Logarithmic-Potential Operator Frameworks and the Riemann Hypothesis: Structural Obstructions Away from the Critical Line

We establish structural obstructions within logarithmic-potential operator frameworks for the Riemann ξ-function away from the critical line. For σ ∈ (0, 1), define the parametrized potential V_σ: = ∂²ₜ-log|ξ (σ+it) | where ξ (s) is the completed Riemann zeta function. Main Result: For all σ ≠ 1/2, the potential V_σ is not a real-valued distribution. Consequently, no self-adjoint Sturm-Liouville operator can be constructed via standard extension methods. Proof Architecture: 1. Functional equation forces parity breaking at σ ≠ 1/22. Non-even functions have complex Fourier transforms3. Distributional derivatives inherit this complexity4. Complex potentials obstruct self-adjoint extensions Each step uses independent mathematical principles (complex analysis, harmonic analysis, distribution theory, operator theory), ensuring non-circularity. This upload includes: - Full technical paper (27 pages) - Elementary explanation for ages 10-12- README with multiple reading levels Keywords: Riemann Hypothesis, operator theory, structural obstruction, functional equation, logarithmic potential MSC 2020: 11M26, 47E05, 35P05