CKMLambdaCert
plain-language theorem explainer
The CKMLambdaCert structure bundles the Wolfenstein A parameter set exactly to 9/11, its distance to the PDG central value 0.826 being less than 0.013, the cubic identity phi cubed equals 2 phi plus 1, and the Cabibbo proxy 1 over phi cubed lying strictly inside the interval from 0.225 to 0.240. Researchers deriving Standard Model flavor parameters from the Recognition Science phi-ladder would cite this certificate when checking consistency of CKM mixing angles with the golden-ratio predictions. The declaration is a plain structure definition,
Claim. Let phi denote the golden ratio. The certificate asserts that the Wolfenstein parameter A equals 9/11, that the absolute difference between this A and 0.826 is less than 0.013, that phi cubed equals 2 phi plus 1, and that 0.225 is less than the reciprocal of phi cubed which is itself less than 0.240.
background
In Recognition Science the golden ratio phi is the self-similar fixed point forced at step T6 of the unified forcing chain. The module CKMLambdaFromPhiLadder extracts CKM Wolfenstein parameters from the phi-ladder. The upstream definition cabibboPhi sets the Cabibbo angle proxy to the reciprocal of phi cubed and records the identity phi cubed equals 2 phi plus 1 that follows from the minimal polynomial of phi. The definition wolfensteinA fixes the Wolfenstein A parameter at the rational 9/11, a value also appearing in GaugeFromCube and AnomalousMagneticMomentFromRS. The module doc states that this A lies inside the PDG band 0.826 plus or minus 0.013 while the Cabibbo proxy is required only to sit inside the wider experimental window (0.225, 0.240).
proof idea
The declaration is a structure definition that directly assembles the four fields from the upstream definitions of wolfensteinA and cabibboPhi together with the explicit numerical bounds supplied in the module.
why it matters
This certificate is instantiated by the downstream definition ckmlambdaCert, supplying a single verified bundle that downstream proofs can cite without repeating the four assertions. It records the structural claim that the Wolfenstein A parameter equals 9/11 (originating in GaugeFromCube) while the Cabibbo proxy remains inside the PDG band. In the larger framework the construction links the phi-ladder fixed point (T6) to Standard Model flavor mixing, supporting the eight-tick octave and the derivation of spatial dimension D equals 3 through the mass and coupling formulas.
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papers checked against this theorem (showing 2 of 2)
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Quark mass hierarchies reveal dual matrix structures
"the normalized quark mass matrix in the hierarchy limit hq23 → 0 ... Mq0 = (KqL)† MqN KqL ... flat matrix MqF = 1/3 [[1,1,1],[1,1,1],[1,1,1]]"
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Lattice QCD inputs enable nuclear-free CKM unitarity test
"We review current efforts by the Fermilab Lattice and MILC collaborations towards a correlated analysis of the lattice inputs needed for this test using Highly Improved Staggered Quarks (HISQ) on the N_f=2+1+1 MILC configurations along with Staggered Chiral Perturbation Theory (SChPT) as a functional form for the chiral-continuum limit."