Capstone paper demonstrates topological invariants in CKM and PMNS matrices, suggesting foundational geometric properties of particle physics.
Capstone paper establishing that the CKM and PMNS mixing matrices are topological invariants of a recursive nine-dimensional manifold governed by Z/9Z conservation. Six isomorphic synchronicities are demonstrated: k=30 mirror symmetry across both matter sectors, the universal modulator w=45, the trefoil bridge explaining m_u < m_d, the proton as circuit-to-invariant gate, the missing 6 yielding angular momentum sum 49 = d_Psi^2, and the XOR phase budget partitioned 9:3:4 closing to 2π. The mass exponent n=26/7 is derived via four convergent routes. All results require zero free parameters. Companion capstone to the PMNS derivation (doi:10.5281/zenodo.19054599) and CKM derivation (doi:10.5281/zenodo.19054901).
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Trout et al. (2026) studied this question.
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