All 3-edge-connected relativistic BC and EPRL spin-networks are integrable

Understand

We prove statement conjectured in [Baez and Barrett:2001] that every 3-edge-connected SL(2,C) spin-network with invariants of certain class is integrable.

• It means that the regularized evaluation (defined by a suitable integral) of such a spin-network is finite.
• Our proof is quite general.
• It is valid for relativistic spin-networks of Barrett and Crane as well as for spin-networks with the Engle-Pereira-Rovelli-Livine intertwiners and for some generalization of both.