Data from Figure 6 – Selection efficiency as a function of $E_\nu$.

Spectrum prediction for ILL's High Flux Reactor, given in 50keV-wide $E_\nu$ bins (centers ranging from 1.8 to 10 MeV). Huber's $^{235}$U prediction in [2 MeV, 8 MeV] is taken from Phys. Rev. C 84 024617 (2011); exponential extrapolations are performed as described in Phys. Rev. Lett. 125 201801 (2020). Relative corrections from Off-equilibrium and Activation are included to obtain the total HFR's spectrum. The IBD cross section we used is based on Strumia-Vissani Phys. Lett. B, 564 42–54 (2003). The IBD yield is simply HFR's spectrum $\times$ IBD cross section. More details can be found in Section 5, where all notations are also introduced.

Data from Figure 14 - STEREO pure-$^{235}$U unfolded spectrum. Error bars are square-roots of diagonal coefficients of the covariance matrix, and include statistical and systematic uncertainties.

Covariance matrix of the unfolded $^{235}$U spectrum, including statistical and systematic uncertainties. It is denoted $V_\Phi$ in Section 8.

Data from Figure 32 – STEREO exclusion and exclusion sensitivity contours at 90% C.L. for 179 days reactor-on (phase-I+II). A full graphical presentation can be downloaded at "Resources" for reference.

Data from Figures 33 and 34 – STEREO exclusion and exclusion sensitivity contours at 95% C.L. for 179 days reactor-on (phase-I+II) using the two-dimensional method. A graphical presentation can be downloaded at "Resources" for reference.

Data from Figures 33 and 34 – STEREO exclusion and exclusion sensitivity contours at 95% C.L. for 179 days reactor-on (phase-I+II) using the two-dimensional method. A graphical presentation can be downloaded at "Resources" for reference.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Two graphs show the results of the scan over the horizontal and vertical displacements of the antiproton beam (see Table 3, before) and the horizontal and vertical angles (on the right). The color represents the intensity of the signal obtained on the MCP from the annihilations of the trapped antiprotons. The parameter space has been organized in this way, assuming that displacements and angles have independent effects, not for physics reasons, but because scanning over the full parameter space would have been impossible time-wise (10 steps per dimension 4 dimensions x 5 min of duration of the script ~35 days!).

Results of the beam steering optimization. Convergence plot of the highest observed number of annihilation events.

Results of the beam steering optimization. Density plots of the evaluations in the four-parameter space dimensions.

Results of the beam steering optimization. Density plots of the evaluations in the four-parameter space dimensions.

Results of the beam steering optimization. Density plots of the evaluations in the four-parameter space dimensions.

Results of the beam steering optimization. Density plots of the evaluations in the four-parameter space dimensions.

Results of the trap closing time optimization. Convergence plot of the highest observed number of annihilation events.

Results of the trap closing time optimization. Number of observed annihilation events as a function of the trap closing time. The result is different from the one in 2022 (Figure 6) because the capture electrode voltage was raised from 10 to 15 kV.

Synchronization results in the asynchronous parallel operation mode, showing the time difference between the start of different parallel scripts, in a schedule of 50 scripts. Both plots are accompanied by a single point plot adjacent on the right, representing the average δT over all 50 runs. In the same-duration script case (a), the high average can be explained by intrinsic delays included in Tamer and Monkey to avoid race conditions. In the different-duration script case (b), a linear trend is visible that comes from the increase in the duration time between different Kaslis. The bottom plot shows δT corrected for the linear trend, showing the average jitter value of -5 to 5 s.

Synchronization results in the asynchronous parallel operation mode, showing the time difference between the start of different parallel scripts, in a schedule of 50 scripts. Both plots are accompanied by a single point plot adjacent on the right, representing the average δT over all 50 runs. In the same-duration script case (a), the high average can be explained by intrinsic delays included in Tamer and Monkey to avoid race conditions. In the different-duration script case (b), a linear trend is visible that comes from the increase in the duration time between different Kaslis. The bottom plot shows δT corrected for the linear trend, showing the average jitter value of -5 to 5 s.

Synchronization results in the asynchronous parallel operation mode, showing the time difference between the start of different parallel scripts, in a schedule of 50 scripts. Both plots are accompanied by a single point plot adjacent on the right, representing the average δT over all 50 runs. In the same-duration script case (a), the high average can be explained by intrinsic delays included in Tamer and Monkey to avoid race conditions. In the different-duration script case (b), a linear trend is visible that comes from the increase in the duration time between different Kaslis. The bottom plot shows δT corrected for the linear trend, showing the average jitter value of -5 to 5 s.

Synchronization results in the synchronous parallel operation mode, showing the time difference between the start of different parallel scripts, in a schedule of 50 scripts. Both in the same-duration case (a) and in the different-duration case (b), the time difference between the start of different parallel scripts is stable around 5 ms, independently of the duration of the scripts. Both plots are accompanied by a single point plot adjacent on the right, representing the average δT over all 50 runs.

Synchronization results in the synchronous parallel operation mode, showing the time difference between the start of different parallel scripts, in a schedule of 50 scripts. Both in the same-duration case (a) and in the different-duration case (b), the time difference between the start of different parallel scripts is stable around 5 ms, independently of the duration of the scripts. Both plots are accompanied by a single point plot adjacent on the right, representing the average δT over all 50 runs.

Scintillator counts of the annihilation of antiprotons inside the Penning trap. The two deltoid-like structures at ≈10 s and ≈25 s are emissions from the accelerators in the AD complex and are present independently of the ongoing trapping.

Difference between the desired voltage on the amplifier channels and the measured output voltage versus the expected voltage before (top) and after (bottom) the amplifier calibration for all eight amplifier channels of one example board. The shown legend identifies the channel numbers of the given board.

Difference between the desired voltage on the amplifier channels and the measured output voltage versus the expected voltage before (top) and after (bottom) the amplifier calibration for all eight amplifier channels of one example board. The shown legend identifies the channel numbers of the given board.