This monograph introduces the Operational Standard Model (OSM), a geometric and algebraic framework that reconstructs six key Standard Model predictions from a single complex equation: w² − w = iπ/2. The solution, wτ, yields—using only π—the Weinberg angle, Higgs-to-W mass ratio, muon-to-electron mass ratio, pion-to-nucleon mass ratio, number of fermion generations, and the CP-violation phase. All predictions are parameter-free at tree level and match experiment to within 1% (except one at 1. 5σ due to experimental uncertainty). The OSM interprets the Native Calculus plane as physical spacetime, with its real and imaginary parts corresponding to mass-squared and charge type. The Standard Model gauge group (U (1) × SU (2) × SU (3) ) is derived from the algebraic process of cloning Hermit units. The uniqueness of three colors and three fermion generations is shown to be structural, not assumed. The framework also recovers special relativity and provides a geometric interpretation of the Higgs mechanism, with the companion pair wτ, wτ˜ forming the Higgs doublet. Designed as a physics-oriented primer for the Hyperoperation Theory Series, this monograph provides the symbolic toolkit and step-by-step procedures for deriving all six predictions from π. It is intended for readers of the OSM programme, serving as a reference for further developments in subsequent monographs (M16b–M19b).
Paweł Łukasz Garycki (Wed,) studied this question.