Paper XLIII of the Brane-Bulk Series The Seven-Dimensional Fano Parent Spacetime B. D. Jagadeesan, MD

The parent spacetime is 7-dimensional. The seven imaginary units {e1, . . . , e7} of the octonion are the seven parent dimensions, connected by the Fano incidence struc- ture of PG(2, 2). Three theorems follow: (1) the two precursor black holes were alge- braically mandatory (Cayley-Dickson anti-involution); (2) space is 3D and a baryon has exactly 3 quarks because a Fano line has exactly 3 points; (3) the 5D Randall-Sundrum geometry is the eective limit of the 7D Fano parent spacetime after colour compact- ication. Wave-particle duality is the self-duality of the Fano plane. Euler's identity eiπ + 1 = 0 is the master equation. 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.