Here is the overall view of the CPW=Chandrasekaran-Penington-Witten paper.
1. Leutheusser-Liu studied large N limit of thermal correlation functions of single trace CFT operators.
2. Further progress was made by Witten in Gravity and Crossed Product [arXiv:2112.12828[hep-th]]. This converts the Type III von Neumann algebras to Type II(infinity) algebra.
3. Above construction has a limitation and what CPW do first is to remove it.
4. Then they go over to the GSL=Generalized Second Law of blackhole thermodynamics.
5. Finally they apply their results to a thought experiment with black holes and wormholes.