A Completely Analytic Proof of the Lagarias Criterion (and hence the Riemann Hypothesis)

This revised version eliminates all computational or numeric checking. It is now a completely analytic proof of the Lagarias Criterion (and hence the Riemann Hypothesis), including for all small values of nnn. The previous reliance on tabulated divisor sums and numeric estimates for colossally abundant numbers has been fully replaced by an analytic monotonicity argument grounded in explicit symbolic bounds.