{"id":"openai-math/A-Negative-Solution-to-the-Finite-Lattice-Representation-Problem","pdf":"https://github.com/openai/math/blob/main/preprints/A-Negative-Solution-to-the-Finite-Lattice-Representation-Problem-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-Negative-Solution-to-the-Finite-Lattice-Representation-Problem-September-24-2026","tags":["universal-algebra","lattice-theory","congruence-lattices"],"score":0,"title":"A negative solution to the finite lattice representation problem","domain":"Algebra","family":"206","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.RA","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Finite lattice representation and undecidability"}