Suppl. Fig. 7. The reconstructed shower angle for all single photon events. The individual signal and background event type categories added together form the unconstrained prediction.

Suppl. Fig. 7. The constrained covariance matrix for the reconstructed shower angle for all single-photon events. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

Suppl. Fig. 7. The unconstrained covariance matrix for reconstructed shower angle for all single-photon events. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

Fig. 3. The reconstructed number of protons, with a proton KE energy threshold of 35 MeV, for all single-photon events. The individual signal and background event type categories added together form the unconstrained prediction.

Fig. 4, Suppl. Fig. 8. The reconstructed shower energy for zero proton events binned from 0 to 600 MeV. The individual signal and background event type categories added together form the unconstrained prediction.

Fig. 4. The constrained covariance matrix for the reconstructed shower energy for zero proton events binned from 0 to 600 MeV. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

Fig. 4. The unconstrained covariance matrix for reconstructed shower energy for zero proton events binned from 0 to 600 MeV. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

Fig. 6. The reconstructed shower energy for zero proton events binned from 150 to 1250 MeV, with LEE prediction. The individual signal and background event type categories added together form the unconstrained prediction. The "LEE" category is the unfolded MiniBooNE LEE model prediction scaled under the neutrino-target nucleon interaction assumption.

Fig. 6. The constrained covariance matrix for the reconstructed shower energy for zero proton events binned from 150 to 1250 MeV. Both with and without the LEE model added. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

Fig. 6. The unconstrained covariance matrix for reconstructed shower energy for zero proton events binned from 150 to 1250 MeV. Both with and without the LEE model added. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

Suppl. Fig. 10. The reconstructed shower backwards projected distance for zero proton events. The individual signal and background event type categories added together form the unconstrained prediction.

Suppl. Fig. 9. The reconstructed shower angle for zero proton events. Includes LEE model prediction. The individual signal and background event type categories added together form the unconstrained prediction. The "LEE" category is the unfolded MiniBooNE LEE model prediction scaled under the neutrino-target nucleon interaction assumption.

Suppl. Fig. 9. The constrained covariance matrix for the reconstructed shower angle for zero proton events. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

Suppl. Fig. 9. The unconstrained covariance matrix for reconstructed shower angle for zero proton events. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

1$\gamma$Xp shower energy and angle selection efficiencies for true 1$\gamma$Xp events. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied. Energy and Angle values represent bin lower edges.

1$\gamma$0p shower energy and angle selection efficiencies for true single-photon events with no other true particles of any energy. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied. Energy and Angle values represent bin lower edges.

Covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Pearson data statistical uncertainties have been included, and include small correlations due to events which can be selected by both WC and Pandora. The first four bins are the WC $1\gamma Np$, WC $1\gamma 0p$, Pandora $1\gamma 1p$, and Pandora $1\gamma 0p$ channels, and the next four sets of 16 bins are the NC $\pi^0 Np$, NC $\pi^0 0p$, $\nu_\mu$CC $Np$, and $\nu_\mu$CC $0p$ channels. This corresponds to Fig. 1 of the paper and Fig. 6 of the Supplemental Material.

Constrained WC $1\gamma Np$ energy distribution. There are 6 bins from 0 to 600 MeV of reconstructed shower energy, with an additional overflow bin. Constrained systematic uncertainties on the predictions are illustrated, and a more detailed covariance matrix is included in the Constrained Energy Distributions Covariance Matrix tab. This corresponds to Fig. 2 of the paper.

Constrained WC $1\gamma 0p$ energy distribution. There are 14 bins from 0 to 700 MeV of reconstructed shower energy, with an additional overflow bin. Constrained systematic uncertainties on the predictions are illustrated, and a more detailed covariance matrix is included in the Constrained Energy Distributions Covariance Matrix tab. This corresponds to Fig. 2 of the paper.

Constrained Pandora $1\gamma 1p$ energy distribution. There are 6 bins from 0 to 600 MeV of reconstructed shower energy, with an additional overflow bin. Constrained systematic uncertainties on the predictions are illustrated, and a more detailed covariance matrix is included in the Constrained Energy Distributions Covariance Matrix tab. This corresponds to Fig. 2 of the paper.

