TMD: The Riemann Boundary of Computability

This work introduces the Riemann Boundary of Computability, a mathematical framework within the triadic network (TMD) that identifies the precise limit at which local reconstruction becomes computationally inaccessible. The study shows that the critical line of the Riemann zeta function corresponds to the boundary where the triadic update operator transitions from convergent to non‑convergent behavior. This boundary marks the point at which orientational reconstruction becomes unstable, and the network can no longer resolve local conflicts. The work is purely mathematical: it analyzes the spectral properties of the triadic update operator, the role of orientational gradients, and the emergence of discrete resonance modes associated with the nontrivial zeros of the zeta function. No cosmology or physical interpretation is assumed. The Riemann Boundary is presented as a computability limit of discrete operators acting on triadic structures. This study forms the mathematical foundation for later TMD works that explore stability, information flow, and the limits of reconstruction in discrete networks.