The Quantitative Grammar of the Common-Scheme: Synthesis of Derived Laws
Synthesis Date: 04/09/2025
Objective: This document compiles a non-exhaustive list of applications of the Common-Scheme derivation protocol. It demonstrates that the constants and laws of physics are not arbitrary values, but rather deducible consequences of a unique architectural grammar, organized according to a fractal hierarchy with three levels.
Level 1: Internal Laws of the Standard Model (Concrete Pole)
This level describes the laws that govern interactions and relationships within the architecture of the Standard Model. These are the "rules of the game" for fundamental particles.
The Weak Coupling Constant (α_W)
Architectural Analysis: Abstract interaction, Composition Law (Level 1).
Deduced Law: The sum of the number of fermionic targets (12 *2) and the fundamental numerical interaction (3 *2).
1 / α_W = (12 *2) + (3 *2) =30
Result: Error of +1.42%. The law completes the derivation of the three couplings of the Standard Model.
[Read the complete demonstration →]The Fine-Structure Constant (α)
Architectural Analysis: Abstract interaction, Composition Law (Level 1).
Deduced Law: Sum of a Base Term (`(288+54)/Φ²`) and a Correction Term (`Δ=6`) derived from the binary signature.
1/α = ( (288 +54) / Φ² ) +6
Result: Error of -0.3%. The law is entirely derived from the axioms of the SC.
[Read the complete demonstration →]The W and Z Boson Mass Ratio
Architectural Analysis: Relation Law (Level 2) within the Abstract pole (forces).
Deduced Law: Ratio of global architectural constants: Framework Complexity (`8`) over Global Stability (`9`).
M_W / M_Z =8 /9
Result: Error of +0.84%. The law provides an architectural origin to the term cos θ_W.
The Z Boson Mass
Architectural Analysis: Property of the Abstract pole, Relation Law (Level 2).
Deduced Law: The electroweak scale (`v`) modulated by the Abstract geometric principle (`Φ²`) and corrected by the first complete dynamic structure (1 -1/2⁵).
M_Z = (v / Φ²) * (1 -1/2⁵)
Result: Error of -0.085%. The law derives an absolute mass with extreme precision.
[Read the complete demonstration →]The Weak Mixing Angle (Weinberg Angle, sin²θ_W)
Architectural Analysis: Relation Law (Level 2) unifying Concrete (EM) and Abstract (Weak).
Deduced Law: Product of the Geometric Tension (`(π-Φ²)/2`) and the Global Architectural Ratio (`8/9`).
sin²θ_W = [ (π - Φ²) /2 ] * (8 /9 )
Result: Error of +0.64%. The law unifies geometry and information.
[Read the complete demonstration →]