Paper CCXVI: General Relativity from BCH G₂

GR = BCH order 2–4 on G2. BCH terminates exactly at order 4 for nilpotent root vectors of height ≤3 (the SU(3) subsector of G2 generating the metric and curvature). Order 5 vanishes for these elements, making GR UV-finite as a theorem. v2 qualification: v1 stated termination at order 4 for 'all' nilpotent G2 elements; correct statement is 'height-≤3 nilpotent elements'; highest root (height 5) has nilpotency degree 6. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.