Why String Theory Works: Division Algebras, Celestial Holography, and the Misidentification of the Fundamental Degrees of Freedom

We prove that the computational successes of string theory are consequences of two mathematical structures: the four normed division algebras and the axioms of two-dimensional conformal field theory. Eight results are established. (1) The Green-Schwarz critical dimensions D in {3,4,6,10} are classified by normed division algebras via the Hurwitz theorem. (2) The Veneziano amplitude and the celestial MHV coefficient are both uniquely fixed by Haar measure on (R+,x). (3) Shadow symmetry Delta2-Delta and T-duality Ralpha'/R are both induced by the unique involutive automorphism t->1/t of (R+,x). (4) The KLT double-copy relation is the amplitude-level consequence of the Sugawara construction. (5) Anomaly cancellation on Gr(2,4) forces exactly three fermion generations. (6) All four-dimensional black hole entropies are reproduced by the Cardy formula applied to the near-horizon 2d CFT, without strings. (7) The Veneziano Regge tower is the off-principal-series (complementary series) component of the Mellin spectral decomposition. (8) The celestial CFT is the unique infrared fixed point of any consistent 4D quantum gravity with the Standard Model.