broad range of new mathematical results produced by an internal frontier model,” and that the repository “currently contains 722 manuscripts organized into 372 related result families,” according to OpenAI’s community post. That figure reflected the catalog at launch; OpenAI withdrew three manuscripts the next day, bringing the live total to 719, where it has held since.
The Verge’s summary of the release captured the central tension succinctly: “OpenAI has revealed solutions to a number of long-standing mathematics problems produced by an unreleased frontier model in a batch of 722 manuscripts,” as The Verge reported, a framing that treats the manuscripts as solutions in waiting rather than settled results. That framing held up better than the manuscript count: three of the 722 did not survive scrutiny past October 7.
Firstpost Tech’s coverage emphasized the verification burden now sitting with the research community, noting that “OpenAI has published hundreds of mathematical results generated by an internal model, opening a new chapter in AI-assisted research while leaving mathematicians to verify the claims.”
FourWeekMBA’s analysis of the repository’s own documentation found that “the repository’s README says the catalogue holds 722 manuscripts in 372 families, that the model was posed approximately 4,000 problems, and that each result used, on average, three hours of ChatGPT Pro thinking compute,” according to FourWeekMBA’s report, confirming the headline compute figures independently of OpenAI’s own marketing copy. The problem count, family count, and compute-per-result figures have not changed since; only the manuscript total has, down to 719 after the October 7 correction.
Competitive Landscape: OpenAI vs. Google DeepMind in AI Mathematics
OpenAI is not the only lab racing to prove its models can do original mathematics. Google DeepMind has run a parallel track for two years, and the two companies’ public benchmarks offer the clearest side-by-side comparison available. At the 2024 International Mathematical Olympiad, DeepMind’s AlphaProof and AlphaGeometry 2 systems together solved four of six problems for a score of 28 out of 42 points, reaching silver-medal standard for the first time, according to DeepMind’s own announcement. A year later, an advanced version of Gemini using Deep Think reasoning scored 35 out of 42 points at the 2025 Olympiad, officially reaching gold-medal standard, according to DeepMind’s blog. OpenAI matched that gold-medal result in the same 2025 Olympiad cycle using a general-purpose reasoning model rather than a dedicated mathematics system, reportedly working the same problems in English within the standard competition time limit.
The October 6 manuscript release pushes that rivalry into new territory. Competition mathematics, however hard, deals with problems that have known answers and fixed difficulty bands. Research-level conjectures do not come with an answer key, which is exactly why the Lean formalization gap matters so much more here than it does in an Olympiad scoring table. DeepMind has generally paired its benchmark claims with transparent methodology papers; OpenAI’s math manuscripts, by contrast, arrive with an unnamed model, undisclosed prompts for all but ten results, and a README that itself flags unresolved reliability concerns, concerns the October 7 withdrawal did little to quiet. The race is no longer just about who can hit a higher score. It is increasingly about who can make research-grade AI mathematics checkable by someone outside the lab that built it.
Research Mathematics Is a Different Game Than Competition Mathematics
Benchmark leaderboards like the ones tracked by LMArena and Artificial Analysis are built for graded, reproducible tasks with a known right answer. Open mathematics research has neither. A model can be state of the art on every public reasoning leaderboard and still produce a research manuscript that collapses on close reading, because leaderboard benchmarks test pattern-matching against known problem types, not the kind of open-ended, no-answer-key exploration the openai/math repository claims to document. That distinction is why mathematicians keep asking for formal verification and reasoning transparency rather than accepting benchmark scores as a proxy for research credibility.
Timeline: How We Got Here
The manuscript release is the latest point in a fast-moving sequence that stretches back through the summer of 2026. The table below lines up the major milestones in AI-assisted mathematics research over the past two years.
| Date | Event | Lab / Source |
|---|---|---|
| July 2024 | AlphaProof and AlphaGeometry 2 score 28/42 at the IMO, reaching silver-medal standard | Google DeepMind |
| July 2025 | Gemini with Deep Think scores 35/42 at the IMO, reaching gold-medal standard | Google DeepMind |
| July 2025 | A general-purpose OpenAI reasoning model also reaches IMO gold-medal standard | OpenAI |
| September 8, 2026 | OpenAI reports agents produced a Navier-Stokes singularity proof, a Millennium Prize problem | OpenAI, via Quanta Magazine |
| September 22, 2026 | Reporting highlights mathematicians’ concern that little was learned from the Navier-Stokes claim | NPR |
| September 29, 2026 | Advisory Group on Mathematics and AI publishes responsible-release recommendations after 600+ replies | AGMAI |
| October 6, 2026 | OpenAI publishes 722 manuscripts in 372 families to the openai/math GitHub repository | OpenAI |
| October 7, 2026 | OpenAI withdraws 3 manuscripts after a sign error and revises 14 others, catalog drops to 719 | OpenAI, via Retraction Watch |
| October 14, 2026 | Catalog holds at 719 manuscripts; Lean formalization coverage reaches 300 of 719 (about 42%) | openai/math repository |
What Changed Between October 6 and October 14
The eight days after launch did more to reshape the release than anything since. The October 7 withdrawal is the only instance, so far, of OpenAI pulling published manuscripts from this catalog rather than simply revising them, and it happened fast enough that many of the first stories about the 722-manuscript drop had barely finished circulating. The Lean formalization work moved in the opposite direction: six new formalizations added in the same window pushed verified coverage to 300 of 719 manuscripts, a sign that at least some of the independent-verification work the Advisory Group asked for in September is happening, even if slower than the pace of new claims.