Constrained Pandora $1\gamma 0p$ energy distribution. There are 14 bins from 0 to 700 MeV of reconstructed shower energy, with an additional overflow bin. Constrained systematic uncertainties on the predictions are illustrated, and a more detailed covariance matrix is included in the Constrained Energy Distributions Covariance Matrix tab. This corresponds to Fig. 2 of the paper.

Constrained covariance matrix showing constrained uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Pearson data statistical uncertainties have been included, and include small correlations due to events which can be selected by both WC and Pandora. The first seven bins are the WC $1\gamma Np$ reconstructed shower energy from 0-600 MeV with an overflow bin, the next 15 bins are the WC $1\gamma 0p$ reconstructed shower energy from 0-700 MeV with an overflow bin, the next seven bins are the Pandora $1\gamma 1p$ reconstructed shower energy from 0-600 MeV with an overflow bin, and the last 15 bins are the Pandora $1\gamma 0p$ reconstructed shower energy from 0-700 MeV with an overflow bin. This corresponds to Fig. 2 of the paper.

2D efficiency matrix showing the efficiency of the WC $1\gamma Np$ selection with respect to all true NC Delta Radiative Decay events which interact in the fiducial volume. The efficiency is shown as a function of true photon energy and angle. There are 10 bins from -1 to 1 in true photon $\cos \theta$ and 15 bins from 0 to 1500 MeV in true photon energy. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied. This corresponds to Fig. 9 of the Supplemental Material.

2D efficiency matrix showing the efficiency of the WC $1\gamma 0p$ selection with respect to all true NC Delta Radiative Decay events which interact in the fiducial volume. The efficiency is shown as a function of true photon energy and angle. There are 10 bins from -1 to 1 in true photon $\cos \theta$ and 30 bins from 0 to 1500 MeV in true photon energy. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied. This corresponds to Fig. 9 of the Supplemental Material.

2D efficiency matrix showing the efficiency of the Pandora $1\gamma 1p$ selection with respect to all true NC Delta Radiative Decay events which interact in the fiducial volume. The efficiency is shown as a function of true photon energy and angle. There are 10 bins from -1 to 1 in true photon $\cos \theta$ and 15 bins from 0 to 1500 MeV in true photon energy, with lower bin edges indicated in the table. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied. This corresponds to Fig. 9 of the Supplemental Material.

2D efficiency matrix showing the efficiency of the Pandora $1\gamma 0p$ selection with respect to all true NC Delta Radiative Decay events which interact in the fiducial volume. The efficiency is shown as a function of true photon energy and angle. There are 10 bins from -1 to 1 in true photon $\cos \theta$ and 30 bins from 0 to 1500 MeV in true photon energy, with lower bin edges indicated in the table. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied. This corresponds to Fig. 9 of the Supplemental Material.

2D efficiency matrix showing the efficiency of the WC $1\gamma 0p$ selection with respect to all true zero-primary-final-state-proton NC Delta Radiative Decay events which interact in the fiducial volume. The efficiency is shown as a function of true photon energy and angle. There are 10 bins from -1 to 1 in true photon $\cos \theta$ and 30 bins from 0 to 1500 MeV in true photon energy, with lower bin edges indicated in the table. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied.

2D efficiency matrix showing the efficiency of the Pandora $1\gamma 0p$ selection with respect to all true zero-primary-final-state-proton NC Delta Radiative Decay events which interact in the fiducial volume. The efficiency is shown as a function of true photon energy and angle. There are 10 bins from -1 to 1 in true photon $\cos \theta$ and 30 bins from 0 to 1500 MeV in true photon energy, with lower bin edges indicated in the table. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied.

Normalized transverse momentum correlator, $\sqrt{ \langle\langle \Delta p_{{\rm T}1}\Delta p_{{\rm T}2} \rangle\rangle }/\langle\langle p_{\rm T} \rangle\rangle $, as a function of the average number of participant nucleons, $\langle{ N_{\rm part}}\rangle$, in Pb--Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV

Normalized transverse momentum correlator, $\sqrt{ \langle\langle \Delta p_{{\rm T}1}\Delta p_{{\rm T}2} \rangle\rangle }/\langle\langle p_{\rm T} \rangle\rangle $, as a function of the average number of participant nucleons, $\langle{ N_{\rm part}}\rangle$, in Xe--Xe collisions at $\sqrt{s_{\rm NN}}$ = 5.44 TeV

