4 problems

Terwilliger systems' rank-generating polynomial factorization conjecture. There exist positive integers $d_1,d_2,\ldots,d_n$ whose sum is $d$ such that

Terwilliger systems' subdegree bound conjecture. The inequality above holds for every TD system.

Koolen's conjecture. For almost all finite connected simple graphs, the Terwilliger algebras coincide with the full matrix algebras.

Nomura–Terwilliger conjecture. With respect to this notation, the following hold: (i) $E^*_0\mathcal{T}E^*_0$ is generated by $E^*_0\mathcal{D}E^*_0$; and (ii) the elements of…