# Family 125: metric facility threshold and a planning-review product experiment

Selected threshold PDF pages 1-5 and 27-35, recovery PDF pages 1-6, scope, threshold Comparator/config/entry, refined-recovery Comparator and three parameter/reduction files were read at the pinned revision. Full source/proof/program acceptance is incomplete. The threshold is for each fixed positive epsilon; arbitrary-size accuracy constants, retained history expansion and surplus-removal enumeration leave practical runtime unestablished. Recovery has a distinct anchor/proxy promise, not inherited by an arbitrary plan.

A separate conventional exact reference checks strict rational metrics, unweighted candidate plans and LP-dual witnesses, with bounded exhaustive small optima. 5,127 reference, 34 existing-solver and four extra dual controls pass. In a generated 24-location case, a solver FEASIBLE plan with cost 12 is independently optimal through a checked dual of12. This validates a finite result, not a general speedup or customer benefit.

Current first product hypothesis: an optimization assurance workbench for consultancy facility-planning reviews, using established solvers and reproducible evidence. Buyer access, recurring need and profitable delivery remain unvalidated; direct source backend deferred. [Revised dossier](../../../../opportunities/011-facility-placement-planner/2026-10-09-v2.md), [first product specification](../../../../plans/optimization-assurance-first-product-2026-10-09-v1.md).