Definition. Restricted-envelope comparison arm [ftip-00JX]

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A restricted-envelope arm declares an allowed intervention class \(\mathcal E_A\subseteq \mathfrak I_A\) for each architecture, specifying the permitted training, post-training, and inference procedures. The classes expose exclusions, search budgets, seeds, and stopping rules. Restrict the evaluation functional of Definition [ftip-00JJ] to \(\mathcal E_A\) and compare the resulting suprema under the same finite cost cap \(C\geq 0\), common evaluation law, and common declared cost accounting.

The measurable, integrable evaluation domain and extended-real conventions of Definition [ftip-00JJ] apply: an empty feasible class has value \(-\infty \), an unbounded-above feasible score set has value \(+\infty \), and a finite supremum need not be attained. The allowed class is part of the comparison, so its envelope is a restriction-dependent quantity, not an unrestricted architectural ceiling.