Flavour from the Wall — Mass hierarchy, quark mixing, and CP violation from zero-mode geometry on the compact time fiber (SQG Flavour, v2, consolidated and self-contained)

Given three generations as winding zero modes on the compact time fiber (SQG Generations, v4), this paper asks what distinguishes them, and answers with a closed model-level analysis of masses, mixing, CP violation, and the neutrino scale. It is self-contained: three declared inputs (the paired zero modes with their single radial ratio r, the local oriented wall, data at the common scale M_Z), then a structural chain carried by two theorems and seven lemmas with complete proofs, each verified symbolically. Hierarchy. Wall locality gives third-generation dominance (rank-one skeleton); finite width gives the doubly geometric spectrum 1 : σ² : σ⁴; the exact 2+1 zero-mode pairing makes the middle generation the antisymmetric winding combination, rigid against every symmetric deformation. The width-independent invariant obeys the exact narrow-wall law J = m₁m₃/m₂² = r²(K−1)/8, with K the kurtosis of the wall profile: the flavour data measure one moment of each sector’s wall. At M_Z: (K_up, K_down, K_lept) = (5.1, 21, 1.6) — the up wall exactly Gaussian in its harmonics, the down wall sub-Gaussian, the lepton wall a resolved pair of insertions. Universal two-channel (Georgi–Jarlskog-type) profiles are excluded by direct fit. Mixing. Middle-state rigidity forbids Cabibbo dominance unless the wall’s fiber-reflection symmetry is broken; the oriented fiber permits it. With two misalignment parameters fitted to |V₁₂|, |V₂₃|, the third element is a prediction: |V₁₃| = 0.0063 vs. observed 0.0037 — a factor 1.7 that is scale-stable, branch-independent, and mechanism-independent. The inversion from mass ratios to wall harmonics is multi-branched; mixing discriminates, excluding the antipodal (half-winding) down branch by two orders of magnitude. CP. For Hermitian wall kernels the exact 2+1 pairing is a generalised CP symmetry: the Jarlskog invariant vanishes identically [proved], and breaking the radial degeneracy is quantitatively insufficient. The oriented fiber admits a T-odd chiral kernel — an even phase c±₁ = c₁e^{iβ} — and β = 0.78° on the down wall reproduces the observed J_CP exactly. The residual deviations (|V_ub|, |V_td|, sin δ) then carry the same factor 1.7: one structural tension, not three, identified as the model’s sharpest repair point. Neutrinos. If the light masses inherit the invariant (normal ordering; declared assumption), the absolute scale is fixed nearly independently of the wall shape: Σm_ν ≈ 59 meV, m_β ≈ 8.8 meV, m_ββ ∈ [1.2, 4.0] meV — a sharp conditional null prediction for KATRIN and next-generation 0νββ. Nine fitted parameters against nine fitted observables; every claim carries an explicit epistemic grade, and every negative result is stated as a result. A prior-work section delimits the model against the vortex programme of Libanov, Troitsky and Frère, whose flavour information is radial and whose neutrino predictions are opposite (inverted hierarchy, m_ββ ≈ 13 meV): the two are experimentally distinguishable. All numbers are reproduced by the seven deterministic scripts included in this deposit. Companion papers: SQG Generations v4 (the mechanism and the pairing theorem this paper rests on); SQG framework paper and companion notes.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-20
DOI
https://doi.org/10.5281/zenodo.22019436
Primary Topic
Neutrino Physics Research
Type
preprint
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Flavour from the Wall — Mass hierarchy, quark mixing, and CP violation from zero-mode geometry on the compact time fiber (SQG Flavour, v2, consolidated and self-contained)

Karol Frank
Zenodo (CERN European Organization for Nuclear Research)
Neutrino Physics Research
preprint

Flavour from the Wall — Mass hierarchy, quark mixing, and CP violation from zero-mode geometry on the compact time fiber (SQG Flavour, v2, consolidated and self-contained)

Karol Frank
preprint en

Abstract

Given three generations as winding zero modes on the compact time fiber (SQG Generations, v4), this paper asks what distinguishes them, and answers with a closed model-level analysis of masses, mixing, CP violation, and the neutrino scale. It is self-contained: three declared inputs (the paired zero modes with their single radial ratio r, the local oriented wall, data at the common scale M_Z), then a structural chain carried by two theorems and seven lemmas with complete proofs, each verified symbolically. Hierarchy. Wall locality gives third-generation dominance (rank-one skeleton); finite width gives the doubly geometric spectrum 1 : σ² : σ⁴; the exact 2+1 zero-mode pairing makes the middle generation the antisymmetric winding combination, rigid against every symmetric deformation. The width-independent invariant obeys the exact narrow-wall law J = m₁m₃/m₂² = r²(K−1)/8, with K the kurtosis of the wall profile: the flavour data measure one moment of each sector’s wall. At M_Z: (K_up, K_down, K_lept) = (5.1, 21, 1.6) — the up wall exactly Gaussian in its harmonics, the down wall sub-Gaussian, the lepton wall a resolved pair of insertions. Universal two-channel (Georgi–Jarlskog-type) profiles are excluded by direct fit. Mixing. Middle-state rigidity forbids Cabibbo dominance unless the wall’s fiber-reflection symmetry is broken; the oriented fiber permits it. With two misalignment parameters fitted to |V₁₂|, |V₂₃|, the third element is a prediction: |V₁₃| = 0.0063 vs. observed 0.0037 — a factor 1.7 that is scale-stable, branch-independent, and mechanism-independent. The inversion from mass ratios to wall harmonics is multi-branched; mixing discriminates, excluding the antipodal (half-winding) down branch by two orders of magnitude. CP. For Hermitian wall kernels the exact 2+1 pairing is a generalised CP symmetry: the Jarlskog invariant vanishes identically [proved], and breaking the radial degeneracy is quantitatively insufficient. The oriented fiber admits a T-odd chiral kernel — an even phase c±₁ = c₁e^{iβ} — and β = 0.78° on the down wall reproduces the observed J_CP exactly. The residual deviations (|V_ub|, |V_td|, sin δ) then carry the same factor 1.7: one structural tension, not three, identified as the model’s sharpest repair point. Neutrinos. If the light masses inherit the invariant (normal ordering; declared assumption), the absolute scale is fixed nearly independently of the wall shape: Σm_ν ≈ 59 meV, m_β ≈ 8.8 meV, m_ββ ∈ [1.2, 4.0] meV — a sharp conditional null prediction for KATRIN and next-generation 0νββ. Nine fitted parameters against nine fitted observables; every claim carries an explicit epistemic grade, and every negative result is stated as a result. A prior-work section delimits the model against the vortex programme of Libanov, Troitsky and Frère, whose flavour information is radial and whose neutrino predictions are opposite (inverted hierarchy, m_ββ ≈ 13 meV): the two are experimentally distinguishable. All numbers are reproduced by the seven deterministic scripts included in this deposit. Companion papers: SQG Generations v4 (the mechanism and the pairing theorem this paper rests on); SQG framework paper and companion notes.

Zenodo (CERN European Organization for Nuclear Research)
Peace, Justice and strong institutions, Reduced inequalities
Neutrino Physics Research
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