Axis Model Fermion Sector: Flavor Mechanics, Mixing, and Parent Interfaces
Andrew Morton · Public preprint · Exact operator algebra and benchmark reconstruction
Develops an exact finite-mode framework for flavor matrices and uses mixing reconstructions to identify the inputs still needed for a predictive theory.
Abstract
We develop a finite-mode framework for fermion flavor built on the public charged-cell authority chain. The constructive parent supplies an exact projector-resolved localized classical cell [1]; the classical supplement establishes linear energy-space stability and the exact classical Poincaré mass hyperboloid of that branch [2]; and the conditional postparent completion supplies the rank-one internal three-cell carrier B_σ^int ∼ (3z^σ, 6x) [3]. A controlled quantum one-cell particle, a physical three-cell particle B_σ^physical, spin and exchange statistics, and Standard Model representation provenance remain separate interfaces. Flavor is represented on the conditional three-mode Hilbert space ℋ₃ = span{|00⟩, |10⟩, |20⟩}. On this space, a finite operator basis spans every Hermitian 3 × 3 flavor kernel, allowing explicit construction of sector Yukawa matrices and the mixing matrices V_CKM = U_uL† U_dL and U_PMNS = U_eL† U_νL. An exact reconstruction of the frozen real CKM benchmark shows that rank-≤2 operator content is insufficient and that a rank-three transition response is required. Minimal one-shell and arbitrary-rank heavy completions are excluded within the fixed projected Legendre-tensor class. Positive local direct-source realizations are classified by a positive-semidefinite source Gram matrix. This establishes complete realizability while leaving the mixed normalization unselected in the absence of a parent-derived flavor selector. Generation counting is likewise conditional because the localized parent does not derive a self-adjoint flavor operator with an isolated, perturbatively stable rank-three spectral projector. A shared implementation verifies that the frozen curvature factors propagate through the canonical CKM benchmark path. The quark-mass interface separates perturbative transport from flavor matching through F_QCD = Z_match/R, and flavor-universal matching is excluded as the source of the observed hierarchy. The resulting framework provides exact finite-mode flavor mechanics, reproducible benchmark mixing reconstructions, no-go theorems for several minimal completions, and explicit parent interfaces for generation selection, electromagnetic charge readout, source normalization, and quark-mass matching.
Abstract references
[1] Localized charged-cell parent
[2] Classical stability and relativistic motion
[3] Multi-cell composition interface
Scope
The algebra spans all Hermitian 3 × 3 flavor kernels and can reconstruct a supplied matrix. A predictive application requires independent selection of the generation space, masses and mixing from the parent theory. The classical-body and weak-representation constructions supply additional conditional structure; a physical quantum matter carrier remains open.
Paper and supporting files
The Zenodo deposit includes manuscript sources, CKM and PMNS notebooks, and recorded benchmark outputs.
Read the current paper and supporting files on Zenodo
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