Islam, Mohammad: A FORMAL PROOF OF A CONSERVATION LAW FOR THE RIEMANN HYPOTHESIS: The Functional Equation Is Provably Silent on the Eigenspace Where the Hypothesis Lives, and the Hypothesis Is Bracketed Between Two Theorem-Grade Walls

We give a single consolidated account of what the analytic structure of the Riemann zeta function does and does not settle about the location of its non-trivial zeros, and we settle the relation between the two exactly. The work has four parts and we mark the grade of each. First, a geometric reformulation, stated at the strength it earns. The Berry-Keating operator H = −i(x d/dx + 1/2) is unitarily equivalent to the dilation generator H′ = −i x d/dx on the multiplicative Hilbert space L²(ℝ⁺, dx