IndisputableMonolith.StandardModel.CKMMatrix
The CKMMatrix module supplies definitions for the Cabibbo angle θ_c and Wolfenstein-parameterized CKM matrix elements in the Recognition Science setting. Flavor physicists embedding the Standard Model into the unified forcing chain would cite these when computing quark mixing amplitudes. The module contains only definitions and imports the base Constants module with no proofs or theorems.
claimThe Cabibbo angle is the mixing parameter θ_c between the first and second quark generations. The CKM matrix is parameterized by Wolfenstein variables λ, A, ρ, η, yielding the elements V_ud, V_us, V_ub, V_cd, V_cs, V_cb.
background
The module operates in the StandardModel domain of Recognition Science, which derives all physics from the single functional equation and the forcing chain T0-T8. It imports the Constants module whose sole content is the RS time quantum τ₀ = 1 tick. Definitions here introduce θ_c for 1-2 generation mixing and the full set of CKM elements expressed through the Wolfenstein parameterization.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
These definitions feed the Standard Model constructions that connect to the mass formula yardstick * φ^(rung - 8 + gap(Z)) and the Berry creation threshold. The module supplies the CKM structure needed for any RS treatment of weak interactions and CP violation, consistent with the eight-tick octave and D = 3.
scope and limits
- Does not compute numerical values for θ_c or Wolfenstein parameters from the phi-ladder.
- Does not establish relations to other RS constants such as the fine-structure alpha band.
- Does not include proofs of CKM unitarity or mixing predictions.
- Does not address higher-generation mixings beyond the listed elements.
depends on (1)
declarations in this module (40)
-
def
cabibboAngle -
theorem
cabibbo_value -
def
wolfenstein_lambda -
def
wolfenstein_A -
def
wolfenstein_rho -
def
wolfenstein_eta -
def
V_ud -
def
V_us -
def
V_ub -
def
V_cd -
def
V_cs -
def
V_cb -
def
V_td -
def
V_ts -
def
V_tb -
def
hypothesis1 -
def
hypothesis2 -
def
hypothesis3 -
def
hypothesis4 -
def
hypothesis5 -
def
hypothesis6 -
def
bestCabibboFit -
structure
GenerationPhases -
def
mixingAngle -
theorem
gen12_mixing_largest -
def
jarlskogInvariant -
theorem
cp_violation_small -
def
unitarityAngle_alpha -
def
unitarityAngle_beta -
def
unitarityAngle_gamma -
theorem
triangle_sum -
def
predictions -
def
J_CP_obs -
theorem
eta_bar_pos -
theorem
rho_bar_pos -
theorem
eta_bar_interval -
theorem
rho_bar_interval -
theorem
unitarity_triangle_valid -
def
experimentalValues -
structure
CKMFalsifier