The CKM Wolfenstein Parameters from Generative Triple Evolution Orbit Arithmetic

We derive all four Wolfenstein parameters of the CKM quark mixing matrix from the arithmetic of the Rule~110 cellular automaton orbit that the Standard Model generation sequence is forced to satisfy~, with zero free parameters. The derivation proceeds in two stages. First, the five quark-sector orbit indices N_ eff are identified with structural formulas in the GTE orbit constants = 3, = 5, = 13: the up quark at = ^2 = 9; the down quark at = = 5; the charm quark at = ^2(2 +1) = 275; the strange quark at = 2 (2 + ) = 186; and the bottom quark at = 2^ -1 = 8191, a Mersenne prime at the Higgs staircase endpoint. None of these values is a free parameter; all are consequences of the GTE cascade structure, machine-certified in Lean~4 with zero for the arithmetic identities. Second, the four Wolfenstein parameters follow. The leading parameter = ^2/(2^ × ) = 9/40 = 0.22500 agrees with the PDG value 0.22500± 0.00067 to 0.000\% (0.000σ); it is machine-certified in Lean~4 ( \_lambda\_formula, zero ). The subleading parameter A = √(N_ eff)(s)/N_ eff(c) = √(186/275) = 0.8224 matches PDG at 0.65σ. The remaining parameters and follow from a deep cross-sector identity: the CKM unitarity triangle radius = /2^ = 3/8 equals the GUT-scale Weinberg mixing angle (M_ GUT) = 3/8 (machine-certified; \_unitarity\_triangle\_radius\_eq\_gut\_weinberg). From = 3/8 and a Mersenne-to-algebraic ratio (γ) = √( / )/ , we obtain = 0.1545 (0.41σ) and = 0.3417 (0.63σ). All nine CKM matrix elements agree with the PDG within 1σ at O( ^4). The CP angle γ = 65.67^ lies -0.023σ from the PDG central value. The Mersenne primality of forces (γ) to be irrational, providing an arithmetic origin for CP violation.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-09
DOI
https://doi.org/10.5281/zenodo.20319415
Primary Topic
Particle physics theoretical and experimental studies
Type
preprint
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preprint

The CKM Wolfenstein Parameters from Generative Triple Evolution Orbit Arithmetic

Nova Spivack
Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
preprint

The CKM Wolfenstein Parameters from Generative Triple Evolution Orbit Arithmetic

Nova Spivack
preprint en

Abstract

We derive all four Wolfenstein parameters of the CKM quark mixing matrix from the arithmetic of the Rule~110 cellular automaton orbit that the Standard Model generation sequence is forced to satisfy~, with zero free parameters. The derivation proceeds in two stages. First, the five quark-sector orbit indices N_ eff are identified with structural formulas in the GTE orbit constants = 3, = 5, = 13: the up quark at = ^2 = 9; the down quark at = = 5; the charm quark at = ^2(2 +1) = 275; the strange quark at = 2 (2 + ) = 186; and the bottom quark at = 2^ -1 = 8191, a Mersenne prime at the Higgs staircase endpoint. None of these values is a free parameter; all are consequences of the GTE cascade structure, machine-certified in Lean~4 with zero for the arithmetic identities. Second, the four Wolfenstein parameters follow. The leading parameter = ^2/(2^ × ) = 9/40 = 0.22500 agrees with the PDG value 0.22500± 0.00067 to 0.000\% (0.000σ); it is machine-certified in Lean~4 ( \_lambda\_formula, zero ). The subleading parameter A = √(N_ eff)(s)/N_ eff(c) = √(186/275) = 0.8224 matches PDG at 0.65σ. The remaining parameters and follow from a deep cross-sector identity: the CKM unitarity triangle radius = /2^ = 3/8 equals the GUT-scale Weinberg mixing angle (M_ GUT) = 3/8 (machine-certified; \_unitarity\_triangle\_radius\_eq\_gut\_weinberg). From = 3/8 and a Mersenne-to-algebraic ratio (γ) = √( / )/ , we obtain = 0.1545 (0.41σ) and = 0.3417 (0.63σ). All nine CKM matrix elements agree with the PDG within 1σ at O( ^4). The CP angle γ = 65.67^ lies -0.023σ from the PDG central value. The Mersenne primality of forces (γ) to be irrational, providing an arithmetic origin for CP violation.

Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
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The CKM Wolfenstein Parameters from Generative Triple Evolution Orbit Arithmetic — Nova Spivack · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS