# Metric facility placement planner

Family 125: The metric <i>k</i>-median approximation threshold and recovery. First review, 8 October 2026.

## Problem and potential new use

Operations teams can evaluate fixed-cardinality facility plans under a valid finite rational metric.

## Applicability and commercial boundary

The approximation guarantee does not cover capacities, nonmetric travel costs or an instance-specific optimality certificate.

## Initial business decision

Conditional engineering. Buyer demand and profitability remain hypotheses. This first pass does not establish a validated commercial market.

## Next verification action

Inspect epsilon-dependent runtime and validate the input metric and candidate set.

## Evidence scope

Catalog statement reviewed; inspect linked opportunity dossier for any deeper source review. This record alone does not establish full manuscript or proof verification.

Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json) for the exact manuscripts and available scope notes.