The Computability Horizon: Why Re(s)=1/2 Is Not a Coincidence / The Riemann Line as a Physical Invariant

The Riemann critical line Re(𝑠) = 1/2 is traditionally viewed as a purely analytic boundary emerging from the structure of the zeta function. This work shows that the critical line is not a mathematical coincidence but a projection of a physical computability horizon arising within Triadic Mesh Dynamics (TMD). The triadic update operator contains a non‑unitary forgetting step that generates an invariant stability boundary ℎ = 1 , where reconstructability of states collapses. When projected into the complex plane, this horizon appears precisely as the line Re(𝑠) = 1/2, providing a physical interpretation of the Riemann critical line and explaining its exceptional role in the theory of the zeta function. The study further demonstrates that the balance between direct and inverse spectral normalization (KSH and Riemann–Maxwell duality) naturally leads to the critical line as an equilibrium point of the underlying discrete structure. Continuous mathematics can observe this boundary but cannot fully explain it, as the phenomenon originates in discrete triadic mechanics rather than in analytic continuation. This work complements the classical mathematical formulation of the Riemann Hypothesis by offering a physical interpretation of why the critical line appears exactly where it does. It opens a new dialogue between mathematics and physics, connecting continuous analysis with discrete computational dynamics.