The summed covariance for all systematic uncertainties except for the flux. The largest of these are due to background modelling and $K^+$ interactions in the detector.

The statistical covariance is nonzero due to the unfolding procedure, which introduces small negative correlations in the statistical uncertainty from bin to bin.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z2$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z3$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z4$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z5$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 60 to 80 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 80 to 100 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 100 to 140 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 140 to 180 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 180 to 220 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 220 to 260 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 260 to 300 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.

Spectra of negatively charged pions at the surface of the T2K replica target, in the polar angle range from 300 to 340 mrad and for longitudinal bin $z6$, as a function of momentum. The normalization is per proton on target.