In this paper, we introduce a novel variational framework rooted in algebraic
geometry for the analysis of the Hardy Z-function. Our primary contribution
lies in the definition and exploration of Δn​(a), a newly
devised discriminant that measures the realness of consecutive zeros of Z(t).
Our investigation into Δn​(a) and its properties yields a
wealth of compelling insights into the zeros of Z(t), including the corrected
Gram's law, the second-order approximation of Δn​(a), and the
discovery of the G-B-G repulsion relation. Collectively, these results provide
compelling evidence supporting a new plausibility argument for the Riemann
hypothesis