A Rigorous Spectral Mapping from the Bu Axiomatic System to String Theory

Abstract

Starting from the seven foundational axioms of Bu Theory (Psy-Physics)—O₀ Earth–Möbius isomorphism, A₃′ standard nilpotent, A₄′ nilpotent connecting law, A₅″ oscillation activation, M₁ super-exponential decay, M₂ Gaussian compatibility, A₈ no-backflow firewall, and A₉ index closure—we construct a parameter-free rigorous spectral mapping Φ between the germ-layer structure of Bu Theory and all core structures of superstring theory. Five mapping theorems respectively lock in: the three-term mass-squared operator (vibrational + winding − normal-ordering), the linear Regge trajectory from derivative-order–spin correspondence, T-duality as a topological homotopy via O₀ conformal flip and M₂ Gaussian measure, BRST nilpotency Q²=0 from the nilpotent algebra a²=0, and the critical spacetime dimension D=10 from the Joyce G₂-manifold index framework with Fano-plane self-dual 3-form integration. All structural constants appearing in the derivation—32 (Möbius double-cover spectral gap 4×8k²), 3 (chiral pairing modulus-squared factor), 6 (quaternionic εijk sum), and 42 (octonionic Fano fijk² sum)—have independent algebraic or geometric origins with zero manual fitting. This work demonstrates that the fundamental spectral structure of string theory may be an inevitable manifestation of deeper topological-algebraic germ layers under classical projection.