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.

The performance of jet energy resolution (JER) for jets with |y| < 2.1 evaluated as a function of pT_truth in different centrality bins. Simulated hard scatter events were overlaid onto events from a dedicated sample of minimum-bias Xe+Xe data. The fit parameters are listed in a sperate table (Extras 1)

The relative magnitude of systematic uncertainties for per-pair normalized xJ distributions in 0-10% Xe+Xe centrality

The relative magnitude of systematic uncertainties for absolutely normalized xJ distributions in 0-10% Xe+Xe centrality

The relative magnitude of systematic uncertainties for rho distributions for leading jets in 0-10% Xe+Xe centrality

Per-pair normalized xJ distribution evaluated in four centrality intervals and given pT1 interval.

Per-pair normalized xJ distribution evaluated in four centrality intervals and given pT1 interval.

Per-pair normalized xJ distribution evaluated in four centrality intervals and given pT1 interval.

Absolutely normalized xJ distribution evaluated in four centrality intervals and given pT1 interval.

Absolutely normalized xJ distribution evaluated in four centrality intervals and given pT1 interval.

Absolutely normalized xJ distribution evaluated in four centrality intervals and given pT1 interval.

Per-pair normalized xJ distribution in Xe+Xe collisions.

Per-pair normalized xJ distribution in Pb+Pb collisions.

Per-pair normalized xJ distribution in Xe+Xe collisions.

Per-pair normalized xJ distribution in Pb+Pb collisions.

Per-pair normalized xJ distribution in Xe+Xe collisions.

Per-pair normalized xJ distribution in Pb+Pb collisions.

Absolutely normalized xJ distribution in Xe+Xe collisions.

Absolutely normalized xJ distribution in Xe+Xe collisions.

Absolutely normalized xJ distribution in Xe+Xe collisions.

Absolutely normalized xJ distribution in Xe+Xe collisions.

Absolutely normalized xJ distribution in Xe+Xe collisions.

Absolutely normalized xJ distribution in Xe+Xe collisions.

The ratios of Xe+Xe and Pb+Pb pair nuclear-modification factors, rho, evaluated as a function of leading jet pT in the same centrality intervals.

The ratios of Xe+Xe and Pb+Pb pair nuclear-modification factors, rho, evaluated as a function of leading jet pT in the same centrality intervals.

The ratios of Xe+Xe and Pb+Pb pair nuclear-modification factors, rho, evaluated as a function of leading jet pT in the same centrality intervals.

The ratios of Xe+Xe and Pb+Pb pair nuclear-modification factors, rho, evaluated as a function of subleading jet pT in the same centrality intervals.

The ratios of Xe+Xe and Pb+Pb pair nuclear-modification factors, rho, evaluated as a function of subleading jet pT in the same centrality intervals.

The ratios of Xe+Xe and Pb+Pb pair nuclear-modification factors, rho, evaluated as a function of subleading jet pT in the same centrality intervals.

The ratios of Xe+Xe and Pb+Pb pair nuclear-modification factors, rho, evaluated as a function of leading jet pT in the same SUM ETFCal intervals (selecting equivalent event activity)

The ratios of Xe+Xe and Pb+Pb pair nuclear-modification factors, rho, evaluated as a function of leading jet pT in the same SUM ETFCal intervals (selecting equivalent event activity)

The ratios of Xe+Xe and Pb+Pb pair nuclear-modification factors, rho, evaluated as a function of leading jet pT in the same SUM ETFCal intervals (selecting equivalent event activity)

The ratios of Xe+Xe and Pb+Pb pair nuclear-modification factors, rho, evaluated as a function of subleading jet pT in the same SUM ETFCal intervals (selecting equivalent event activity)

The ratios of Xe+Xe and Pb+Pb pair nuclear-modification factors, rho, evaluated as a function of subleading jet pT in the same SUM ETFCal intervals (selecting equivalent event activity)

The ratios of Xe+Xe and Pb+Pb pair nuclear-modification factors, rho, evaluated as a function of subleading jet pT in the same SUM ETFCal intervals (selecting equivalent event activity)

Parameter a,b, and c from JER fits in Figure 1b.

Per-pair normalized xJ distribution in Xe+Xe collisions for selected Pb+Pb centrality and pT1 bin.

Per-pair normalized xJ distribution in Xe+Xe collisions for selected Pb+Pb centrality and pT1 bin.

Per-pair normalized xJ distribution in Xe+Xe collisions for selected Pb+Pb centrality and pT1 bin.

Per-pair normalized xJ distribution in Xe+Xe collisions for selected Pb+Pb centrality and pT1 bin.

