Hoang Ốc (Six-House Building Ages) (越南六宅運)

HOANG ỐC — the Vietnamese six-house age system every family consults before building (and traditionally before marrying): each counted age (tuổi mụ) falls in one of six cung — Nhất Cát, Nhì Nghi and Tứ Tấn Tài auspicious; Tam Địa Sát, Ngũ Thọ Tử and Lục Hoang Ốc to be avoided — and a house is not begun in a bad-cung year (families mượn tuổi, borrow an elder's auspicious age, rather than wait). HALF OF THE SAO HẠN ROUND'S DEFERRAL, CLOSED BY DIAGNOSIS: earlier probes found inconsistent rows across sites; the full-rule re-probe showed WHY — the tradition's two formulations (decade milestones 10→Nhất Cát…60→Lục; and the digit-sum (tens+units) mod 6) are ALGEBRAICALLY IDENTICAL, proven at load over every age 10–99, while a widespread CORRUPTED '+6 years same cung' list circulates that breaks at every decade crossing (21 is Tam Địa Sát by both true methods, not Lục — pinned at load so the corruption can never creep in). Two witnesses with concordant worked examples (33 → Lục Hoang Ốc, 38 → Ngũ Thọ Tử) asserted at load. The tuổi mụ counted-age convention disclosed; the sibling hạn-8 layer remains DEFERRED by name (its published rows are still mutually inconsistent). Vietnamese becomes four systems. Pure compute, no LLM.

Cost: 1 TIAN Points per call. tRPC procedure hoangOc.check.