IndisputableMonolith.Foundation.CKMLambdaFromPhiLadder
The module predicts the Wolfenstein A parameter of the CKM matrix to equal exactly 9/11 by mapping it to a rung on the phi-ladder. Flavor physicists and model builders working on quark mixing would cite the result for its RS-native rational value inside the PDG band. The module consists of a chain of definitions that fix A via the phi-ladder rung formula and certify consistency with the imported Constants base unit.
claim$A = 9/11$, where $A$ is the Wolfenstein parameter in the standard CKM parametrization, obtained by assigning the appropriate rung on the phi-ladder with base unit $τ_0 = 1$ tick.
background
Recognition Science places physical parameters on the phi-ladder, with each rung scaled by a power of the golden ratio phi and referenced to the fundamental time quantum $τ_0 = 1$ tick supplied by the imported Constants module. The present module introduces the Wolfenstein A parameter together with auxiliary objects such as cabibboPhi and CKMLambdaCert. These definitions apply the Recognition Composition Law to products and ratios on the ladder to obtain the exact fraction 9/11 and to place the corresponding CKM lambda inside the experimental band.
proof idea
This is a definition module, no proofs. It directly assigns the value 9/11 to the Wolfenstein A parameter from the phi-ladder rung formula and supplies supporting definitions that certify the result lies in the PDG band.
why it matters in Recognition Science
The module supplies the RS-native prediction for the Wolfenstein A parameter that enters broader CKM constructions in the framework. It realizes the self-similar fixed point T6 and the eight-tick octave T7 in the quark flavor sector, furnishing a concrete testable value that aligns with the alpha inverse band. The result feeds downstream CKM matrix definitions and lambda certification lemmas within the same module.
scope and limits
- Does not derive the remaining Wolfenstein parameters B, rho, or eta.
- Does not address CP-violating phases in the CKM matrix.
- Does not extend the phi-ladder assignment to the lepton or neutrino sectors.
- Does not incorporate running of the parameters with energy scale.