A negative solution to the finite lattice representation problem
Source: github.com/openai/math/tree/main/preprints/A-Negative-Solut…
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.