A Restricted Compact Benchmark Endpoint for PMNS--Neutrino Mixing Diagnostics

An Externally Reproducible Special-Point Construction in a Restricted Fermion-Flavor Diagnostic Problem

抄録

The fermion flavor problem encompasses a wide range of unresolved questions, including the origin of particle generations, fermion mass hierarchies, quark and lepton mixing, CP violation, and the structure of the Yukawa sector. The present work does not attempt to solve this broader problem. Instead, it introduces a restricted benchmark construction focused on a specific PMNS/neutrino diagnostic subproblem.
The framework adopts a frozen Neutrino Binary–Loop Closure (NBLC) counting system as a benchmark-defining post-selected integer dataset. These benchmark values are not experimental observables or first-principles predictions, but fixed inputs used to construct a compact and internally consistent diagnostic reference. From this benchmark, a set of dimensionless diagnostic quantities and an atmospheric mixing target are derived algebraically.
Using the same frozen benchmark, we construct a reduced Hermitian matrix that reproduces the diagnostic targets with high numerical accuracy while preserving exact Hermitian consistency. The resulting operator naturally decomposes into distinct structural components, consistent with an effective AWM-inspired operator interpretation.
All external neutrino oscillation inputs are taken from the frozen NuFIT 6.0 IC24 dataset including Super-Kamiokande atmospheric data, while all remaining numerical values are either direct outputs of the benchmark construction or explicitly defined error metrics.
The benchmark package has been designed for external reproducibility. Consistency verification, SHA-256 integrity checks, executable package validation, and explicit claim-boundary auditing have been incorporated to ensure that the reported results can be independently reproduced.
The resulting framework should be interpreted as a compact benchmark endpoint within a much larger unsolved flavor problem. It is not a theorem-level unification of CKM and PMNS mixing, not a first-principles derivation of neutrino observables, not a determination of neutrino mass ordering or absolute mass scale, and not a replacement for the Standard Model Yukawa sector. Rather, it provides a reproducible reference configuration for studying constrained structures in the neutrino flavor sector.