On the Structure of the Riemann Zeta Function: Boundary Completeness, Defect Observables, and Variance Constraints
Łukasz Bojanowski · Zenodo (CERN European Organization for Nuclear Research) · 2026
This work presents a structural approach to the Riemann Hypothesis based on global consistency rather than the localization of individual zeros. We introduce the notion of boundary completeness for the zeta zero process and construct unfolding-invariant defect observables that detect transverse deviations from the critical line. The analysis establishes a boundary/bulk dichotomy: any effective one-dimensional (boundary) description of the zeros is complete if and only if no transverse defects are present. Using the explicit formula, we show that the existence of an off–critical zero necessarily produces super-quadratic growth in the variance of prime counting fluctuations. This leads to a minimal variance condition that is shown to be equivalent to the Riemann Hypothesis. The main result is a rigorous conditional proof of the Riemann Hypothesis under this minimal variance constraint, together with a precise identification of the remaining analytic gap. No specific upper bounds are assumed; only the exclusion of a single, well-defined growth pattern is required. Beyond its mathematical content, the paper demonstrates a mode of sustained human–AI collaborative reasoning in which artificial systems are used to stabilize, interrogate, and structurally verify complex arguments rather than replace mathematical intuition.