From ω to Cross-Sections: An Organising Architecture for the Standard Model

The Standard Model's dimensionless parameters are derived here as consequences of a single algebraic axiom, ω² + ω + 1 = 0. A seven-layer derivation chain produces, in strict sequence: the colour number Nc = 3; a ladder of framework integers kH, kgrav, kₛ, kW, kGUT, kEM; six exact cross-product identities that link them rigidly; the three Standard-Model gauge couplings; and the full cross-section predictions for e+e− annihilation, with the form Nc · Σ Qq² arising at successive flavour thresholds. Each step is a mathematical consequence of the previous one; the argument is a chain of derivations in which every link enables the next. The cosmological constant problem, the strong-CP problem, the hierarchy, and the Yukawa hierarchy each receive an algebraic resolution rather than a dynamical one. No free parameters enter beyond the electroweak scale v = 246 GeV. This document's foundation paper is linked below"https: //zenodo. org/records/19641512