A Structural Model Relating Prime Gaps and Zeta Zeros

This work develops a structural and topological approach to the relationship between prime gaps and the zeros of the Riemann zeta function. For a capacity bound MM, a prime-induced simplicial complex KMKM is constructed whose vertices, edges, and triangles encode multiplicative constraints among primes. From normalized simplex densities, three convergent constants arise. These constants describe complementary aspects of arithmetic organization: a multiplicative component, an additive (shifted) component, and a coupling term measuring the structural discrepancy between them. Within this framework, prime gaps are interpreted as emerging from the interaction of additive and multiplicative modes. A resonance-type expression links the three constants to the first nontrivial imaginary part of a zeta zero. The model further suggests a transfer-operator picture in which the balance between the two arithmetic modes naturally stabilizes at the critical line σ=1/2σ=1/2. The approach is computationally grounded. Convergence properties of the constants are documented for large MM, and the accompanying datasets and source code provide reproducible numerical experiments supporting the structural observations. This work does not claim a formal proof of the Riemann Hypothesis. It is presented as a structural and topological model intended to stimulate further mathematical investigation.