Definition. Sandbox [ftip-004S]
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    Fix an interactive realization \(\mathsf {Env}_{\mathsf T}\) from the declared task interface, a measurable evidence space \(\mathcal E_{\rm box}\), and a cost dimension \(m\geq 1\). A sandbox specifies an allowed action set \(\mathcal A^{\rm box}_{\mathsf T}\subseteq \mathcal A_{\mathsf T}\) that is measurable, a cost bound \(b_{\rm box}\in \mathbb R_+^m\), and, for each \(x\in \mathcal X_{\mathsf T}\) and \(0\leq t<T_{\max }\), an execution kernel

    \[ K_{t}^{\rm box,x}: \mathcal S_{\mathsf T}\times \mathcal A^{\rm box}_{\mathsf T} \rightsquigarrow \mathcal S_{\mathsf T}\times \mathcal O^{\rm obs}_{\mathsf T} \times \mathcal E_{\rm box}\times \mathbb R_+^m, \]

    It also specifies, for each \(x\in \mathcal X_{\mathsf T}\), a reset kernel

    \[ \mathsf {Reset}^{x}_{\rm box}:\{\ast \}\rightsquigarrow \mathcal S_{\mathsf T}\times \mathcal O^{\rm obs}_{\mathsf T} \times \mathcal E_{\rm box}\times \mathbb R_+^m. \]

    For an allowed action, the state--observation marginal of \(K_t^{\rm box,x}\) is the kernel \(K_t^x\) in the task realization; the state--observation marginal of the reset kernel is \(\rho _0^x\). The remaining coordinates record reproducible evidence and a realized cost increment. An admitted stopped trajectory must have componentwise cumulative cost at most \(b_{\rm box}\).

    The sandbox semantics include permissions, kernel and reset versions, evidence encoding, and cost accounting. A tool name or API schema alone does not determine these fields.