Market and Industry Impact
Recruiting Signal vs. Commercial Reality
For OpenAI, a public, large-scale mathematics release serves multiple business purposes at once. It is a recruiting signal to the small pool of research mathematicians and formal-verification engineers the company competes for against DeepMind, Anthropic, and a handful of well-funded startups. It is also a capability demonstration aimed at enterprise and government customers who care about reasoning depth, not just chatbot fluency, in domains like quantitative finance, cryptography research, and scientific computing. The unreleased status of the underlying model, however, limits the direct commercial payoff: customers cannot buy access to whatever system produced these manuscripts, only to OpenAI’s existing public models, which may or may not share its capabilities.
Regulatory Scrutiny Compounds After the Retraction
The release also lands amid heightened regulatory attention on how AI labs describe their own systems’ capabilities. The FTC has opened a three-company probe into OpenAI and Anthropic over AI agent behavior, and claims about an unreleased model solving century-old mathematics problems are the kind of statement that regulators, academic watchdogs, and competitors will want independently checked rather than taken on faith. The October 7 withdrawal adds a concrete data point to that conversation: a release that needed a correction five days after launch is a harder case to wave off as fully vetted. OpenAI’s decision to publish Lean formalizations for 300 of the 719 manuscripts — a sizable minority, though not yet a majority — is a partial hedge against that scrutiny, giving outside reviewers a mechanical way to check a meaningful share of the claims without needing access to the model itself.
What This Means for Developers and Enterprises
Software engineers and technical teams evaluating OpenAI’s public products should treat the math manuscript release as a signal about research direction, not a spec sheet for any model currently available through the API. The manuscripts were produced by a system OpenAI has not shipped, and the company has given no public timeline for releasing it. Teams building on OpenAI’s current public models, discussed in comparisons like GPT-6 Astra versus Gemini 4 Argon versus DeepSeek, should not assume the reasoning depth shown in the math repository is present in production endpoints today. OpenAI’s broader push into agentic products, including the recently launched Dots agent, runs on separate, already-released models rather than the unnamed system behind the math manuscripts.
What is more directly useful to developers is the Lean tooling pattern itself. Pairing a large language model’s output with a formal verification layer, rather than trusting the model’s self-reported reasoning, is a pattern that is increasingly showing up outside pure mathematics, in areas like automated theorem-proving for software correctness and formal verification of smart contracts. Engineering teams experimenting with LLM-generated proofs or formal specifications can learn from OpenAI’s repository structure even if they never touch the underlying mathematics: publish the artifact, publish the verification, and flag explicitly what has not yet been checked.
Risk Factors and Open Questions
Reproducibility and Verification Risk
Several open questions hang over the release. First, the roughly 58 percent of the catalog without a full Lean formalization rests on trust in a model OpenAI has not made available for independent testing, which is precisely the arrangement the Advisory Group’s September recommendations asked labs to move away from. Second, with reasoning summaries published for only 10 of 719 manuscripts, outside mathematicians auditing a given result have little visibility into how the model actually arrived at it, beyond the final written proof. Third, the claimed progress on named conjectures, including Mahler’s conjecture and a reported Kaplansky zero-divisor counterexample according to FourWeekMBA’s reading of the repository, has not yet been confirmed through traditional peer review, and mathematics history is full of claimed proofs that did not survive expert scrutiny. Fourth, the October 7 withdrawal confirms that OpenAI’s own internal review did not catch every error before publication, which raises a practical question for the roughly 58 percent of the catalog still waiting on Lean verification: how many of those manuscripts contain a similar mistake that simply has not been found yet.
Reputational Risk for OpenAI
There is also a reputational risk dimension specific to OpenAI. The company’s research credibility on mathematics claims had already been tested once this year by the Navier-Stokes episode, where named mathematicians credited human researchers over the AI system for the key insight. A second high-profile release that again drew criticism over verification and transparency, even one this large, was always going to be a reputational risk on its own; the October 7 withdrawal, landing before the mathematics community had even finished digesting the original 722-manuscript drop, compounds it further and risks reinforcing a narrative that OpenAI treats mathematics results primarily as marketing material rather than peer-reviewable science, a framing the Advisory Group explicitly warned against in its September recommendations. That narrative sits alongside a wider pattern of scrutiny on how AI labs talk about their own systems’ capabilities and risks, the same scrutiny driving Anthropic’s existential-risk disclosures ahead of its own IPO.
