The First Geometric Structure of Space Time Number Theory Linking to Riemann Zeros

This preprint introduces a discrete geometric framework—Spatial Time Numeric Theory (STNT)—and demonstrates its spectral correspondence with the non-trivial zeros of the Riemann zeta function. We construct an explicit Hermitian adjacency operator H_N on the n × n square lattice, where diagonal entries are populated by the first non-trivial zeros t_k and trivial zeros −2k, and off-diagonal couplings k² = 1 encode the unit-interval geometry of STNT. For the 9-cell case (n = 3, N = 16), numerical diagonalization yields a real spectrum exhibiting tight bracketing: each Riemann zero t_k is enclosed by a pair of eigenvalues λ_k⁻ < t_k < λ_k⁺, with interlacing gaps Δ_k = λ_k⁺ − λ_k⁻ < 0.31 for k = 1, 2, 3, 4. We provide the complete 16 eigenvalues and the Python code for verification. The Hermiticity of H_N guarantees λ_k ∈ ℝ for all N. We propose the STNT-Riemann Correspondence Conjecture: limN → ∞ Δ_k(N) = 0 which would imply t_k ∈ ℝ and thus locate all non-trivial zeros on the critical line Re(s) = 1/2. The results provide numerical evidence for the Hilbert-Pólya spectral approach to the Riemann Hypothesis.