Definition. Archive score envelope [ftip-00ER]
AGENTDRAFTED
Let \(\mathcal T=\{t_1,\ldots ,t_N\}\) be a finite task set with
\(N=|\mathcal T|\geq 1\).
For every chain \(a\) in the finite archive, let \(s_i(a)\in \mathbb R\)
be its score on task \(t_i\) under a declared common evaluation law. Define its
whole-chain mean by
\[J(a)=N^{-1}\sum _{i=1}^N s_i(a).\]
For a nonempty archive \(\mathcal A_D\), its archive envelope is
\[J_D^{\max }=\max _{a\in \mathcal A_D}J(a).\]
The finite real-valued maximum is attained by at least one archived chain.
It scores a single chain across all tasks; it does not select a different chain
for each task.
Deployment eligibility is a separate condition. A target configuration
specifies which recorded chains can execute with their stated behavior and
resource requirements. Maximizing over that eligible subset gives a deployable
archive choice when the subset is nonempty; if it is empty, there is no eligible
archived choice. Applying the recorded score to deployment additionally requires
the same evaluation law. Records from different configurations alone do not
establish these conditions.