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 HN on the n × n square lattice, where diagonal entries are populated by the first non-trivial zeros tₖ 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 tₖ is enclosed by a pair of eigenvalues λₖ⁻ < tₖ < λₖ⁺, with interlacing gaps Δₖ = λₖ⁺ − λₖ⁻ < 0. 31 for k = 1, 2, 3, 4. We provide the complete 16 eigenvalues and the Python code for verification. The Hermiticity of HN guarantees λₖ ∈ ℝ for all N. We propose the STNT-Riemann Correspondence Conjecture: lim₍ → ∞ Δₖ (N) = 0 which would imply tₖ ∈ 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.