LLM-assisted defect discovery has a precision crisis: plausible-but-wrong reports overwhelm maintainers and degrade credibility for real findings. We present Refute-or-Promote, an inference-time reliability pattern combining Stratified Context Hunting (SCH) for candidate generation, adversarial kill mandates, context asymmetry, and a Cross-Model Critic (CMC). Adversarial agents attempt to disprove candidates at each promotion gate; cold-start reviewers are intended to reduce anchoring cascades; cross-family review can catch correlated blind spots that same-family review misses. Over a 31-day campaign across 7 targets (security libraries, the ISO C++ standard, major compilers), the pipeline killed roughly 79% of 171 candidates before advancing to disclosure (retrospective aggregate); on a consolidated-protocol subset (lcms2, wolfSSL; n=30), the prospective kill rate was 83%. Outcomes: 4 CVEs (3 public, 1 embargoed); LWG 4549 accepted to the C++ working paper; 5 merged C++ editorial PRs; 3 compiler conformance bugs; 8 merged security-related fixes without CVE; an RFC 9000 errata filed under committee review; and 1+ FIPS 140-3 normative compliance issues under coordinated disclosure -- all evaluated by external acceptance, not benchmarks. The most instructive failure: ten dedicated reviewers unanimously endorsed a non-existent Bleichenbacher padding oracle in OpenSSL's CMS module; it was killed only by a single empirical test, motivating the mandatory empirical gate. No vulnerability was discovered autonomously; the contribution is external structure that filters LLM agents' persistent false positives. As a preliminary transfer test beyond defect discovery, a simplified cross-family critique variant also solved five previously unsolved SymPy instances on SWE-bench Verified and one SWE-rebench hard task.