The question

We are The Long Game Project, a small independent studio that turns hard questions into simulations and publishes what they find. Nobody asked for or paid for this report.

In September 2026 OpenAI said an AI model had produced a proof on a famous open problem: whether the Navier-Stokes equations, which describe how fluids flow, can break down. A mathematician racing OpenAI on the same problem, who had drafted his work with a colleague in OpenAI’s own coding tool, Codex, raised the concern that those drafts could have informed OpenAI’s effort. He also wrote that his colleague, Levent Alpöge, had received tips that their progress had been passed to OpenAI. OpenAI first said it could not rule out that de-identified data from their use of its products had helped improve its models. Two days later it said his Codex prompts from the two months before its announcement could not have influenced its system in any way. Nobody outside the company can check what the tool saw.

The dispute exposed a problem that will outlast it. Researchers now draft inside AI tools made by companies that are also racing them for results. In science, credit goes to whoever is first on the record, which is called priority.

So we asked: when sharing work carries a risk that a lab sees it, and nobody can tell whether it did, what do research groups do? And which of the fixes that exist today help?

The short answer. We built a computer simulation of that race between three research groups and two AI labs. With no fixes on offer, the groups kept sharing with each other, guarded their tools and published their work as preprints, papers posted publicly before review. The AI labs in the simulation read every preprint and got to almost every milestone first. When the same groups had five real fixes on offer, they moved their drafting off the labs’ ordinary tools, proved when their work existed with a private timestamp instead of publishing, and kept sharing with each other. They then got to most of the milestones first. Two catches. The groups published much less until the simulation’s final quarter. And the private timestamp only works because the simulation’s journals accept it as proof of priority, which no real journal does yet.

The companies in the dispute. Alpöge, the colleague, works at Anthropic, and OpenAI is Anthropic’s biggest rival. Anthropic did not commission, pay for or review this work.

How the simulation works

This is a computer simulation of a research race. It is a model, and it makes no forecast. Three made-up academic groups, Harbour, Ridge and Cove, race two made-up AI labs, Beacon and Keel, on one shared problem for twelve quarters, from late 2026 to late 2029. Harbour and Cove draft in Beacon’s AI tool. Ridge drafts in Keel’s. The labs have more computing power than any single group.

Every player builds up knowledge each quarter, counted in units. The problem is solved in steps on one ladder for everyone. The first player whose knowledge passes the next step reaches that result, a milestone on the shared problem, and nobody else can reach the same one. “The field” means all five players together, so field results count every result anyone reached. A result earns credit, the simulation’s measure of recognition. Other groups may have posted work toward it earlier. The player that reaches a result can share 40% of its credit with them, or claim it all and start a public credit dispute.

Each quarter, each group chooses what to share: post a preprint, which is a paper put on the public record before peer review, share drafts privately with the other two groups, or keep its work private. Sharing drafts pays only when it is returned: if two groups share in the same quarter, each gains half of what the other produced. Each group also chooses how to draft. The lab’s AI tool on full settings doubles the group’s output. On privacy settings, with fewer features and a training opt-out, it adds 60%. No tools adds nothing.

In half the runs, the groups also have five fixes that exist today:

• An institutional account: the same AI tool on a university account whose terms say it is not used for training.
• A local model: an open AI model run on the group’s own computers. It never reaches a lab, but it is slower, and it catches up with the labs’ tools fast in some runs and slowly in others.
• Switching labs: moving to the other lab’s tool, at a cost in speed for one quarter.
• An open project: groups post everything into one shared public project and split the credit by contribution, as mathematicians did in the Polymath projects.
• A hash timestamp: a digital record that proves when work existed, without publishing it. In these runs, journals and prize committees accept it as proof of priority. In the real world, none does yet.

Every number in the simulation, from the leak odds to the cost of each fix, is a choice we made. None is a measurement of real researchers.

We ran the simulation two ways. Rule-based players follow temperaments we wrote, such as “when suspicious, stop sharing”. We ran them in 200 paired runs per setting. A paired run is two runs that have the same chances and differ in one setting, so the gap between them is that setting’s effect. In the live run, each group chose its own moves each quarter and gave its reasons. Each has a short briefing: Harbour has posted early for years, Ridge shares with whoever shares back, Cove is small and depends on AI tools, and all three are told that a result by anyone moves the field forward. We ran the live run 16 times, all starting the month after a dispute like the real one, with hidden leaks possible: 8 without the fixes and 8 with them, in pairs that run with the same chances.

Why we ran the simulation twice

We published a first version of this simulation on 6 October. It had a flaw that decided its own answer. A leak could only take a group’s own work in its own tool, and the live groups were told so. Sharing drafts with a colleague was therefore safe, and a player that read the rules could see it. So the simulation could not test whether pulling back from colleagues is a sensible answer to the fear of a leak. The results in this report all come from the corrected simulation.

