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A negative solution to the finite lattice representation problem

Source: github.com/openai/math/tree/main/preprints/A-Negative-Solut…

OpenAI

OpenAI Mathopenai-math/A-Negative-Solution-to-the-Finite-Lattice-Representation-ProblemSep 24, 2026math.RAAI-generatedscore 0 · 🔥 1 post

We give a negative solution to the finite lattice representation problem. We prove that there is a finite nonempty lattice that is not the full congruence lattice of any finite nonempty algebra of any finite signature.

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OpenAI and the finite lattice representation problem - William DeMeowilliamdemeo.orgWilliam DeMeo

OpenAI has released two machine-written manuscripts that claim a negative answer to the finite lattice representation problem. What they prove, which parts a careful reading could check, where the risk sits, what the proof assumes, and how much of it is already formalized in Lean.

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