Gokul's Self-Adjoint Divisor Lattice: A Discrete Arithmetic Origin of the Riemann Symmetry

This paper introduces the Gokul's Divisor Lattice Model, a discrete self-adjoint framework revealing the arithmetic origin of the Riemann symmetry. Gokul’s Divisor Density Law states that the total divisor density of all positiveintegers is ζ(1), and its spectral constant is Euler’s constant γ.The model is built from the divisor and forbidden-divisor densities, forming a compact Hilbert–Schmidt operator whose spectrum exhibits mirror balance around ½. Euler’s constant γ acts as the spectral phase aligning the local and global components of the lattice. Analytical proofs and numerical tests confirm bounded, real, and symmetric behavior of the normalized spectral field (10⁻⁴–10⁻³ amplitude range). The results demonstrate how the divisor lattice inherently reproduces the functional symmetry ζ(s)=ζ(1−s) without analytic continuation.