We investigate spectral properties of a family of finite-dimensional pseudo-Hermitian operators constructed on hierarchical fractal graphs. Numerical analysis reveals systematic convergence of the spectrum to the critical line ℜ (s) = 1/2 as the system dimension increases, with machine-precision agreement observed for systems of order 10⁴ vertices. The limiting spectral statistics agree with predictions of random matrix theory for the Gaussian Symplectic Ensemble. Connections to the Hilbert-Polya conjecture and quantum chaos are discussed.
Roman V. Savenkov (Mon,) studied this question.