What are the two conditions under which the closed-loop rollout trajectory terminates?

Explain the step-by-step history initialization and concatenation update mechanism for trajectory $\xi$ throughout a harness execution rollout.

Place the following events of an execution step $t$ in their correct chronological order according to harness kernel dynamics.

Explain why the rollout terminates at step 10, what observation $o_{10}$ is recorded, and how this termination differs from normal task completion.

In the formal execution rollout framework, how is the agent harness $h$ defined as a 4-tuple?

During the execution rollout of an agent harness, the backbone model $\pi_\psi$ is frozen.

Analyze the formal definition and arguments of the function $\text{Rollout}(\tau, \pi_\psi, h, C_\tau; \Pi)$, detailing the role of each argument in governing the resulting closed-loop trajectory $\xi$.

Match each mathematical construct from the execution kernel dynamics to its precise role.

Order the lifecycle phases of an execution rollout from initial setup to completion.

Analyze the kernel dynamics at step $t = 3$. Explain what observation $o_3$ is produced, why the rollout continues rather than terminating, and what condition would have caused termination at step 3.

In the harness kernel dynamics, how does the evaluation of an emitted action differ based on the partition of $\mathcal{A}$?

At the beginning of an agent harness rollout, the event history $\xi_{<1}$ is initialized as an empty set.

Match each mathematical symbol from the harness rollout formulation to its corresponding role.