The Koide Formula from Octonion Algebra

The Koide relation Q = 2/3 for charged lepton masses is derived from a single axiom: constraint exists. This axiom is the sole foundation of the present framework. Because constraint exists, the physical world exists as a nontrivial structured reality, and the algebraic, geometric, informational, and dynamical domains relevant to physics arise as derived consequences rather than independent assumptions. In the algebraic domain generated by this axiom, the normed division algebra hierarchy leads to octonions as the unique 8-dimensional realization. Octonion structure generates G2 automorphisms, triality, and three generations. Representation theory proves that Q = ISU (2) ⊂ SU (3) = 2/3 exactly, through rigorous steps combining Dynkin indices, G2 root geometry, weight formulas, and renormalization group fixed-point analysis. The derivation establishes that, at information saturation, the Koide parameter equals the Dynkin index through Casimir operator scaling in beta functions—proven as a theorem, not assumed. Holographic entropy bounds on the coset G2/SU (3) provide the information-theoretic foundation. No additional axioms. No free parameters. Agreement with experimental measurement Qₑxp = 0. 666661 ± 0. 000007 within 1σ. The charged lepton mass relation is therefore presented not as an isolated numerical coincidence, but as a derived consequence of the same single axiom that generates the physical world: constraint exists. Related resourcesAdditional preprints, theoretical frameworks, and ongoing work by the author are available at: https: //murad-ahmadov. github. io/