  Recent evidence appears to confirm that the ultra-high-energy primary cosmic
ray spectrum consists mostly of protons. The fact that these protons can
traverse large distances to reach Earth allows us to place bounds on Lorentz
violations. The protons neither emit vacuum Cerenkov radiation nor
$\beta$-decay into neutrons, and this constrains six previously unmeasured
coefficients in the neutron sector at the 5 x 10^(-14) level. Among the
coefficients bounded here for the first time are those that control
spin-independent boost anisotropy for neutrons. This is a phenomenon which
could have existed (in light of the preexisting bounds) without additional fine
tuning. There are also similar bounds for others species of hadrons. The bounds
on Lorentz violation for neutral pions are particularly strong, at the 4 x
10^(-21) level, eleven orders of magnitude better than previous constraints.
