If someone ate a meal, became satiated and immediately vomited, should he still recite Birkat HaMazon, or would that be a blessing in vain?

This source-based Torah study examines the question: If someone ate a meal, became satiated and immediately vomited, should he still recite Birkat HaMazon, or would that be a blessing in vain? It follows the canonical Hebrew discussion through the weekly Torah portion and the Jewish sources cited there. This localized discovery layer is a concise abstract, not a full translation and not a practical ruling. Any halakhic, medical, legal, security, bereavement, political, mystical or other sensitive claim remains subject to the canonical review status and should not be treated as individualized advice or as an empirical conclusion.