Per-pair normalized xJ distribution in Xe+Xe collisions for selected Pb+Pb centrality and pT1 bin.

Per-pair normalized xJ distribution in Xe+Xe collisions for selected Pb+Pb centrality and pT1 bin.

Per-pair normalized xJ distribution in Xe+Xe collisions for selected Pb+Pb centrality and pT1 bin.

Per-pair normalized xJ distribution in Xe+Xe collisions for selected Pb+Pb centrality and pT1 bin.

Per-pair normalized xJ distribution in Xe+Xe collisions for selected Pb+Pb centrality and pT1 bin.

Correlation matrix for the individual sources of systematic uncertainty considered in the analysis, for the combined opposite sign (OS) and same sign (SS) binned-template profile likelihood fit to data. The OS or SS refers to the charge signs of the primary lepton and the soft muon. The gamma parameters are NPs used to describe the effect of the limited statistics of the samples.

The unfolded differential charge asymmetry as a function of the transverse momentum of the top pair system. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NNLO in QCD and NLO in EW theory are listed. The scale uncertainty is obtained by varying renormalisation and factorisation scales independently by a factor of 2 or 0.5 around $\mu_0$ to calculate the maximum and minimum value of the asymmetry, respectively. The nominal value $\mu_0$ is chosen as $H_T/4$. The variations in which one scale is multiplied by 2 while the other scale is divided by 2 are excluded. Finally, the scale and MC integration uncertainties are added in quadrature.

The unfolded differential charge asymmetry as a function of the longitudinal boost of the top pair system. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NNLO in QCD and NLO in EW theory are listed. The scale uncertainty is obtained by varying renormalisation and factorisation scales independently by a factor of 2 or 0.5 around $\mu_0$ to calculate the maximum and minimum value of the asymmetry, respectively. The nominal value $\mu_0$ is chosen as $H_T/4$. The variations in which one scale is multiplied by 2 while the other scale is divided by 2 are excluded. Finally, the scale and MC integration uncertainties are added in quadrature.

The unfolded inclusive leptonic asymmetry. The unfolded $A_C^{\ell\bar{\ell}}$ is obtained in the reduced phase-space defined by the requirement $|\Delta |\eta_{\ell\bar{\ell}}||<2.5$. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NLO in QCD and NLO in EW theory are listed. The theory uncertainty is obtained by varying both scales by a factor of 0.5 or 2.0 to calculate the minimum and maximum value of the asymmetry, respectively.

The unfolded differential leptonic asymmetry as a function of the invariant mass of the di-lepton pair. The unfolded $A_C^{\ell\bar{\ell}}$ is obtained in the reduced phase-space defined by the requirement $|\Delta |\eta_{\ell\bar{\ell}}||<2.5$. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NLO in QCD and NLO in EW theory are listed. The theory uncertainty is obtained by varying both scales by a factor of 0.5 or 2.0 to calculate the minimum and maximum value of the asymmetry, respectively.

The unfolded differential leptonic asymmetry as a function of the transverse momentum of the di-lepton pair. The unfolded $A_C^{\ell\bar{\ell}}$ is obtained in the reduced phase-space defined by the requirement $|\Delta |\eta_{\ell\bar{\ell}}||<2.5$. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NLO in QCD and NLO in EW theory are listed. The theory uncertainty is obtained by varying both scales by a factor of 0.5 or 2.0 to calculate the minimum and maximum value of the asymmetry, respectively.

The unfolded differential leptonic asymmetry as a function of the longitudinal boost of the di-lepton pair. The unfolded $A_C^{\ell\bar{\ell}}$ is obtained in the reduced phase-space defined by the requirement $|\Delta |\eta_{\ell\bar{\ell}}||<2.5$. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NLO in QCD and NLO in EW theory are listed. The theory uncertainty is obtained by varying both scales by a factor of 0.5 or 2.0 to calculate the minimum and maximum value of the asymmetry, respectively.

Individual 68% and 95% CL bounds on the relevant Wilson coefficients of the SM Effective Field Theory in units of $\text{TeV}^{-2}$. The bounds are derived from the $A_C^{t\bar{t}}$ inclusive measurement. The experimental uncertainties are accounted for, in the form of the complete covariance matrix that keeps track of correlations between bins for the differential measurement. The theory uncertainty from the NNLO QCD + NLO EW calculation is included by explicitly varying the renormalization and factorization scales, or the parton density functions, in the calculation and registering the variations in the intervals.

