$11.5$ hours is around $p^\mathrm{noise}_\mathrm{3-fold}(33)\approx3.3\times10^{-81}$ and can be considered impossible. Thus, our statistical analysis underlines the strong evidence for time-correlated photon triplets in only one temporal measurement bin. We also notice in the histogram that the accidentals, stemming from neighboring pulses along $\tau_3-\tau_2$ and $\tau_1-\tau_2$, also deviate significantly from the noise-dominated fit curve. This behavior indicates the suspected pseudo-time-correlations of the accidentals due to generation in neighboring pulses. We refer the kind readership to Appendix B, where we provide arguments for the validity of Poisson statistics of noise-related three-fold coincidences.

Our findings verify the generation of $33\pm5.7$ time-correlated photon triplets per $11.5$ hours at the expected relative arrival times. From the absolute number of triplets within the whole measurement duration, we deduce a success probability for the detection of photon triplets $P^\mathrm{exp}_\mathrm{triplet}=\left(6.25\pm1.3\right)\times10^{-11}$ per pump pulse. In order to compare this value with the success probability expected from our experimental circumstances, we take the set pump power and wavelength, $\mathbf{P}_\mathrm{p}$ and $\lambda_\mathrm{p}$, the pump laser repetition rate $R_\mathrm{rep}$ and the efficiencies of the three measurement arms, $\eta_\mathrm{i1}$, $\eta_\mathrm{s2}$ and $\eta_\mathrm{i2}$, into account. From separate measurements we inferred the individual PDC conversion efficiencies, $P_\mathrm{PDC,1}=\left(8.1\pm0.1\right)\times10^{-8}$ and $P_\mathrm{PDC,2}=\left(2.7\pm0.1\right)\times10^{-7}$ pairs per pump photon. Additionally, the 