CMP.6:10 - Architectural Rationale

Update construction, finite-step control and stopping belong together because each changes what the algorithm can return. MATH.10 derives conditions from variations and MATH.21 constructs objects through convergence. CMP.6 supplies the effective rule, its repeated execution and the finite answer required from it.

CMP.5 can furnish a bound or an easier update subproblem; CMP.4 explores alternative candidates. CMP.7 can use the update to construct a learner, while keeping optimization progress distinct from performance on further cases. These are complementary algorithmic methods rather than one universal optimizer.