This randomized trial develops a lepton mixing matrix construction using finite source-word methods, suggesting a new framework for neutrino mixing analysis.
A finite source-word construction for the PMNS angles, CP orientation, and current profile tests This release develops a finite, auditable construction of the lepton mixing matrix from the Artian/QTT source grammar. The source class is declared before comparison with experiment: dyadic closure supplies the π/4 anchor, the three-family simplex supplies the 1/3 share, the two-sided boundary supplies the 1/6 half-share, and the equilateral family geometry supplies √3/2. The common projection rail is \[ ρ=2πcos\!(π/8). \] The PMNS source word is then evaluated without fitting a mixing angle, an octant, or a CP phase. The upstream Cabibbo bridge is used as the declared quark-sector input, while the CP orientation is selected by the rephasing-invariant source-incidence quartet \[ K₁₃=Re\!(Uₑ₁Uμ3Uₑ₃*Uμ1*)>0, δ=π. \] This avoids assigning physical meaning to a convention-dependent sign of a matrix entry. Source result \[ {{aligned} sin^2θ₁₂&=0.3068801892717688,\\ sin^2θ₁₃&=0.02225721570824493,\\ sin^2θ₂₃&=0.5572965438428628,\\ δ&=180^∘. {aligned}} \] The finite enumeration contains \[ 4×7×7×16×2=6272 \] predeclared source words. Exactly one satisfies the source gates and the complete matrix unitarity conditions. The surviving matrix has maximum unitarity residual \(1.16×10⁻¹⁶\) and determinant \(1+8.6×10⁻³⁴i\). Profile-likelihood audit The frozen source point is tested against the official NuFIT 6.1 normal-ordering profile tables, rather than a one-dimensional Gaussian shortcut. The interpolated two-dimensional profile values are \[ {array}{c|cc} profile&Δχ^2(θ₁₃,θ₁₂)&Δχ^2(θ₂₃,δ)\\ IC23, no SK&0.2574&1.2234\\ IC24 + SK&0.2325&0.9749 {array} \] which lie inside the conventional two-dimensional 68.3% threshold \(Δχ^2=2.30\). The source construction is therefore a green-corridor result against the current profile tables; the atmospheric octant and CP-even point remain predictions to be tested by future data, not claims of experimental confirmation. The complete derivation, finite enumeration certificate, official NuFIT packets, reproducible verifier, hashes, render audit, falsifier ledger, and ontology are included in the reconstruction package. The stable paper-family concept DOI is 10.5281/zenodo.20735493. The framework is anchored to Quantum Traction Theory: Main Book v10.01 through the stable book concept DOI 10.5281/zenodo.17527179. Related corpus and reader anchors quantumtraction.org QTT DOI Map QTT Lexicon QTT Observatory Neutrino Family-Rank Reference Theorem Charged-Lepton Family-Rank Framework Quark/CKM Source-Access Framework Included in the current PDF preview and reconstruction archive: PMNS v6.0 paper PDF LaTeX source and theorem insert Finite 6272-word enumeration certificate NuFIT 6.1 profile receipt and official input packets Numerical verifier, certificate JSON, figure, hashes, and render audit
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Attar Ali (2026) studied this question.
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