Individual 68% and 95% CL bounds on the relevant Wilson coefficients of the SM Effective Field Theory in units of $\text{TeV}^{-2}$. The bounds are derived from the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement. The experimental uncertainties are accounted for, in the form of the complete covariance matrix that keeps track of correlations between bins for the differential measurement. The theory uncertainty from the NNLO QCD + NLO EW calculation is included by explicitly varying the renormalization and factorization scales, or the parton density functions, in the calculation and registering the variations in the intervals.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ inclusive measurement. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement for $\beta_{z,t\bar{t}}$ $\in$ [0,0.3]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement for $\beta_{z,t\bar{t}}$ $\in$ [0.3,0.6]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement for $\beta_{z,t\bar{t}}$ $\in$ [0.6,0.8]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement for $\beta_{z,t\bar{t}}$ $\in$ [0.8,1]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement for $m_{t\bar{t}}$ < 500 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement for $m_{t\bar{t}}$ $\in$ [500,750] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement for $m_{t\bar{t}}$ $\in$ [750,1000] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement for $m_{t\bar{t}}$ $\in$ [1000,1500] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement for $m_{t\bar{t}}$ > 1500 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$ measurement for $p_{T,t\bar{t}}$ < 30 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$ measurement for $p_{T,t\bar{t}}$ $\in$ [30,120] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$ measurement for $p_{T,t\bar{t}}$ > 120 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ inclusive measurement. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement for $\beta_{z,\ell\bar{\ell}}$ $\in$[0,0.3]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement for $\beta_{z,\ell\bar{\ell}}$ $\in$[0.3,0.6]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement for $\beta_{z,\ell\bar{\ell}}$ $\in$[0.6,0.8]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement for $\beta_{z,\ell\bar{\ell}}$ $\in$[0.8,1]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement for $m_{\ell\bar{\ell}}$ < 200 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement for $m_{\ell\bar{\ell}}$ $\in$ [200,300] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement for $m_{\ell\bar{\ell}}$ $\in$ [300,400] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement for $m_{\ell\bar{\ell}}$ > 400 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $p_{T,\ell\bar{\ell}}$ measurement for $p_{T,\ell\bar{\ell}}$ < 20 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $p_{T,\ell\bar{\ell}}$ measurement for $p_{T,\ell\bar{\ell}}$ $\in$ [20, 70] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $p_{T,\ell\bar{\ell}}$ measurement for $p_{T,\ell\bar{\ell}}$ > 70 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{t\bar{t}}$ inclusive measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{\ell\ell}$ inclusive measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{\ell\ell}$ vs $p_{T,\ell\bar{\ell}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Covariance matrix for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement. The total (stat. + syst.) uncertainties are considered.

Covariance matrix for the $A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$ measurement. The total (stat. + syst.) uncertainties are considered.

Covariance matrix for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement. The total (stat. + syst.) uncertainties are considered.

Covariance matrix for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement. The total (stat. + syst.) uncertainties are considered.

Covariance matrix for the $A_C^{\ell\ell}$ vs $p_{T,\ell\bar{\ell}}$ measurement. The total (stat. + syst.) uncertainties are considered.

Covariance matrix for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement. The total (stat. + syst.) uncertainties are considered.

NuE background+LEE fractional covariance matrix after the 1mu1p constraint from arXiv:2110.14080

NuE background fractional covariance matrix before the 1mu1p constraint from arXiv:2110.14080

NuE background+LEE fractional covariance matrix before the 1mu1p constraint from arXiv:2110.14080

NuE simulation from arXiv:2110.14080

Covariance matrix of the $\nu_\mu$CC inclusive total cross section per nucleon in neutrino energy bins.

Covariance matrix of the $\nu_\mu$CC inclusive differential cross section per nucleon in muon energy bins.

Covariance matrix of the $\nu_\mu$CC inclusive differential cross section per nucleon in hadronic energy transfer bins.

Additional smearing matrix of the $\nu_\mu$CC inclusive total cross section per nucleon in neutrino energy bins.

Additional smearing matrix of the $\nu_\mu$CC inclusive differential cross section per nucleon in muon energy bins.

Additional smearing matrix of the $\nu_\mu$CC inclusive total cross section per nucleon in neutrino energy bins.

Partially contained $\nu_e$CC signal efficiency as a function of true neutrino energy. Each bin shows the fraction of Monte-Carlo $\nu_e$ CC events with true neutrino interaction vertex in the fiducial volume (3 cm inside the TPC active volume) which are selected in this channel.

Fully contained $\nu_e$CC true neutrino energy vs reconstructed neutrino energy. Each bin shows the relative number of selected fully contained Monte-Carlo $\nu_e$ CC events with true neutrino interaction vertex in the fiducial volume (3 cm inside the TPC active volume) which have the corresponding true neutrino energy and reconstructed neutrino energy values. Each axis has 60 bins covering an energy range from 0 to 3 GeV, corresponding to 0.05 GeV per bin.