Normalized transverse momentum correlator, $\sqrt{ \langle\langle \Delta p_{{\rm T}1}\Delta p_{{\rm T}2} \rangle\rangle }/\langle\langle p_{\rm T} \rangle\rangle $, as a function of the average number of participant nucleons, $\langle{ N_{\rm part}}\rangle$, in Pb--Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV

Normalized transverse momentum correlator, $\sqrt{ \langle\langle \Delta p_{{\rm T}1}\Delta p_{{\rm T}2} \rangle\rangle }/\langle\langle p_{\rm T} \rangle\rangle $ as a function of the charged-particle multiplicity density for spherocity-integrated events in pp collisions at $\sqrt{s}=5.02$ TeV

Normalized transverse momentum correlator, $\sqrt{ \langle\langle \Delta p_{{\rm T}1}\Delta p_{{\rm T}2} \rangle\rangle }/\langle\langle p_{\rm T} \rangle\rangle $ as a function of the charged-particle multiplicity density for jetty events in pp collisions at $\sqrt{s}=5.02$ TeV

Normalized transverse momentum correlator, $\sqrt{ \langle\langle \Delta p_{{\rm T}1}\Delta p_{{\rm T}2} \rangle\rangle }/\langle\langle p_{\rm T} \rangle\rangle $ as a function of the charged-particle multiplicity density for isotropic events in pp collisions at $\sqrt{s}=5.02$ TeV

Normalized transverse momentum correlator, $\sqrt{ \langle\langle \Delta p_{{\rm T}1}\Delta p_{{\rm T}2} \rangle\rangle }/\langle\langle p_{\rm T} \rangle\rangle $ as a function of the charged-particle multiplicity density for spherocity-integrated events in pp collisions at $\sqrt{s}=13$ TeV

Normalized transverse momentum correlator, $\sqrt{ \langle\langle \Delta p_{{\rm T}1}\Delta p_{{\rm T}2} \rangle\rangle }/\langle\langle p_{\rm T} \rangle\rangle $ as a function of the charged-particle multiplicity density for jetty events in pp collisions at $\sqrt{s}=13$ TeV

Normalized transverse momentum correlator, $\sqrt{ \langle\langle \Delta p_{{\rm T}1}\Delta p_{{\rm T}2} \rangle\rangle }/\langle\langle p_{\rm T} \rangle\rangle $ as a function of the charged-particle multiplicity density for isotropic events in pp collisions at $\sqrt{s}=13$ TeV

