We construct a family of self-adjoint operators from the Redheffer matrix and von Mangoldt weights, and compare their spectra to the non-trivial zeros of the Riemann zeta function. A Monte Carlo analysis reveals that the observed spectral proximity is not statistically significant: random target points in the same interval are hit with equal accuracy, and the apparent convergence ⟨err⟩→0 is an eigenvalue density artifact. The paper's genuine mathematical content is a proven theorem over function fields: the Euler operator over F_q[t] has exact eigenvalues λ_k = k²(log q)² with multiplicity q^k (Theorem 16.1). The complete degeneracy breaking from F_q[t] (9 distinct eigenvalues out of 511) to Z (511 out of 511) is documented as a structural observation. Supplementary Python scripts reproduce all numerical results, including the null hypothesis test. Status: one proven theorem, a negative statistical result, and structural observations — not a proof of RH.