1Cademy - Harness Execution Rollout and Kernel Dynamics

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Theory

Harness Execution Rollout and Kernel Dynamics

Executing an agent harness $h = (M, P, A, F)$ with a frozen backbone model $\pi_\psi$ on a task $\tau$ with capability registry $C_\tau$ under protocol $\Pi$ induces a closed-loop trajectory:

$\xi \sim \text{Rollout}(\tau, \pi_\psi, h, C_\tau; \Pi) = (s_1, e_1, o_1, \dots, s_T, e_T, o_T)$

Execution initializes with an empty event history xi_{<1} = emptyset and protocol state $s_1 \in \mathcal{S}$ . At each step $t$ , the action module emits $e_t \in \mathcal{A} = \mathcal{U} \sqcup \mathcal{Y}$ , where $\mathcal{U}$ is the set of executable calls and $\mathcal{Y}$ is the set of terminal outputs. The execution kernel then evaluates $e_t$ :

$o_t = \begin{cases} \text{Exec}(e_t; C_t), & e_t \in \mathcal{U} \bot, & e_t \in \mathcal{Y} \end{cases}$

where $\bot$ is the terminal null observation. The history updates via concatenation xi_{le t} = xi_{<t} oplus (s_t, e_t, o_t), terminating when $e_t \in \mathcal{Y}$ or upon reaching a protocol- or budget-bounded stopping limit $T$ .

Updated 2026-10-02

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