  Recent measurements of the inelastic and total proton-proton cross section at
the LHC, and at cosmic ray energies by the Auger experiment, have
quantitatively confirmed fits to lower energy data constrained by the
assumption that the proton is asymptotically a black disk of gluons. We show
that data on \bar p(p)p,\pi^\mp p, and K^\mp p forward scattering support the
related expectation that the asymptotic behavior of all cross sections is
flavor independent. By using the most recent measurements from ATLAS, CMS,
TOTEM and Auger, we predict \sigma^{pp}_{\rm tot} (\sqrt s=8 {\rm TeV})=100.6
\pm 2.9 mb and \sigma^{pp}_{\rm tot} (\sqrt s=14 {\rm TeV})=110.8 \pm 3.5 mb,
as well as refine the total cross section \sigma^{pp}_{\rm tot} (\sqrt s=57
{\rm TeV})=139.6 \pm 5.4 mb. Our analysis also predicts the total \pi^\mp \pi^+
cross sections as a function of \sqrt s.
