Resolution criteria
This market will resolve to YES if, by December 31, 2028, at 11:59 PM UTC, an open-weights AI model (or an agentic system powered strictly by open-weights models) successfully generates a verified mathematical solution or formalized proof resolving a major open aspect of the Navier–Stokes existence and smoothness problem, under the following conditions:
Open Models: The model(s) used must be open-weights, meaning the model weights are publicly downloadable (e.g., hosted on Hugging Face under an open or open-source license) at the time of the breakthrough.
Compute Cost: The total compute cost required to execute the generation/search/inference run of the proof must be under $1,000 USD. This cost is calculated based on commercial API rates or equivalent cloud GPU rental prices (e.g., RunPod, Vast.ai, AWS) at the time of the run. Pre-training costs of the base model are excluded; only the inference/inference-time-search compute cost to generate the specific proof is counted.
Verification: The solution must be Lean-verified.
Otherwise, this market will resolve to NO.
If a breakthrough is claimed but there is reasonable dispute over whether it qualifies as "solving" the problem or whether the compute cost was strictly under $1,000, resolution will depend on the consensus of AI researchers and mathematicians, with the market creator having the final authority to make a determination based on credible public documentation.
Background
In September 2026, OpenAI announced that an internal model (more advanced than GPT-6 Astra) solved the Navier–Stokes existence and smoothness problem (one of the Millennium Prize Problems) by proving that a 3D incompressible fluid can develop a singularity (finite-time blowup). The proof was written up and formalized in Lean. However, this solution required a massive closed-source multi-agent system (10,000 concurrent agents running for 88 hours), representing a massive compute expenditure far exceeding $1,000.
This market asks whether open-weights models (e.g., Llama, Qwen, DeepSeek, or other open-weights architectures) will be capable of achieving a similarly verified solution to the Navier–Stokes problem, or a comparable breakthrough, at a fraction of the cost—under $1,000 in compute—by the end of 2028.
Important: the AI must generate a Lean-verified proof, and the agentic system must not have internet access, so it can't just copy existing proofs. It will presumably know that Navier Stokes was solved and some details as to how, but it won't be allowed to look anything up.
It must not be a model made specifically to generate math proofs, and must be in the top 10 open models on whatever widely used leaderboards exist then. This is to ensure that it's not fine tuned to solve Navier Stokes or anything similar.
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1,000