Remainder at Boundaries: A SRNUDT Structural Argument for the Riemann Hypothesis

The Riemann Hypothesis, which holds that all non-trivial zeros of the Riemann zeta function lie on the critical line Re(s) = 1/2, has remained unproved since Riemann's 1859 conjecture. Existing approaches attempt to show that zeros cannot be off the critical line. This paper takes a different approach: it provides a structural reason why zeros must be on the line. We apply the principle of Scale-Recursive Non-Uniform Domain Tiling (SRNUDT; Ploof 2026a, 2026c) to the organizational structure of the prime numbers. Primes constitute a SRNUDT tiling of the positive integers: irreducible sovereign domains whose collective behavior generates all multiplicative structure. The non-trivial zeros of the zeta function encode the remainder of this tiling, the deviation of actual prime distribution from its smooth average, which the organizing principle generates but cannot absorb into its leading-order behavior. The critical line Re(s) = 1/2 is the SRNUDT boundary of the zeta function's domain: the fixed point of the functional equation duality, the symmetry axis between the two dual domains of the function. The SRNUDT principle, that remainder lives at boundaries, that what a system generates but cannot contain propagates to the interface between organizational levels, then implies that the zeros (the prime tiling's remainder) must lie on the boundary (Re(s) = 1/2). This is the Riemann Hypothesis. We present this as a structural argument, identify the mathematical formalization required to make it rigorous, and connect it to existing approaches including the Hilbert-Polya conjecture, Montgomery pair correlation, and the Lee-Yang theorem. The paper is explicitly a research program proposal, not a completed proof.