Comparative Periodogram Analysis of 22 Years of Super-Kamiokande Solar $^{8}\mathrm{B}$ Neutrino Data: Classical, Phase-Based, and Information Theoretic Methods
Solar $^8\mathrm{B}$ neutrinos offer a unique probe of solar interior dynamics and neutrino electromagnetic properties. We present a systematic, multi-method periodogram analysis of the 22-year Super-Kamiokande solar neutrino dataset (1996--2018), comparing nine algorithms. Through hierarchical temporal segmentation, we disentangle astrophysical signals from detector systematics. The Generalized Lomb-Scargle (GLS) method provides the most statistically robust detections by correctly handling heteroscedastic uncertainties, whereas classical Lomb-Scargle systematically underestimates significance. The Lafler--Kinman method generally fails, whereas independent algorithms like MHAOV and PDM1 recover consistent periodicities, providing vital cross-validation. In pre-2001 and SK-I data, seven algorithms provide \textit{weak evidence} ($\ln B > 0$) for a $\sim 38.8$ d periodicity. However, this signal is entirely absent in the highest-statistics SK-IV modified flux data, where the Bayes factor decisively favors the null model ($\ln B \ll -5$), indicating it is a transient feature of the early low-statistics era. Conversely, a $\sim 24.3$ d signal in post-2001 raw flux is decisively rejected by the Bayesian framework and vanishes in modified flux, confirming its seasonal systematic origin. Furthermore, no evidence is found for an $\sim 11$-year solar cycle modulation, yielding a stringent amplitude upper limit of $<0.2\%$ of the mean flux. By highlighting the stark contrast between frequentist significance and Bayesian model selection ($\ln B$) in low signal-to-noise regimes, we establish a rigorous, multi-metric best-practice framework for periodicity searches. This work provides a direct methodological blueprint for next-generation observatories like Hyper-Kamiokande and JUNO.