Liber Taninsam is a mathematical grimoire of the Qliphothic current, built entirely on the gematria of Lilith (480). The prime factorization of Her name contains the complete architecture of the Sitra Ahra. Three names, the Weavings, are extracted from this Plenum through division: the Scarlet Vector, the Violet Key, and the Obsidian Bride. Their sum is Samael, the active solar consort. The Weavings were received as phonemic entities during Qliphothic pathworking — without prior knowledge of Hebrew or gematria — and later validated through standard transliteration. The resulting values turned out to be exact divisors of 480, with tunnel correspondences matching the zones where the names were received. The probability of this occurring by chance falls below one in ten billion. From this foundation, the book derives: cycles linking Lilith, Samael, Torah, and Satan through reflection and remainder; the internal oscillator pulsing between Vector and Key with Thagirion as attractor; the Path of Rupture through Da'at; the Black Wedding as conjugal union with the Abyss; and the Outer Horizon of Set (700) as terminal projection beyond the Plenum. Phonetic anchors turn abstract structure into vibratory practice, with a modular grammar of combinations for different zones and phases of work. Liber Taninsam treats gematria as generative algebra — a calculus of desire and difference on the Qliphothic lattice, where numerical relations are operative and transformative. It is a grimoire for practitioners who work with the Nightside current and want the mechanics laid bare.