Productive Failure in Agentic Mathematics: An Auditable Connected-Domination Case Study

AI-assisted mathematics must distinguish generative plausibility from validated scientific status. We study this reliability problem through connected domination in connected triangle-free graphs of minimum degree at least four. Exact search recovers the known 10-vertex Crown(5) obstruction, disproving the investigated $c_4=2$ strengthening. Our main finite result determines $(s_4(8),\ldots,s_4(15))=(2,2,4,4,4,5,6,6)$ over 9,600,128 non-isomorphic target graphs. Orders 8–14 are optimized instance-by-instance, while order 15 uses exhaustive universal upper-bound certification plus exact matching lower-bound instances. The census is apparently unreported in our targeted audit, without a priority claim. The global floor-form bound $\gamma_c(G)\le\left\lfloor n(G)/2-1\right\rfloor$ remains conjectural. Methodologically, we implement an executable evidence gate: a generative model may propose claims and evidence requests, but deterministic validation of scope and typed artifacts alone promotes claim status. The order-15 equality demonstrates evidence composition, requiring complete coverage, a universal upper bound, and a matching exact instance. This enforces validity without asserting that the workflow improves discovery.