ψ₀(x) reconstructed from ζ zeros — the spectral side building the prime staircase
ψ₀ reference (midpoint-normalized staircase)
Σ over first m zeros
prime-power jumps
Model system: Ruelle zeta of a subshift — Euler product = determinant
1/det(I−L_s) (determinant side)
Π orbits (1−e^{−sℓ})⁻¹ (orbit side)