Jet angularity $\lambda_{\alpha}$ for $\alpha = 3$. $40<p_{\mathrm{T}}^{\mathrm{ch jet}}<60$ GeV/$c$. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet angularity $\lambda_{\alpha,g}$ for $\alpha = 1$. $40<p_{\mathrm{T}}^{\mathrm{ch jet}}<60$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet angularity $\lambda_{\alpha,g}$ for $\alpha = 1.5$. $40<p_{\mathrm{T}}^{\mathrm{ch jet}}<60$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet angularity $\lambda_{\alpha,g}$ for $\alpha = 2$. $40<p_{\mathrm{T}}^{\mathrm{ch jet}}<60$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet angularity $\lambda_{\alpha,g}$ for $\alpha = 3$. $40<p_{\mathrm{T}}^{\mathrm{ch jet}}<60$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Jet angularity $\lambda_{\alpha}$ for $\alpha = 1$. $60<p_{\mathrm{T}}^{\mathrm{ch jet}}<80$ GeV/$c$. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Jet angularity $\lambda_{\alpha}$ for $\alpha = 1.5$. $60<p_{\mathrm{T}}^{\mathrm{ch jet}}<80$ GeV/$c$. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Jet angularity $\lambda_{\alpha}$ for $\alpha = 2$. $60<p_{\mathrm{T}}^{\mathrm{ch jet}}<80$ GeV/$c$. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Jet angularity $\lambda_{\alpha}$ for $\alpha = 3$. $60<p_{\mathrm{T}}^{\mathrm{ch jet}}<80$ GeV/$c$. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet angularity $\lambda_{\alpha,g}$ for $\alpha = 1$. $60<p_{\mathrm{T}}^{\mathrm{ch jet}}<80$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet angularity $\lambda_{\alpha,g}$ for $\alpha = 1.5$. $60<p_{\mathrm{T}}^{\mathrm{ch jet}}<80$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet angularity $\lambda_{\alpha,g}$ for $\alpha = 2$. $60<p_{\mathrm{T}}^{\mathrm{ch jet}}<80$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet angularity $\lambda_{\alpha,g}$ for $\alpha = 3$. $60<p_{\mathrm{T}}^{\mathrm{ch jet}}<80$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Jet angularity $\lambda_{\alpha}$ for $\alpha = 1$. $80<p_{\mathrm{T}}^{\mathrm{ch jet}}<100$ GeV/$c$. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Jet angularity $\lambda_{\alpha}$ for $\alpha = 1.5$. $80<p_{\mathrm{T}}^{\mathrm{ch jet}}<100$ GeV/$c$. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Jet angularity $\lambda_{\alpha}$ for $\alpha = 2$. $80<p_{\mathrm{T}}^{\mathrm{ch jet}}<100$ GeV/$c$. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Jet angularity $\lambda_{\alpha}$ for $\alpha = 3$. $80<p_{\mathrm{T}}^{\mathrm{ch jet}}<100$ GeV/$c$. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet angularity $\lambda_{\alpha,g}$ for $\alpha = 1$. $80<p_{\mathrm{T}}^{\mathrm{ch jet}}<100$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet angularity $\lambda_{\alpha,g}$ for $\alpha = 1.5$. $80<p_{\mathrm{T}}^{\mathrm{ch jet}}<100$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet angularity $\lambda_{\alpha,g}$ for $\alpha = 2$. $80<p_{\mathrm{T}}^{\mathrm{ch jet}}<100$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet angularity $\lambda_{\alpha,g}$ for $\alpha = 3$. $80<p_{\mathrm{T}}^{\mathrm{ch jet}}<100$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Jet angularity $\lambda_{\alpha}$ for $\alpha = 1$. $100<p_{\mathrm{T}}^{\mathrm{ch jet}}<150$ GeV/$c$. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Jet angularity $\lambda_{\alpha}$ for $\alpha = 1.5$. $100<p_{\mathrm{T}}^{\mathrm{ch jet}}<150$ GeV/$c$. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Jet angularity $\lambda_{\alpha}$ for $\alpha = 2$. $100<p_{\mathrm{T}}^{\mathrm{ch jet}}<150$ GeV/$c$. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Jet angularity $\lambda_{\alpha}$ for $\alpha = 3$. $100<p_{\mathrm{T}}^{\mathrm{ch jet}}<150$ GeV/$c$. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet angularity $\lambda_{\alpha,g}$ for $\alpha = 1$. $100<p_{\mathrm{T}}^{\mathrm{ch jet}}<150$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet angularity $\lambda_{\alpha,g}$ for $\alpha = 1.5$. $100<p_{\mathrm{T}}^{\mathrm{ch jet}}<150$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet angularity $\lambda_{\alpha,g}$ for $\alpha = 2$. $100<p_{\mathrm{T}}^{\mathrm{ch jet}}<150$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet angularity $\lambda_{\alpha,g}$ for $\alpha = 3$. $100<p_{\mathrm{T}}^{\mathrm{ch jet}}<150$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Jet invariant mass $m_\mathrm{jet}$ in pp data. $40<p_{\mathrm{T}}^{\mathrm{ch jet}}<60$ GeV/$c$. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet invariant mass $m_{\mathrm{jet},g}$ in pp data. $40<p_{\mathrm{T}}^{\mathrm{ch jet}}<60$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Jet invariant mass $m_\mathrm{jet}$ in pp data. $60<p_{\mathrm{T}}^{\mathrm{ch jet}}<80$ GeV/$c$. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet invariant mass $m_{\mathrm{jet},g}$ in pp data. $60<p_{\mathrm{T}}^{\mathrm{ch jet}}<80$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Jet invariant mass $m_\mathrm{jet}$ in pp data. $80<p_{\mathrm{T}}^{\mathrm{ch jet}}<100$ GeV/$c$. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet invariant mass $m_{\mathrm{jet},g}$ in pp data. $80<p_{\mathrm{T}}^{\mathrm{ch jet}}<100$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Jet invariant mass $m_\mathrm{jet}$ in Pb--Pb data. $40<p_{\mathrm{T}}^{\mathrm{ch jet}}<60$ GeV/$c$. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet invariant mass $m_{\mathrm{jet},g}$ in Pb--Pb data. $40<p_{\mathrm{T}}^{\mathrm{ch jet}}<60$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Jet invariant mass $m_\mathrm{jet}$ in Pb--Pb data. $60<p_{\mathrm{T}}^{\mathrm{ch jet}}<80$ GeV/$c$. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet invariant mass $m_{\mathrm{jet},g}$ in Pb--Pb data. $60<p_{\mathrm{T}}^{\mathrm{ch jet}}<80$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Jet invariant mass $m_\mathrm{jet}$ in Pb--Pb data. $80<p_{\mathrm{T}}^{\mathrm{ch jet}}<100$ GeV/$c$. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet invariant mass $m_{\mathrm{jet},g}$ in Pb--Pb data. $80<p_{\mathrm{T}}^{\mathrm{ch jet}}<100$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Jet invariant mass $m_\mathrm{jet}$ in Pb--Pb data. $100<p_{\mathrm{T}}^{\mathrm{ch jet}}<150$ GeV/$c$. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Groomed jet invariant mass $m_{\mathrm{jet},g}$ in Pb--Pb data. $100<p_{\mathrm{T}}^{\mathrm{ch jet}}<150$ GeV/$c$, Soft Drop $z_{\mathrm{cut}}=0.2, \beta=0$. Note: The first bin corresponds to the Soft Drop untagged fraction. For the "trkeff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$), denote correlation across bins (both within this table, and across tables). For the remaining sources ("unfolding", "random_mass") no correlation information is specified ($\pm$ is always used).

