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.

$\Delta \chi^2$ map of phase-I+II data calculated by a raster-scan method. To be used in combination with the $\Delta \chi^2_{\text{crit},x}$ values to generate exclusion contours at $x$% C.L. for phase-I+II data. Additional explanations are given there.

Data from Figure 34 – STEREO exclusion and exclusion sensitivity contours at 95% C.L. for 179 days reactor-on (phase-I+II) using the raster-scan method. A graphical presentation can be downloaded at "Resources" for reference.

Data from Figure 34 – STEREO exclusion and exclusion sensitivity contours at 95% C.L. for 179 days reactor-on (phase-I+II) using the raster-scan method. A graphical presentation can be downloaded at "Resources" for reference.

Data from Figure 34 – STEREO exclusion and exclusion sensitivity contours at 95% C.L. for 179 days reactor-on (phase-I+II) using the CLs method. A graphical presentation can be downloaded at "Resources" for reference.

Data from Figure 34 – STEREO exclusion and exclusion sensitivity contours at 95% C.L. for 179 days reactor-on (phase-I+II) using the CLs method. A graphical presentation can be downloaded at "Resources" for reference.

The $\Delta \chi^2_{\text{crit},x}$ map accounts for the fact that the $\Delta \chi^2$ values of the oscillation fit do not follow a $\chi^2$ distribution with 2 degrees of freedom. Therefore, the $\Delta \chi^2_{\text{crit},x}$ value for x% C.L. of each point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ in the parameter space, $\Delta \chi^2_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$, is determined from the $\Delta \chi^2$ obtained in pseudo-experiments at that point, such that $\Delta \chi^2 \leq \Delta \chi^2_{\text{crit},x}$, for $x$% of the pseudo-experiments. Applying these $\Delta \chi^2_{\text{crit},x}$ values to the $\Delta \chi^2$ map obtained with the data, $x$% C.L. exclusion contours are obtained. The point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is excluded by the data at $x$% C.L. if $\Delta \chi^2(\sin^2(2\theta_{ee}), \Delta m^2_{41}) > \Delta \chi^2_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$. In order to obtain the $\Delta \chi^2_{\text{crit},x}$ map, $10^4$ pseudo-experiments were generated for each point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ in the parameter space, taking into account all statistical and systematic uncertainties. The $\Delta \chi^2$ value of a pseudo-experiment is calculated by subtracting the $\chi^2$ value of the best-fit in the parameter space from the $\chi^2$ value of the fit at the $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ used in the generation of the pseudo-dataset, where all nuisance parameters are free within their pull terms. When combining the exclusion contours with other experimental data, special care should be exercised. The assumption of a standard $\chi^2$ law instead of the provided $\Delta \chi^2_{\text{crit},x}$ values derived from non-standard $\chi^2$ distributions leads to slightly modified contours. In addition, the contours were derived using a raster-scan in several fixed values of $\Delta m_{41}^2$. While this method is particularly suited to derive exclusion contours, it cannot be used to calculate allowed confidence regions for $\Delta m_{41}^2$ and consequently two-dimensional allowed confidence regions. This is because $\Delta \chi^2$ values are not reflecting the likelihood of individual $\Delta m_{41}^2$ values. Thus, a direct comparison of $\Delta \chi^2$ values across different $\Delta m_{41}^2$ values is not possible in a statistically meaningful way. When generating the exclusion contours with the aforementioned procedure, spurious exclusion regions at low values of $\sin^2(2\theta_{ee})$ can be encountered for some values of $\Delta m^2_{41}$. These should be ignored and are owed to the raster-scan procedure used to generate the maps.

$\Delta \chi^2$ map of phase-I+II data calculated by the two-dimensional method. To be used in combination with the $\Delta \chi^2_{\text{crit},x}$ values of the two-dimensional method to generate exclusion contours at $x$% C.L. for phase-I+II data. Additional explanations are given there.

