Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: Family 206. Finite lattice representation: counterexamples and undecidability
Family claims › Algebra · lines 1400–1405
OpenAI@2026-10-07#rem:oai-206
Some finite lattices are not congruence lattices of any finite algebra, answering the finite lattice representation problem negatively. Moreover, no algorithm decides whether a finite lattice has such a representation, or whether it is a full subgroup interval of a finite group.
The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.
Nearby in this section
- remark: Remark: Family 193. Serre's intersection-multiplicity conjecture
- remark: Remark: Family 194. Lech's multiplicity conjecture
- remark: Remark: Family 195. A counterexample to the small Cohen–Macaulay module conjecture
- remark: Remark: Family 196. A counterexample to Kaplansky's zero-divisor conjecture
- remark: Remark: Family 197. Nonsofic groups and group-ring counterexamples
- remark: Remark: Family 198. A counterexample to the little finitistic-dimension conjecture
- remark: Remark: Family 199. Counterexamples to conjectures of Auslander–Reiten, Tachikawa, and Nakayama
- remark: Remark: Family 200. Eisenbud–Green–Harris and lex-plus-powers in characteristic zero