Measured muon multiplicity distribution compared with simulations from CORSIKA Monte Carlo generator using QGSJET-II-04 (top), SIBYLL 2.3 (middle), and EPOS-LHC (bottom) as hadronic interaction models for proton and iron primary cosmic rays. Iron points are slightly shifted to the right to avoid overlapping with the data points. The total uncertainties in the MC simulations are given by the vertical bars, while the boxes give the systematic uncertainties of the data and the vertical bars the statistical ones.

Measured muon multiplicity distribution compared with simulations from CORSIKA Monte Carlo generator using QGSJET-II-04 (top), SIBYLL 2.3 (middle), and EPOS-LHC (bottom) as hadronic interaction models for proton and iron primary cosmic rays. Iron points are slightly shifted to the right to avoid overlapping with the data points. The total uncertainties in the MC simulations are given by the vertical bars, while the boxes give the systematic uncertainties of the data and the vertical bars the statistical ones.

Measured muon multiplicity distribution compared with simulations from CORSIKA Monte Carlo generator using QGSJET-II-04 (top), SIBYLL 2.3 (middle), and EPOS-LHC (bottom) as hadronic interaction models for proton and iron primary cosmic rays. Iron points are slightly shifted to the right to avoid overlapping with the data points. The total uncertainties in the MC simulations are given by the vertical bars, while the boxes give the systematic uncertainties of the data and the vertical bars the statistical ones.

Measured muon multiplicity distribution compared with simulations from CORSIKA Monte Carlo generator using QGSJET-II-04 (top), SIBYLL 2.3 (middle), and EPOS-LHC (bottom) as hadronic interaction models for proton and iron primary cosmic rays. Iron points are slightly shifted to the right to avoid overlapping with the data points. The total uncertainties in the MC simulations are given by the vertical bars, while the boxes give the systematic uncertainties of the data and the vertical bars the statistical ones.

Measured muon multiplicity distribution compared with simulations from CORSIKA Monte Carlo generator using QGSJET-II-04 (top), SIBYLL 2.3 (middle), and EPOS-LHC (bottom) as hadronic interaction models for proton and iron primary cosmic rays. Iron points are slightly shifted to the right to avoid overlapping with the data points. The total uncertainties in the MC simulations are given by the vertical bars, while the boxes give the systematic uncertainties of the data and the vertical bars the statistical ones.

