Your causal description is incomplete; the loopy part requires expanding T1:
T0: Omega accurately simulates the agent at T1-T2, determines that the agent will one-box, and puts money in both of the boxes. Omega’s brain/processor contains a (near) copy of the part of the causal diagram at T1 and T2.
T1: The agent deliberates about whether to one-box or two-box. She draws a causal diagram on a piece of paper. It does not contain T1, because it isn’t really useful for her to model her own deliberation as she deliberates. But it does contain T2, and a shallow copy of T0, including the copy of T2 inside T0.
T2: The agent irrevocably commits to one-boxing.
The loopy part is at T1. Forward arrows mean “physically causes”, and backwards arrows mean “logically causes, via one part of the causal diagram being copied into another part”.
Your causal description is incomplete; the loopy part requires expanding T1:
T0: Omega accurately simulates the agent at T1-T2, determines that the agent will one-box, and puts money in both of the boxes. Omega’s brain/processor contains a (near) copy of the part of the causal diagram at T1 and T2.
T1: The agent deliberates about whether to one-box or two-box. She draws a causal diagram on a piece of paper. It does not contain T1, because it isn’t really useful for her to model her own deliberation as she deliberates. But it does contain T2, and a shallow copy of T0, including the copy of T2 inside T0.
T2: The agent irrevocably commits to one-boxing.
The loopy part is at T1. Forward arrows mean “physically causes”, and backwards arrows mean “logically causes, via one part of the causal diagram being copied into another part”.