New sum rules of the Koide type

We report a mass rule of Koide type with inverse shape, \[m_i=M^{(d)} (w_0+w_i)^{-2}.\] It applies to the down-quark sector with numerical precision comparable to that of the direct charged-lepton sum rule $m_i=M^{(l)} (z_0+z_i)^{2}$. For central mass values, Koide ratio reaches exactly $2/3$ near 280 TeV under Standard Model renormalisation-group running. We also review other rules of the direct kind involving quarks. --- Source: arXiv:2606.10060v1 - http://arxiv.org/abs/2606.10060v1 PDF: https...