Limits on neutron Lorentz violation from the stability of primary cosmic ray protons

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 5x10(-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 4x10(-21) level, eleven orders of magnitude better than previous constraints.