$\Delta \chi^2$ map of phase-I+II data calculated by the two-dimensional method. To be used in combination with the $\Delta \chi^2_{\text{crit},x}$ values of the two-dimensional method to generate exclusion contours at $x$% C.L. for phase-I+II data. Additional explanations are given there.

The $\Delta \chi^2_{\text{crit},x}$ map accounts for the fact that the $\Delta \chi^2$ values of the oscillation fit do not follow a $\chi^2$ distribution with 2 degrees of freedom. Therefore, the $\Delta \chi^2_{\text{crit},x}$ value for x% C.L. of each point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ in the parameter space, $\Delta \chi^2_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$, is determined from the $\Delta \chi^2$ obtained in pseudo-experiments at that point, such that $\Delta \chi^2 \leq \Delta \chi^2_{\text{crit},x}$, for $x$% of the pseudo-experiments. Applying these $\Delta \chi^2_{\text{crit},x}$ values to the $\Delta \chi^2$ map obtained with the data, $x$% C.L. exclusion contours are obtained. The point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is excluded by the data at $x$% C.L. if $\Delta \chi^2(\sin^2(2\theta_{ee}), \Delta m^2_{41}) > \Delta \chi^2_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$. In order to obtain the $\Delta \chi^2_{\text{crit},x}$ map, $10^4$ pseudo-experiments were generated for each point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ in the parameter space, taking into account all statistical and systematic uncertainties. The $\Delta \chi^2$ value of a pseudo-experiment is calculated by subtracting the $\chi^2$ value of the best-fit in the parameter space from the $\chi^2$ value of the fit at the $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ used in the generation of the pseudo-dataset, where all nuisance parameters are free within their pull terms. When combining the exclusion contours with other experimental data, special care should be exercised. The assumption of a standard $\chi^2$ law instead of the provided $\Delta \chi^2_{\text{crit},x}$ values derived from non-standard $\chi^2$ distributions leads to modified contours. In addition, for the interpretation of derived allowed confidence regions, one should always consider additional available information, in particular rate information. This is especially advisable considering the expected distribution of best-fit points in a prediction-free shape-only analysis, as discussed in the main publication.

The $\Delta \chi^2_{\text{crit},x}$ map accounts for the fact that the $\Delta \chi^2$ values of the oscillation fit do not follow a $\chi^2$ distribution with 2 degrees of freedom. Therefore, the $\Delta \chi^2_{\text{crit},x}$ value for x% C.L. of each point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ in the parameter space, $\Delta \chi^2_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$, is determined from the $\Delta \chi^2$ obtained in pseudo-experiments at that point, such that $\Delta \chi^2 \leq \Delta \chi^2_{\text{crit},x}$, for $x$% of the pseudo-experiments. Applying these $\Delta \chi^2_{\text{crit},x}$ values to the $\Delta \chi^2$ map obtained with the data, $x$% C.L. exclusion contours are obtained. The point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is excluded by the data at $x$% C.L. if $\Delta \chi^2(\sin^2(2\theta_{ee}), \Delta m^2_{41}) > \Delta \chi^2_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$. In order to obtain the $\Delta \chi^2_{\text{crit},x}$ map, $10^4$ pseudo-experiments were generated for each point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ in the parameter space, taking into account all statistical and systematic uncertainties. The $\Delta \chi^2$ value of a pseudo-experiment is calculated by subtracting the $\chi^2$ value of the best-fit in the parameter space from the $\chi^2$ value of the fit at the $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ used in the generation of the pseudo-dataset, where all nuisance parameters are free within their pull terms. When combining the exclusion contours with other experimental data, special care should be exercised. The assumption of a standard $\chi^2$ law instead of the provided $\Delta \chi^2_{\text{crit},x}$ values derived from non-standard $\chi^2$ distributions leads to modified contours. In addition, for the interpretation of derived allowed confidence regions, one should always consider additional available information, in particular rate information. This is especially advisable considering the expected distribution of best-fit points in a prediction-free shape-only analysis, as discussed in the main publication.

