Can a public Shabbat violator or an apostate who sins defiantly be counted toward a quorum required by halakhah?

This source-based Torah study examines the question: Can a public Shabbat violator or an apostate who sins defiantly be counted toward a quorum required by halakhah? The canonical Hebrew discussion develops the issue through the weekly Torah portion and the sources cited there, preserving the distinctions, tensions, and practical implications of the original text. This localized discovery layer does not add any new halakhic, medical, legal, scientific, historical, theological, or empirical ruling or claim beyond the canonical Hebrew source.