The Hilbert-Pólya Operator: A Candidate Construction via Redheffer-Mangoldt Symmetrization (v3 with Extended Tests and Honest Assessment)

Version 3: Extended numerical tests up to n=5000 and honest reassessment. The operator H_n = (R_n D_n + D_n R_n^T)/2 combines the Redheffer matrix with logarithmic weights. Key correction: extended tests reveal that non-zeta-zero points are approximated equally well by the spectrum (spectral density problem), undermining the spectral exclusivity claim from v2. The paper now presents both positive evidence (zeta zero approximation, log(p) eigenvalues, explicit formula connection) and negative evidence (spectral density, non-monotone convergence, unproven essential self-adjointness). Includes the extended test script for reproducibility. Previous 'theorems' (Attractor, Essential Self-Adjointness) downgraded to conjectures.