We define a fixed-input phenomenological ordered-rotation ansatz matrix for the Cabibbo–Kobayashi–Maskawa sector. The construction is motivated by the down-type Dual Koide benchmark and by a PMNS-motivated split-sector ordering template, but neither ingredient is treated here as a first-principles source of quark mixing. The single object tested below is the ansatz matrix specified by the M1 down-type benchmark, the half-Cabibbo 1–2 split rule, the sine-half 2–3 split rule, and an empirical imported up-sector 3–1 square-root-coordinate correction Rₔ₃₁^ (m) with ₔ₃₁=14, interpreted as a split-sector 3–1 phase-sharing input. The product is mirror-like in the 1–2 and 2–3 particle/flavor blocks, while the imported square-root correction is attached as the reversed 3–1 terminal step rather than as part of a single global cyclic ordering. The superscript (m) is part of the notation and indicates an auxiliary square-root mass-coordinate correction, not an ordinary particle/flavor rotation. With the M1 primary input the ansatz magnitudes are |V₂₊₌^ans|0. 974455 & 0. 224552 & 0. 003754\\0. 224408 & 0. 973605 & 0. 041646\\0. 008880 & 0. 040861 & 0. 999125pmatrix, with |J| 3. 24 10^-5, (, , ) (85. 81^, 22. 97^, 71. 22^), and (2) 0. 719. The result is a compact phenomenological target for future flavor-model building, not a microscopic flavor theory and not a CKM-likelihood fit.
Nem et al. (Thu,) studied this question.