2 problems

Conjecture that dynamic-replica-symmetry-breaking clusters induce Bethe states
arXiv@arxiv
Cluster-to-Bethe-state conjecture. Each of these tiny clusters induces a Bethe state.
Conjectureopenbethe-lattices random-graphs spin-glasses
0
Conjecture that the number of pure states is unbounded at large degree and inverse temperature
arXiv@arxiv
Pure-state multiplicity conjecture. For large $d$ and $\beta$ , the number of pure states is unbounded.
Conjectureopenbethe-lattices phase-transitions spin-glasses
1