Partially contained $\nu_e$CC true neutrino energy vs reconstructed neutrino energy. Each bin shows the relative number of selected partially contained Monte-Carlo $\nu_e$ CC events with true neutrino interaction vertex in the fiducial volume (3 cm inside the TPC active volume) which have the corresponding true neutrino energy and reconstructed neutrino energy values. Each axis has 60 bins covering an energy range from 0 to 3 GeV, corresponding to 0.05 GeV per bin.

Fully contained $\nu_\mu$CC true neutrino energy vs reconstructed neutrino energy. Each bin shows the relative number of selected fully contained Monte-Carlo $\nu_\mu$ CC events with true neutrino interaction vertex in the fiducial volume (3 cm inside the TPC active volume) which have the corresponding true neutrino energy and reconstructed neutrino energy values. Each axis has 60 bins covering an energy range from 0 to 3 GeV, corresponding to 0.05 GeV per bin.

Partially contained $\nu_\mu$CC true neutrino energy vs reconstructed neutrino energy. Each bin shows the relative number of selected partially contained Monte-Carlo $\nu_\mu$ CC events with true neutrino interaction vertex in the fiducial volume (3 cm inside the TPC active volume) which have the corresponding true neutrino energy and reconstructed neutrino energy values. Each axis has 60 bins covering an energy range from 0 to 3 GeV, corresponding to 0.05 GeV per bin.

Fully contained $\nu_e$CC data, signal, background, and LEE(x=1) predictions. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The background includes neutral current events, $\nu_\mu$CC events, events with a true neutrino interaction vertex outside the fiducial volume (3 cm inside the TPC active volume), and cosmic ray backgrounds. The signal includes the remaining intrinsic $\nu_e$CC events. The LEE(x=1) includes the predicted excess from an unfolding of the MiniBooNE LEE under a $\nu_e$CC hypothesis.

Partially contained $\nu_e$CC data, signal, background, and LEE(x=1) predictions. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The background includes neutral current events, $\nu_\mu$CC events, events with a true neutrino interaction vertex outside the fiducial volume (3 cm inside the TPC active volume), and cosmic ray backgrounds. The signal includes the remaining intrinsic $\nu_e$CC events. The LEE(x=1) includes the predicted excess from an unfolding of the MiniBooNE LEE under a $\nu_e$CC hypothesis.

Fully contained $\nu_\mu$CC data, signal, and background predictions. Events in the $\nu_e$CC or $\pi^0$ selections have been removed. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The background includes neutral current events, $\nu_e$CC events, $\nu_\mu$CC events with greater than or equal to one $\pi^0$, events with a true neutrino interaction vertex outside the fiducial volume (3 cm inside the TPC active volume), and cosmic ray backgrounds. The signal includes the remaining $\nu_\mu$CC events.

Partially contained $\nu_\mu$CC data, signal, and background predictions. Events in the $\nu_e$CC or $\pi^0$ selections have been removed. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The background includes neutral current events, $\nu_e$CC events, $\nu_\mu$CC events with greater than or equal to one $\pi^0$, events with a true neutrino interaction vertex outside the fiducial volume (3 cm inside the TPC active volume), and cosmic ray backgrounds. The signal includes the remaining $\nu_\mu$CC events.

Fully contained $\nu_\mu$CC$\pi^0$ data, signal, background predictions. Events in the $\nu_e$CC selection have been removed. Note that the rightmost bin is an overflow bin, containing all events with reconstructed $\pi^0$ kinetic energy greater than 1 GeV. The background includes neutral current events, $\nu_e$CC events, $\nu_\mu$CC events without a $\pi^0$, events with a true neutrino interaction vertex outside the fiducial volume (3 cm inside the TPC active volume), and cosmic ray backgrounds. The signal includes the remaining $\nu_\mu$CC$\pi^0$ events.

Partially contained $\nu_\mu$CC$\pi^0$ data, signal, and background predictions. Events in the $\nu_e$CC selection have been removed. Note that the rightmost bin is an overflow bin, containing all events with reconstructed $\pi^0$ kinetic energy greater than 1 GeV. The background includes neutral current events, $\nu_e$CC events, $\nu_\mu$CC events without a $\pi^0$, events with a true neutrino interaction vertex outside the fiducial volume (3 cm inside the TPC active volume), and cosmic ray backgrounds. The signal includes the remaining $\nu_\mu$CC$\pi^0$ events.

