Flavor Hierarchies as Geometric Readouts of a Common Kernel:A Structural Framework with Constrained Sector-Dependent Projections

A reproducible low-dimensional framework for CKM hierarchy, parameter identifiability, and sector-dependent flavor readout

抄録

We investigate a hierarchy-based framework in which flavor observables are organized as sector-dependent geometric readouts of a common structural kernel.
The framework introduces a three-level hierarchy coordinate together with a complex kernel that combines geometric distance and phase information. Within this picture, fermion masses, quark mixing, lepton mixing, CP-sensitive observables, and chirality are interpreted as different projections or readout maps acting on the same underlying structural backbone.
The purpose of this work is to distinguish between the common structural ansatz, the sector-dependent readout assumptions, and the numerical results supported by reproducible analyses.
For the quark sector, the magnitudes of the CKM matrix elements are described by a simple hierarchy-based parameterization in which adjacent mixing strengths are determined by exponential suppression along the hierarchy coordinate, while the non-adjacent transition is represented as a composite suppression proportional to the product of the adjacent mixings. This provides a compact structural interpretation of the observed hierarchy among CKM elements. A fixed benchmark coefficient reproduces the correct order of magnitude for the smallest mixing element, although it does not exactly match the adopted reference value.
Numerical and analytical tests further indicate that the currently investigated readout schemes for fermion masses, PMNS mixing, and CP-related observables do not yet achieve the same level of reproducible support as the CKM-magnitude parameterization.