$\Delta \chi^2$ map of phase-I+II data calculated by the raster-scan method. To be used in combination with the $\Delta \chi^2_{\text{crit},x}$ values of the raster-scan method to generate exclusion contours at $x$% C.L. for phase-I+II data. Additional explanations are given there.

$\Delta \chi^2$ map of phase-I+II data calculated by the raster-scan method. To be used in combination with the $\Delta \chi^2_{\text{crit},x}$ values of the raster-scan method to generate exclusion contours at $x$% C.L. for phase-I+II data. Additional explanations are given there.

The $\Delta \chi^2_{\text{crit},x}$ and $\Delta \chi^2$ values in the raster-scan method serve the same purpose as in the two-dimensional method. The explanations given there also apply here, with the following changes: Instead of the two free oscillation parameters $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$, the raster-scan method fits only $\sin^2(2\theta_{ee})$ as free oscillation parameter while repeating the fit for several fixed values of $\Delta m_{41}^2$. While this method is particularly suited to derive exclusion contours, it cannot be used to calculate allowed confidence regions for $\Delta m_{41}^2$ and consequently two-dimensional allowed confidence regions. This is because $\Delta \chi^2$ values are not reflecting the likelihood of individual $\Delta m_{41}^2$ values. Thus, a direct comparison of $\Delta \chi^2$ values across different $\Delta m_{41}^2$ values is not possible in a statistically meaningful way. Moreover, when generating the exclusion contours with the aforementioned procedure, spurious exclusion regions at low values of $\sin^2(2\theta_{ee})$ can be encountered for some values of $\Delta m^2_{41}$. These should be ignored and are owed to the raster-scan procedure used to generate the maps.

The $\Delta \chi^2_{\text{crit},x}$ and $\Delta \chi^2$ values in the raster-scan method serve the same purpose as in the two-dimensional method. The explanations given there also apply here, with the following changes: Instead of the two free oscillation parameters $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$, the raster-scan method fits only $\sin^2(2\theta_{ee})$ as free oscillation parameter while repeating the fit for several fixed values of $\Delta m_{41}^2$. While this method is particularly suited to derive exclusion contours, it cannot be used to calculate allowed confidence regions for $\Delta m_{41}^2$ and consequently two-dimensional allowed confidence regions. This is because $\Delta \chi^2$ values are not reflecting the likelihood of individual $\Delta m_{41}^2$ values. Thus, a direct comparison of $\Delta \chi^2$ values across different $\Delta m_{41}^2$ values is not possible in a statistically meaningful way. Moreover, when generating the exclusion contours with the aforementioned procedure, spurious exclusion regions at low values of $\sin^2(2\theta_{ee})$ can be encountered for some values of $\Delta m^2_{41}$. These should be ignored and are owed to the raster-scan procedure used to generate the maps.

$\Delta T$ map of phase-I+II data calculated by the CLs method. To be used in combination with the $\Delta T_{\text{crit},x}$ values of the CLs method to generate exclusion contours at $x$% C.L. for phase-I+II data. Additional explanations are given there.

$\Delta T$ map of phase-I+II data calculated by the CLs method. To be used in combination with the $\Delta T_{\text{crit},x}$ values of the CLs method to generate exclusion contours at $x$% C.L. for phase-I+II data. Additional explanations are given there.

