Is greeting a non-Jew first a halakhic rule or an act of exceptional piety?

This source-based Torah study examines: Is greeting a non-Jew first a halakhic rule or an act of exceptional piety? It follows the canonical Hebrew discussion through the parasha and classical Jewish sources. This localized discovery layer is a concise summary rather than a full translation of the article; practical, halakhic, medical, legal, historical, mystical or empirical claims remain source-framed and subject to the canonical review status.