Predictions: Where This Goes Next
Based on the pattern established across 2024 through 2026, several developments look likely in the coming months. First, expect the mathematics community, through the Advisory Group on Mathematics and AI or a successor body, to push for a neutral, non-lab-controlled archive for AI-generated proofs, rather than continuing to accept GitHub repositories hosted directly by the labs making the claims, a push the October 7 withdrawal will likely reinforce. Second, expect OpenAI to keep expanding Lean formalization coverage in follow-up updates to the openai/math repository; the catalog already moved to 300 of 719 manuscripts (about 42 percent) by October 14, and the remaining 58 percent gap is still the single most criticized aspect of the release and the cheapest one to visibly improve. Third, expect Google DeepMind to respond with its own large-scale research mathematics release within the next two to three quarters, continuing the tit-for-tat benchmark competition that has defined the AlphaProof-to-Gemini-Deep-Think progression. Fourth, expect continued pressure on OpenAI to disclose a release timeline for the unnamed internal model itself, especially if external mathematicians begin independently reproducing or challenging specific manuscripts. Fifth, expect this episode to feature directly in ongoing regulatory conversations about AI capability claims, given the FTC’s existing interest in how OpenAI and Anthropic describe their systems’ behavior and capabilities.
How This Compares to Past AI Math Claims
Context matters here because AI-generated mathematics claims have a mixed track record of holding up, and the October 7 withdrawal of three manuscripts from this very release is itself a small data point in that record. The field moved from AlphaGeometry’s narrow, geometry-specific olympiad solver in 2024 to general-purpose reasoning models hitting IMO gold-medal scores just a year later, a genuinely fast capability curve. But competition mathematics and open research mathematics are different disciplines with different failure modes: an Olympiad problem has a known, graded answer, while a research conjecture does not, and the only real check is whether the broader mathematical community can verify, replicate, or formally confirm the result over time. Measured against that bar, the October 6 release is best read as a large, partially-verified claim rather than a settled scientific milestone, with the Lean-formalized subset — 300 of 719 manuscripts as of October 14 — representing the most defensible portion of the collection and the remaining manuscripts awaiting the kind of scrutiny that took mathematicians months to apply to the earlier Navier-Stokes announcement.
Frequently Asked Questions
What did OpenAI release on October 6, 2026?
OpenAI published 722 mathematics manuscripts, organized into 372 result families, to the public openai/math GitHub repository under an Apache-2.0 license. OpenAI withdrew three of those manuscripts the next day after a sign error and revised 14 others, so the catalog has held at 719 manuscripts since October 7. The manuscripts were produced by an internal frontier model that OpenAI has not named or released publicly.
Did OpenAI withdraw or correct any of the manuscripts?
Yes. On October 7, 2026, OpenAI withdrew three manuscripts after a sign error invalidated one argument and the two further papers that depended on it, and separately revised 14 additional manuscripts to fix smaller issues. The catalog has held at 719 manuscripts since, down from the 722 originally published on October 6.
What model generated the math manuscripts?
OpenAI has not disclosed the model’s name. It is described only as an unreleased internal frontier model, and the company has given no public timeline for releasing it.
How many of the manuscripts have been formally verified?
As of October 14, 2026, 300 of the 719 manuscripts in the catalog — about 42 percent — carry a Lean formalization, after six new formalizations were added in the week following the October 6 release. The remaining roughly 58 percent rely on the model’s own written proof without independent machine verification.
Is the Navier-Stokes claim from September 2026 related to this release?
Yes. In September 2026, OpenAI said its agents had produced a proof involving the Navier-Stokes equations, one of the Clay Mathematics Institute’s Millennium Prize Problems. That episode, and the criticism it drew from mathematicians over credit and transparency, directly preceded the Advisory Group on Mathematics and AI’s September 29 recommendations, which the October 6 release responds to in part.
What did the Advisory Group on Mathematics and AI recommend?
The group, after collecting more than 600 replies from mathematicians, recommended that AI labs deposit results in an independent scholarly repository, disclose the model name, exact prompts, reasoning summaries, time spent, and compute cost for every released result, and formalize proofs wherever possible. It stated it does not endorse labs testing advanced problems on proprietary, inaccessible models and asked them to stop.
How does this compare to Google DeepMind’s math AI work?
DeepMind’s AlphaProof and AlphaGeometry 2 reached IMO silver-medal standard in 2024 with a score of 28/42, and an advanced Gemini Deep Think model reached gold-medal standard in 2025 with 35/42. OpenAI matched the 2025 gold-medal result with a general-purpose reasoning model. The October 6 release moves the competition from graded competition problems into open research mathematics, where verification is harder and slower.
Can developers access the model that produced these results?
No. The model is internal and unreleased. Developers using OpenAI’s public API products are working with different, already-released models, and should not assume equivalent mathematical reasoning depth.
Where can I view the manuscripts myself?
The full collection of 719 manuscripts is published at the openai/math repository on GitHub, including preprint PDFs, source files, citation instructions, and the associated Lean formalization library where available.
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