Exhaustive generation of orthomodular lattices with exactly one nonquantum state

We propose a kind of reverse Kochen-Specker theorem that amounts to generating orthomodular lattices with exactly one state that do not admit properties of the Hilbert space. We apply MMP algorithms to obtain smallest orthomodular lattices with 35 atoms and 35 blocks (35–35) and all other ones up to 38–38. We find out that all but one of them admit exactly one state and discover several other properties of them. Previously known such orthomodular lattices have 44 atoms and 44 blocks or more. We present some of them in our notation.