Promethean Acquiescence names a pivotal shift in the AI era: the habitual, willing surrender of human judgment to our own technology. Building on Günther Anders’ “Promethean Shame,” this converged definition and framework introduces Cognitive Capitulation—the endpoint where verification effectively ceases—and translates big ideas into measurable, governable practice. What’s inside: clear definitions and operational triggers (authority heuristics, epistemic outsourcing, convenience nudges); a two‑part measurement toolkit—the Promethean Acquiescence Scale (PAS) and Cognitive Capitulation Index (CCI)—for monthly dashboards; a Humans‑in‑the‑Loop governance library aligned with NIST AI RMF (Govern/Map/Measure/Manage) and EU AI Act human‑oversight expectations; and an implementation roadmap for safety/compliance use cases. This whitepaper proposes a philosophical insight into a compliance‑ready playbook for appropriate reliance on AI—so leaders can see, measure, and manage when comfort becomes capitulation.