IndisputableMonolith.Foundation.CKMLambdaFromPhiLadder
The module derives the Wolfenstein A parameter as exactly 9/11 from the phi-ladder applied to CKM matrix elements in Recognition Science. Flavor physicists comparing quark mixing data to theory would cite the result for its parameter-free prediction. The module organizes the derivation through sibling definitions that compose the Recognition Composition Law with the phi fixed point to fix the relevant rung gaps.
claimThe Wolfenstein parameter satisfies $A = 9/11$, obtained by mapping phi-ladder rungs to the CKM matrix via the Recognition Composition Law $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$.
background
The module imports the RS time quantum $ au_0 = 1$ tick from Constants. It builds on the phi-ladder mass assignment yardstick $ imes \phi^{rung-8 + gap(Z)}$ and the J-cost function $J(x) = (x + x^{-1})/2 - 1$ that satisfies the Recognition Composition Law. Sibling declarations introduce cabibboPhi, phi3_eq, and related quantities to extract the Wolfenstein A from these structures.
proof idea
This is a module collecting definitions and theorems; the core derivations in siblings apply the Recognition Composition Law to the phi fixed point to obtain exact fractions for the CKM parameters.
why it matters in Recognition Science
The module supplies the CKM Lambda derivation that supports the forcing chain from T5 J-uniqueness and T6 phi fixed point to observable flavor mixing. It contributes to the mass formula and alpha band predictions by fixing A without adjustable parameters.
scope and limits
- Does not derive the full CKM matrix or CP phases.
- Does not incorporate loop corrections or running couplings.
- Does not address neutrino or lepton mixing sectors.