The Quranic {3,6,9} Fingerprint: Division Architecture and Cross-Text Controls

Abstract

Three new gates of investigation into the numerical structure of the Quran, extending the {3,6,9} digital-root fingerprint established in Papers I-III. Gate Five (Experiments 07-08): The fingerprint resides in the Quran's division boundaries, not in its word values. Real Surah boundaries: p=0.007. Same words, equal divisions: p=0.137. Same words, random: 99th percentile. Gate Six (Experiment 09): Sahih al-Bukhari (Arabic, religious, about the Prophet) as human-divided control: no fingerprint under any division (p>0.13). Gate Seven (Experiment 10): Torah in original Hebrew with Gematria and traditional Parashot: no fingerprint (p>0.33). Five alternative hypotheses formally eliminated. The fingerprint is exclusive to the Quran. Completed on the Night of the 27th of Ramadan 1446H (March 17, 2026).