What question did this study set out to answer?

This work aims to derive the CP-violating phase from BCT void geometry without free parameters.

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March 22, 2026Open Access

BCT Letter 87 — CP Violation from BCT Void Geometry

Key Points

This work aims to derive the CP-violating phase from BCT void geometry without free parameters.
Derived the CP-violating phase from BCT void geometry.
Calculated the cos(δ_CP) using octahedral void diameter.
Matched derived CP phase with Particle Data Group (PDG) value.
Found cos(δ_CP) = 0.414214 and δ_CP = 65.530°, closely matching PDG value of 65.44°±0.85°.
Established a geometric relationship between void diameters and quark mixing.
Demonstrated that geometry encodes the universe's matter-antimatter asymmetry.

Abstract

Letter 87 of the BCT Superfluid Lattice Model programme. The CP-violating phase of the CKM quark mixing matrix — responsible for the matter-antimatter asymmetry of the universe — is derived from BCT void geometry with zero free parameters. The result: cos (δCP) = 2rₒct = √2−1 = 0. 414214, giving δCP = arccos (√2−1) = 65. 530°, matching the PDG value 65. 44°±0. 85° with error +0. 131%. The CP phase is the arccosine of the octahedral void diameter. Together with the Cabibbo angle sin (θC) = 2rₜet (Letter 86), the geometric parallel is exact: the tetrahedral void diameter gives quark generation mixing; the octahedral void diameter gives CP violation. The matter-antimatter asymmetry of the universe is encoded in the geometry of the BCT Planck-scale vacuum. Predictions #124–#125.

BCT Letter 87 — CP Violation from BCT Void Geometry

Key Points

Abstract

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