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AI 科研/形式驗證

OpenAI Releases Navier–Stokes Singularity Proof and Lean Certificate, but Mathematical Verification Is Just Beginning

OpenAI claims that an unreleased multi-agent system more capable than GPT‑6 Astra has constructed a proof that the three-dimensional Navier–Stokes equations lose smoothness in finite time under smooth external forcing. The team also released a Lean 4 formalization, but formal verification does not mean the mathematical community has accepted it as a solution to the Millennium Prize Problem.

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26 Testing Prompts Fail to Reliably Improve Coding Agents; More Tests Do Not Mean Higher Accuracy

A Zstandard implementation experiment compared 26 conditions, including TDD, fuzzing, property-based testing, and formal verification. None consistently outperformed the default group, which received no additional instructions. Agents often correctly identified high-risk areas, yet generated invalid inputs, proved irrelevant properties, or encoded incorrect outputs into tests.