predictions
plain-language theorem explainer
Recognition Science supplies four approximate relations for the CKM Wolfenstein parameters drawn from the golden ratio and eight-tick phases. A particle physicist testing flavor-mixing models against PDG data would cite these values when checking consistency with observed lambda and eta. The definition simply enumerates the relations as a list of strings without further derivation or proof steps.
Claim. The Recognition Science predictions for the CKM parameters are: $λ ≈ (φ−1)^2/φ ≈ 0.236$, $A$ related to $φ$, the CP phase $η$ arising from eight-tick asymmetry, and unitarity angles constrained by $φ$.
background
The StandardModel.CKMMatrix module derives the 3×3 unitary CKM matrix from φ-quantized mixing angles linked to the eight-tick phase structure. The fundamental time quantum is one tick, and phases are multiples of π/4 for k = 0 to 7. Upstream results include the phase definition from EightTick, which supplies the periodic phases used for asymmetry, and the tick constant from Constants, which sets the RS-native time scale. The module doc states the core insight that CKM elements emerge from these φ-quantized angles.
proof idea
This definition constructs a fixed list of four string statements directly from the phi-ladder relations and eight-tick asymmetry. It applies the phase lemma to set the CP phase and uses the phi value from the forcing chain to approximate lambda, with no tactics or reductions beyond literal enumeration.
why it matters
This definition supplies the concrete numerical targets for CKM parameters inside the Recognition Science Standard Model derivation. It connects to the eight-tick octave (T7) and phi fixed point (T6) from the forcing chain. The module doc notes these predictions would be profound if verified and points to a potential PRD paper on CKM from golden ratio geometry. No downstream theorems reference it yet.
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