Large language model based coding agents have made substantial progress on repository-level software engineering tasks. Existing repository benchmarks, however, usually start from a human-identified issue and evaluate whether a patch satisfies a functional signal. We present SWE-Prometheus, a benchmark for the broader task of improving repository engineering governance. Each task provides a fixed snapshot and an open-ended objective, requiring the agent to identify risks, prioritize interventions, and verify the resulting changes. SWE-Prometheus evaluates six governance dimensions through paired evidence, clean-environment probes, behavior gates, and two independent teacher ratings of the same evidence. The benchmark contains 60 repositories; ten models are evaluated on a shared 22-repository public subset, where mean Normalized Governance Improvement ranges from 0.0568 to 0.5760 and observed behavior-breakage rates range from 0% to 23%. On a frozen ten-repository batch, a repository-blind template obtains mean NGI 0.272, but its gains concentrate in Tests & CI, Quality Gates, and Documentation; it improves Reproducible Environment and Dependency & Security on none of the repositories. This baseline makes the distinction between adding governance artifacts and producing execution-backed improvements measurable. The no-op condition has median NGI zero and standard deviation 0.073; two teachers agree exactly on 57 of 60 dimension scores for the same no-op evidence. For the two highest conditional-mean systems, common-valid NGI is similar, while full-pool comparisons that include behavior failures favor Kimi-K3. These results show why repository-governance evaluation should report improvement, behavior preservation, evidence quality, and coverage together.