NC$\pi^0$ data, signal, and background predictions. Events in the $\nu_e$CC selection have been removed. Note that the rightmost bin is an overflow bin, containing all events with reconstructed $\pi^0$ kinetic energy greater than 1 GeV. The background includes $\nu_e$CC events, $\nu_\mu$CC events, neutral current events without a $\pi^0$, events with a true neutrino interaction vertex outside the fiducial volume (3 cm inside the TPC active volume), and cosmic ray backgrounds. The signal includes the remaining NC$\pi^0$ events.

7 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.0), the standard prediction with no low energy excess. No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.1). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.2). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.3). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.4). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.5). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.6). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.7). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.8). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.9). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.0), the median unfolded MiniBooNE LEE under a $\nu_e$CC hypothesis. No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.1). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.2). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.3). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.4). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.5). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.6). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.7). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.8). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.9). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

7 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=2.0). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC PC channel. The 53-78th bins/rows/columns correspond to the $\nu_\mu$CC FC channel. The 79-104th bins/rows/columns correspond to the $\nu_\mu$CC PC channel. The 105-115th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 116-126th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 127-137th bins/rows/columns correspond to the NC$\pi^0$ channel.

Fully contained $\nu_e$CC $0pX\pi$ data, prediction, and LEE(x=1) predictions. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The LEE(x=1) includes the predicted excess from an unfolding of the MiniBooNE LEE under a $\nu_e$CC hypothesis.

Partially contained $\nu_e$CC $0pX\pi$ data, prediction, and LEE(x=1) predictions. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The LEE(x=1) includes the predicted excess from an unfolding of the MiniBooNE LEE under a $\nu_e$CC hypothesis.

Fully contained $\nu_e$CC $NpX\pi$ data, prediction, and LEE(x=1) predictions. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The LEE(x=1) includes the predicted excess from an unfolding of the MiniBooNE LEE under a $\nu_e$CC hypothesis.

Partially contained $\nu_e$CC $NpX\pi$ data, prediction, and LEE(x=1) predictions. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The LEE(x=1) includes the predicted excess from an unfolding of the MiniBooNE LEE under a $\nu_e$CC hypothesis.

Fully contained $\nu_\mu$CC $0pX\pi$ data, prediction, and LEE(x=1) predictions. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The LEE(x=1) includes the predicted excess from an unfolding of the MiniBooNE LEE under a $\nu_e$CC hypothesis.

Partially contained $\nu_\mu$CC $0pX\pi$ data, prediction, and LEE(x=1) predictions. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The LEE(x=1) includes the predicted excess from an unfolding of the MiniBooNE LEE under a $\nu_e$CC hypothesis.

Fully contained $\nu_\mu$CC $NpX\pi$ data, prediction, and LEE(x=1) predictions. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The LEE(x=1) includes the predicted excess from an unfolding of the MiniBooNE LEE under a $\nu_e$CC hypothesis.

Partially contained $\nu_\mu$CC $NpX\pi$ data, prediction, and LEE(x=1) predictions. Note that the rightmost bin is an overflow bin, containing all events with reconstructed neutrino energy greater than 2.5 GeV. The LEE(x=1) includes the predicted excess from an unfolding of the MiniBooNE LEE under a $\nu_e$CC hypothesis.

11 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.0), the standard prediction with no low energy excess. No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.1). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.2). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.3). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.4). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.5). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.6). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.7). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.8). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=0.9). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.0), the median unfolded MiniBooNE LEE under a $\nu_e$CC hypothesis. No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.1). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.2). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.3). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.4). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.5). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.6). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.7). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.8). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=1.9). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.

11 channel 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. For the data statistical uncertainty covariance matrix, (only diagonal elements, not included here), the Neyman, Pearson, or combined Neyman and Pearson (CNP) techniques can be used. This corresponds to LEE(x=2.0). No constraints have been applied at this stage. The 1-26th bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ FC channel. The 27-52nd bins/rows/columns correspond to the $\nu_e$CC $0pX\pi$ PC channel. The 53-78th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ FC channel. The 79-104th bins/rows/columns correspond to the $\nu_e$CC $NpX\pi$ PC channel. The 105-130th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ FC channel. The 131-156th bins/rows/columns correspond to the $\nu_\mu$CC $0pX\pi$ PC channel. The 157-182nd bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ FC channel. The 183-208th bins/rows/columns correspond to the $\nu_\mu$CC $NpX\pi$ PC channel. The 209-219th bins/rows/columns correspond to the CC$\pi^0$ FC channel. The 220-230th bins/rows/columns correspond to the CC$\pi^0$ PC channel. The 231-241st bins/rows/columns correspond to the NC$\pi^0$ channel.