IndisputableMonolith.Physics.CKMGeometry
The CKMGeometry module supplies geometric definitions for CKM matrix elements, centering on the relation that sets V_ub equal to half the fine-structure constant via leakage from the cubic ledger. Particle physicists deriving quark mixing parameters from RS geometry without empirical fits would cite these expressions. The module consists of targeted definitions that link alpha-derived quantities to specific CKM predictions.
claim$V_{ub} = \alpha/2$ (fine-structure leakage); $V_{cb}^{\rm pred} = 1/24$; $V_{us}^{\rm pred} = \phi^{-3} - (3/2)\alpha$
background
The module sits inside the Recognition Science derivation of physics from the cubic ledger Q3. It imports the RS time quantum τ₀ = 1 tick from Constants, the constructive derivation of α⁻¹ via Gauss-Bonnet vertex deficits from AlphaDerivation, and rigorous interval bounds on φ and α from the Numerics.Interval modules. PhiSupport supplies the identity φ² = φ + 1 that underpins the phi-ladder rung assignments.
Local notation follows MixingGeometry for edge-dual couplings between generations. The module therefore translates ledger geometry directly into CKM element magnitudes without additional fitting parameters.
proof idea
This is a definition module, no proofs. It assembles the listed sibling definitions (V_ub_pred, V_cb_pred, V_us_pred, V_cb_geom, V_cb_match) by direct substitution of the alpha and phi expressions already established in the imported Alpha and PhiBounds modules.
why it matters in Recognition Science
The definitions feed CKMElementScoreCard for direct comparison of geometric predictions against PDG values, CKM for the Jarlskog invariant construction, MixingDerivation for the full topological proof of the mixing matrix, and HubbleTension for the dark-energy density link. The module thereby supplies the explicit V_ub = α/2 step required by the phi-ladder application to quark generations.
scope and limits
- Does not derive the full CKM matrix or CP phases.
- Does not perform statistical fits to experimental data.
- Does not extend to PMNS neutrino mixing.
- Does not compute higher-order radiative corrections.
used by (4)
depends on (7)
declarations in this module (20)
-
def
V_us_exp -
def
V_us_err -
def
V_cb_exp -
def
V_cb_err -
def
V_ub_exp -
def
V_ub_err -
def
V_ub_pred -
def
V_cb_geom -
def
V_cb_pred -
def
V_us_pred -
theorem
V_cb_from_cube_edges -
theorem
V_cb_match -
theorem
alpha_lower_bound -
theorem
alpha_upper_bound -
theorem
V_ub_match -
theorem
phi_inv3_lower_bound -
theorem
phi_inv3_upper_bound -
theorem
V_us_match -
structure
T11Cert -
def
t11_V_cb_verified