cabibbo_parameter
plain-language theorem explainer
The definition supplies the RS-native Cabibbo mixing scale as phi raised to the power minus eleven. Researchers deriving CKM elements from torsion geometry on the Q3 cube cite this value to build the mixing hierarchy. It is realized as a direct one-line assignment from the golden ratio.
Claim. The Cabibbo parameter is defined by $V_{us} = phi^{-11}$, where $phi$ is the golden ratio fixed point of the self-similar map in the Recognition Science forcing chain.
background
The CKM Derivation module starts from torsion mismatch between up-type and down-type sectors on the Q3 cube. The generation torsion schedule assigns differences of 11 between the first and second generation, so that sin(theta_C) approximates phi to the minus eleven. This definition anchors the subsequent rs_V_us, rs_V_cb, and rs_V_ub constructions that appear in the hierarchy and unitarity theorems.
proof idea
The declaration is a one-line definition that directly assigns the value phi raised to the integer power -11.
why it matters
This definition supplies the base element for cabibbo_parameter_pos, ckm_hierarchy, ckm_unitarity_structural, rs_V_us, rs_V_cb, and rs_V_ub in the same module. It realizes the RS approach to the Cabibbo angle from the torsion schedule {0,11,17} stated in the module documentation and connects to the phi-ladder mass formula and T5 J-uniqueness in the broader framework.
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