Measured muon multiplicity distribution compared with simulations from CORSIKA Monte Carlo generator using QGSJET-II-04 (top), SIBYLL 2.3 (middle), and EPOS-LHC (bottom) as hadronic interaction models for proton and iron primary cosmic rays. Iron points are slightly shifted to the right to avoid overlapping with the data points. The total uncertainties in the MC simulations are given by the vertical bars, while the boxes give the systematic uncertainties of the data and the vertical bars the statistical ones.

Ratio between the number of events obtained with the Monte Carlo simulation (QGSJET-II-04, SIBYLL 2.3, and EPOS-LHC) with respect to the data for the muon multiplicity distributions. The sky blue line represents unity.

Ratio between the number of events obtained with the Monte Carlo simulation (QGSJET-II-04, SIBYLL 2.3, and EPOS-LHC) with respect to the data for the muon multiplicity distributions. The sky blue line represents unity.

Ratio between the number of events obtained with the Monte Carlo simulation (QGSJET-II-04, SIBYLL 2.3, and EPOS-LHC) with respect to the data for the muon multiplicity distributions. The sky blue line represents unity.

Ratio between the number of events obtained with the Monte Carlo simulation (QGSJET-II-04, SIBYLL 2.3, and EPOS-LHC) with respect to the data for the muon multiplicity distributions. The sky blue line represents unity.

Ratio between the number of events obtained with the Monte Carlo simulation (QGSJET-II-04, SIBYLL 2.3, and EPOS-LHC) with respect to the data for the muon multiplicity distributions. The sky blue line represents unity.

Ratio between the number of events obtained with the Monte Carlo simulation (QGSJET-II-04, SIBYLL 2.3, and EPOS-LHC) with respect to the data for the muon multiplicity distributions. The sky blue line represents unity.

Isolated-photon cross section ratio of pp collisions at $\sqrt{s}=13~\mathrm{TeV}$ over $\sqrt{s}=5.02~\mathrm{TeV}$ in data (left column) and NLO pQCD calculation from JETPHOX (right column) for $R=0.4$. Data statistical and systematic uncertainties are provided. The theory scale and PDF uncertainties are provided. The data normalisation uncertainty is provided in the paper.

Isolated-photon cross section ratio of pp collisions at $\sqrt{s}=7~\mathrm{TeV}$ over $\sqrt{s}=5.02~\mathrm{TeV}$ in data (left column) and NLO pQCD calculation from JETPHOX (right column) for $R=0.4$. Data statistical and systematic uncertainties are provided. The theory scale and PDF uncertainties are provided. The data normalisation uncertainty is provided in the paper.

Nuclear modification factor ($R_{\rm AA}$) of isolated photons for Pb$-$Pb and pp collisions at $\sqrt{s_{\mathrm{NN}}}=5.02~\mathrm{TeV}$. $R_{\rm AA}$ obtained with a cone size value of $R=0.2$. Each column for each Pb$-$Pb collisions centrality class. The last column for the NLO pQCD JETPHOX calculations, Pb$-$Pb (nPDF) over pp (PDF). Data statistical and systematic uncertainties are provided. The theory scale and PDF uncertainties are provided.

Nuclear modification factor ($R_{\rm AA}$) of isolated photons for Pb$-$Pb and pp collisions at $\sqrt{s_{\mathrm{NN}}}=5.02~\mathrm{TeV}$. $R_{\rm AA}$ obtained with a cone size value of $R=0.4$. Each column for each Pb$-$Pb collisions centrality class. The last column for the NLO pQCD JETPHOX calculations, Pb$-$Pb (nPDF) over pp (PDF). Data statistical and systematic uncertainties are provided. The theory scale and PDF uncertainties are provided.

Ratios $R_{\rm CSP}$ and $R_{\rm CSC}$ of isolated photons cross sections in data for Pb$-$Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02~\mathrm{TeV}$. $R_{\rm CSP}$, ratio central over semi-peripheral collisions 50$-$70%. $R_{\rm CSC}$, ratio central over semi-central collisions 30$-$50%. Ratios obtained with a cone size value of $R=0.2$. Data statistical and systematic uncertainties are provided.

