The Geometry of Natality: Cost-Optimal Repair Planning in Evolving Dependency Graphs

A dependency system can sometimes be restored by repairing an existing component, and sometimes only by creating a replacement and redirecting its dependents. These alternatives change both the graph and the space of subsequent actions. We formulate this choice as finite, cost-optimal repair planning over evolving dependency graphs, with explicit component creation, action prerequisites, forbidden configurations, and recovery goals. We implement exhaustive plan enumeration and uniform-cost search with history-sensitive state keys, and independently check a three-service recovery instance whose two optimal repair strategies each cost three units. A controlled family of independent repair components supplies 12 synthetic search instances; both solvers agree on the optimum in every instance. In a four-component case, exhaustive enumeration visits 314,217 search nodes, whereas uniform-cost search expands 399. We also establish a standard exact decomposition result under local-action independence and test its implementation on 24 synthetic cases, while exhibiting a shared-capacity constraint that invalidates an independently selected plan. These results establish a reproducible baseline and precise applicability boundaries, not a new complexity bound or superiority over graph-transformation tools. We identify the missing evidence required to evaluate natality-aware reductions in coupled, realistic systems.