The $\Delta T_{\text{crit},x}$ and $\Delta T$ values in the CLs method fulfil a similar purpose as the $\Delta \chi^2_{\text{crit},x}$ and $\Delta \chi^2$ values in the two-dimensional method. The explanations given there also apply here, with the following changes: The CLs method differs from the two-dimensional method as it normalises the confidence level of the oscillation-hypothesis to the confidence level of the null-hypothesis (i.e. no-oscillation-hypothesis), instead of the best-fit. The $\Delta T$ value of a dataset at the parameter space-point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is computed by subtracting the $\chi^2$ value of the fit under the no-oscillation hypothesis from the $\chi^2$ value of the fit with the oscillation parameters fixed to $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$. With this definition, $\Delta T$ values can be positive or negative as opposed to $\Delta \chi^2$ values. Note that the values used to compare with are $-\Delta T$ and not $\Delta T$ directly. The CLs value of a parameter space-point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is defined as $\text{CL}_\text{s}(\sin^2(2\theta_{ee}), \Delta m^2_{41}):=(1-p_1)/(1-p_0)$ where $(1-p_0)$ and $(1-p_1)$ are the confidence levels of the dataset, determined from the distributions of $-\Delta T$ created in pseudo-experiments assuming the oscillation parameters $[0,0]$ and $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$, respectively. The point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is excluded by the data at $x$% C.L. if $\Delta T(\sin^2(2\theta_{ee}), \Delta m^2_{41}) < \Delta T_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$. Note the flipped sign with respect to the two-dimensional method and the raster-scan method. More information on the CLs method can be found at "Resources".

The $\Delta T_{\text{crit},x}$ and $\Delta T$ values in the CLs method fulfil a similar purpose as the $\Delta \chi^2_{\text{crit},x}$ and $\Delta \chi^2$ values in the two-dimensional method. The explanations given there also apply here, with the following changes: The CLs method differs from the two-dimensional method as it normalises the confidence level of the oscillation-hypothesis to the confidence level of the null-hypothesis (i.e. no-oscillation-hypothesis), instead of the best-fit. The $\Delta T$ value of a dataset at the parameter space-point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is computed by subtracting the $\chi^2$ value of the fit under the no-oscillation hypothesis from the $\chi^2$ value of the fit with the oscillation parameters fixed to $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$. With this definition, $\Delta T$ values can be positive or negative as opposed to $\Delta \chi^2$ values. Note that the values used to compare with are $-\Delta T$ and not $\Delta T$ directly. The CLs value of a parameter space-point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is defined as $\text{CL}_\text{s}(\sin^2(2\theta_{ee}), \Delta m^2_{41}):=(1-p_1)/(1-p_0)$ where $(1-p_0)$ and $(1-p_1)$ are the confidence levels of the dataset, determined from the distributions of $-\Delta T$ created in pseudo-experiments assuming the oscillation parameters $[0,0]$ and $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$, respectively. The point $[\sin^2(2\theta_{ee}), \Delta m^2_{41}]$ is excluded by the data at $x$% C.L. if $\Delta T(\sin^2(2\theta_{ee}), \Delta m^2_{41}) < \Delta T_{\text{crit},x}(\sin^2(2\theta_{ee}), \Delta m^2_{41})$. Note the flipped sign with respect to the two-dimensional method and the raster-scan method. More information on the CLs method can be found at "Resources".

Map of mean $\Delta \chi^2$ values derived from simulations of phase-I+II and calculated by the two-dimensional method. To be used analogously to the $\Delta \chi^2$ map of phase-I+II data in combination with the $\Delta \chi^2_{\text{crit},x}$ values of the two-dimensional method to generate sensitivity contours at $x$% C.L. for phase-I+II. Additional explanations are given there.

Most probable charge deposit signal normalised to that of minimum ionising particles as a function of $\beta\gamma$ for cosmic-ray muons (dE/dx). Statistical uncertainties as vertical error bars. Uncertainties in momentum and thus $\beta \gamma$ determination are drawn as horizontal error bars.

Most probable charge deposit signal normalised to that of minimum ionising particles as a function of $\beta\gamma$ for cosmic-ray muons (dE/dx + TR). Statistical uncertainties as vertical error bars. Uncertainties in momentum and thus $\beta \gamma$ determination are drawn as horizontal error bars.

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.