Ratios $R_{\rm CSP}$ and $R_{\rm CSC}$ of isolated photons cross sections in data for Pb$-$Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02~\mathrm{TeV}$. $R_{\rm CSP}$, ratio central over semi-peripheral collisions 50$-$70%. $R_{\rm CSC}$, ratio central over semi-central collisions 30$-$50%. Ratios obtained with a cone size value of $R=0.4$. Data statistical and systematic uncertainties are provided.

Groomed relative transverse momentum, $k_{\text{T,g}}$, spectra measured in pp collisions. $60 < p_{\text{T,ch jet}}^{\text{}} < 80\:\text{GeV}/c$, Soft drop $z_{\text{cut}} = 0.2$, $\beta = 0$ For the "trk eff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$) denote correlation across bins. For the remaining sources ("unfold"), no correlation information is specified (i.e. $\pm$ is always used). In the publication, the quadrature sum of all sources of systematic uncertainty is reported, neglecting the sign information reported here.

Groomed relative transverse momentum, $k_{\text{T,g}}$, spectra measured in 30--50% Pb-Pb collisions. $60 < p_{\text{T,ch jet}}^{\text{}} < 80\:\text{GeV}/c$, Soft drop $z_{\text{cut}} = 0.2$, $\beta = 0$ For the "trk eff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$) denote correlation across bins. For the remaining sources ("unfold,bkg,non_closure"), no correlation information is specified (i.e. $\pm$ is always used). In the publication, the quadrature sum of all sources of systematic uncertainty is reported, neglecting the sign information reported here.

Groomed relative transverse momentum, $k_{\text{T,g}}$, spectra measured in 0--10% Pb-Pb collisions. $60 < p_{\text{T,ch jet}}^{\text{}} < 80\:\text{GeV}/c$, Soft drop $z_{\text{cut}} = 0.2$, $\beta = 0$ For the "trk eff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$) denote correlation across bins. For the remaining sources ("unfold,bkg,non_closure"), no correlation information is specified (i.e. $\pm$ is always used). In the publication, the quadrature sum of all sources of systematic uncertainty is reported, neglecting the sign information reported here.

Groomed $k_{\text{T,g}}$ ratio of 30--50% Pb-Pb to pp collisions. $60 < p_{\text{T,ch jet}}^{\text{}} < 80\:\text{GeV}/c$, Dynamical grooming $a = 1.0$ For the "trk eff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$) denote correlation across bins. For the remaining sources "(unfold,bkg,non_closure)", no correlation information is specified (i.e. $\pm$ is always used). In the publication, the quadrature sum of all sources of systematic uncertainty is reported, neglecting the sign information reported here.

Groomed $k_{\text{T,g}}$ ratio of 0--10% Pb-Pb to pp collisions. $60 < p_{\text{T,ch jet}}^{\text{}} < 80\:\text{GeV}/c$, Dynamical grooming $a = 1.0$ For the "trk eff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$) denote correlation across bins. For the remaining sources "(unfold,bkg,non_closure)", no correlation information is specified (i.e. $\pm$ is always used). In the publication, the quadrature sum of all sources of systematic uncertainty is reported, neglecting the sign information reported here.

Groomed $k_{\text{T,g}}$ ratio of 30--50% Pb-Pb to pp collisions. $60 < p_{\text{T,ch jet}}^{\text{}} < 80\:\text{GeV}/c$, Soft drop $z_{\text{cut}} = 0.2$, $\beta = 0$ For the "trk eff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$) denote correlation across bins. For the remaining sources "(unfold,bkg,non_closure)", no correlation information is specified (i.e. $\pm$ is always used). In the publication, the quadrature sum of all sources of systematic uncertainty is reported, neglecting the sign information reported here.

Groomed $k_{\text{T,g}}$ ratio of 0--10% Pb-Pb to pp collisions. $60 < p_{\text{T,ch jet}}^{\text{}} < 80\:\text{GeV}/c$, Soft drop $z_{\text{cut}} = 0.2$, $\beta = 0$ For the "trk eff" and "generator" systematic uncertainty sources, the signed systematic uncertainty breakdowns ($\pm$ vs. $\mp$) denote correlation across bins. For the remaining sources "(unfold,bkg,non_closure)", no correlation information is specified (i.e. $\pm$ is always used). In the publication, the quadrature sum of all sources of systematic uncertainty is reported, neglecting the sign information reported here.