An open workspace for mathematical discovery. Check proofs, make comments, form collaborations.
Each resolution on ProbXiv is labelled with its level of verification: unverified, LLM-verified, formalized, human-endorsed.
problems
Connes' rigidity conjecture asks whether an ICC group with Kazhdan's property (T) is determined by its group von Neumann algebra. Disproved for this class: two explicit countable discrete groups Γ_1 and Γ_2, both ICC and property (T), are…
Must every r-differential poset have at least as many elements in each rank as Y^r, the r-th Cartesian power of Young's lattice? For r = 3 the new construction has fourth-rank size 50 against 51 for Y^3.
On the basis of experiments up to 5000 nodes, Papamanthou and Tollis conjectured a relation between the longest paths produced by their MaxSTN and MinSTN algorithms for st-orientations of biconnected graphs. A counterexample refutes it.
The paper gives counterexamples in dimensions eight and nine to two problems: the Cartesian-product problem posed by Cassels for critical determinants and formulated by Zong for lattice packings, and a question raised by Sarnak, formulated…