Mongolian Calendar (Tsagaan Sar) (蒙古曆)

The Mongolian lunisolar calendar (Монгол цаглабар) — the Tögs Buyantu zurkhai of Sümbe Khambo Ishbaljir (1747), the reckoning behind ЦАГААН САР, the White Moon new year. Served by the SAME Kalacakra arithmetic as the Tibetan engine's four schools — the Mongolian lineage is the parameter set this house verified as 'newGenden' — and the proof is empirical: all THIRTEEN published Tsagaan Sar dates in hand (2024-02-10, 2025-03-01, and the full 2026–2036 table) reproduce EXACTLY and are asserted at load, including 2025, the year the Mongolian and Lhasa reckonings split (Phugpa Losar 28 Feb, Tsagaan Sar 1 Mar — both served by this house, neither averaged). Any Gregorian date returns the Mongolian year (12-animal cycle with Mongolian names, хулгана through гахай, and the five elements), the month by NUMBER in the Mongolian manner (Нэгдүгээр сар — the first month IS the White Moon), and the lunar day with the Kalacakra structure kept and NAMED: skipped days (chad) and doubled days (lhag) are disclosed, not smoothed — Tsagaan Sar 2025 itself opened on lunar day 2 because day 1 was skipped, and the payload says so. Plus this year's and next year's Tsagaan Sar dates on every response. Mongolia becomes the catalogue's 32nd tradition. Pure computation, no LLM.

Cost: 2 TIAN Points per call. tRPC procedure mongolian.date.