9 problems

Inverse-level conjecture. The cosmological constant satisfies

Boundary-Hilbert-space conjecture. The boundary Hilbert space of $A$ is spanned by $\mathfrak q$-deformed spin-network states

Boundary-state conjecture. The boundary states of $A$ are $\mathfrak{q}$-deformed spin-network states of the quantum group $\operatorname{SU}(2)_{\mathfrak{q}}$, with…

Let $G_1\bowtie G_2$ be the group associated with the Lie algebra case, and let $G_1\ltimes G_2^*$ be the skeletal 2-group associated with the skeletal Lie 2-algebra case. Suppose…

Holonomy operator ordering conjecture. The holonomy operator around $\mathcal L$ acts on spin-network states as

U(N) spinor representation conjecture. The space of such functions is isomorphic to

Barrett–Baez conjecture. Every 3-edge-connected $SL(2,\mathbb C)$ spin-network with invariants of this class is integrable; equivalently, the regularized evaluation of every such s…

Garoufalidis–Van der Veen integrality conjecture. The renormalized bracket should be integral, namely

Volume conjecture for classical spin networks. For any spin network $(\Gamma,\gamma)$ without trivial components and without bridges, equivalently 2-edge-connected,