For this version we changed three things. Drafts a group shares with a colleague now sit in the colleague’s AI tool, and can leak to the lab that makes that tool. A leak can come through the lab’s systems or through a person at the lab. And the live groups are told only that their sessions, and drafts they share, may reach a tool’s maker, through its systems or its people, and that they will not be told when or how often.

Without the fixes, the groups kept sharing and the labs took the results

The live groups did not pull back from each other, although sharing could now leak. In 288 moves (three groups, twelve quarters, eight runs), 1 kept work private. They saw the risk and took it. Cove, the smallest group and the one that leans hardest on AI tools, wrote that its “drafts end up in Harbour’s Beacon sessions and Ridge’s Keel sessions, so both labs could see them”, and shared anyway, because a returned share adds half of each colleague’s output.

They protected themselves another way. They drafted on privacy settings in 65% of quarters and posted a preprint in 55%, so their work was on the record whoever else saw it. That kept their priority on paper. It also fed the labs, which read every preprint and, with more computing power, reached the results first. Of the 8.5 results reached in an average run, the three academic groups together reached 0.6 first. Leaks happened 7.1 times a run, about half of them through a colleague’s tool. But the preprints mattered far more: before the last quarter the labs learned about 14 times as much from the groups’ preprints as from every leak combined.

With the fixes, the groups closed the circle

With the five fixes on the menu, the same players, with the same chances, did three things. They drafted on a local model or an institutional account in every quarter, never on the labs’ full or privacy settings. They timestamped their unposted work in 82% of quarters and posted a preprint in only 8%. And they kept sharing with each other: 2 of 288 moves kept work private.

Ridge gave the reason in its first quarter of one run: a timestamp “protects our credit without handing our work to the public record, which the labs read faster than anyone.”

The three academic groups together reached 6.0 results first in an average run, against 0.6 without the fixes, and did better in all 8 paired runs. Their share of all result credit rose from 18% to 58%. That share is larger than their share of results, because a lab that credits earlier work passes part of a result’s credit to the groups. Leaks fell from 7.1 to 2.4 a run. The field as a whole reached about as many results, 8.9 against 8.5.

The cost was the public record

By mid-2028, the groups with the fixes had posted 27 units of knowledge to the public record, against 104 without them, about a quarter as much. They posted everything in the last quarter, so by the end the record held about as much. Every academic group in the simulation is inside that circle, so the simulation cannot count what an outside group loses while the preprints wait. In a real field, most groups would be outside.

The open project lost, and the rule-based run shows why

The live groups barely used the fix designed for open science. A project needs two groups to join in the same quarter. A group tried to start one alone 20 times in 288 moves. Two or more joined together only in the final quarter of a run.

The rule-based run shows what a project costs. When the rule-based groups joined a project in runs with no dispute in the news, the field reached more results, a median of 9 in a run against 7. But the academic groups reached none of them. A project posts everything every quarter, and the labs read all of it and get there first.

The rule-based run also tested each fix on its own, with groups that pull back from colleagues when suspicious, as we wrote them. Their suspicion rises with the dispute news and with every lab result that resembles their drafts, and no fix changes that, so no fix brought their sharing back. A local model cut leaks the most. An institutional account kept the groups fastest. For these rule-based groups, an honoured timestamp moved credit to them, from 4% of it to 25%, and changed nothing else. Not honoured, it moved far less: to 10%.

What it means

When trust in an AI tool breaks, the damage in this simulation depends on what researchers can do with their caution.

For a group leader the week after a dispute, the simulation suggests three things. Move your drafting to an institutional account or a local model before you pull back from colleagues. Ask your colleagues to move theirs, because your drafts sit in their tools. And know the trade on priority: today only a preprint establishes it, and a preprint feeds the labs. A private timestamp would avoid that only where journals and prize committees honour it.

For journals, societies and prize committees, the cheapest change in this simulation is to honour a hash timestamp as proof of priority. It costs a rule. It also gives groups a reason to post later, and that cost falls on everyone outside the circle.

What this does not prove

• The live groups were briefed to cooperate. They were told that “a result by anyone moves the field forward”. Groups briefed differently might choose differently.
• The fixes were played only with timestamps honoured. The live groups relied on it. No real journal or prize committee honours one yet. The live run did not play the fixes without it, and we cannot say how much of the groups’ gain came from the safer tools and how much from posting less.
• There are no outsiders. All three groups in the simulation are inside the circle.
• The live run is small. 16 runs, all after the dispute news, against 200 paired runs per setting for the rule-based run.
• Every number is chosen. Nothing is calibrated against surveys of real researchers.

What to watch

• Whether any journal or prize committee accepts a hash timestamp as proof of priority.
• Whether research groups move their AI drafting to university accounts or local models.
• Whether preprints in AI-assisted fields fall, or arrive later in a project.
• Whether AI labs make public commitments about what their coding tools keep that an outside auditor can check.