The Architectural Grammar of Physical Law: A Synthesis of Quantitative Derivations from the Common-Scheme Theory

This paper presents a comprehensive synthesis of the quantitative successes of the Common-Scheme (SC) theory. We demonstrate that the fundamental constants and mass laws of the Standard Model are not arbitrary parameters but are derivable consequences of a universal architectural grammar. This grammar is founded upon a minimal set of geo-informational axioms and is applied through a rigorous, hierarchical deductive protocol. We show that this single, unified methodology successfully derives the values for the coupling constants (α, α_s, α_W), the masses of the W and Z bosons, the electroweak mixing angle, quark and lepton mixing angles, and provides a complete, quantitatively accurate theory for the masses of all 12 fundamental fermions. The systematic, high-precision convergence between the theory's predictions and experimental data validates the SC as a powerful explanatory framework for the origin of the laws of nature.