Solar phase transitions in null-model diagnostics: window-dependent regimes in total solar irradiance

Overview We introduce a null-diagnostic framework in which null-model selection is treated as a physical statement about time-series structure. Rather than asking whether the Sun is anomalous, we ask under which null assumptions the series becomes statistically indistinguishable from its reference distribution—and how this depends on observational scale. Method For a scalar series F(t), we define four scale-sensitive indicators: D★ (Drift): Secular trend strength A★ (Autocorrelation): Integrated autocorrelation time G★ (Degeneracy): Period estimation uncertainty (σ_P / P) η★ (Coverage): Window length / rotation period Using fixed thresholds and a hierarchical decision rule: DEGENERACY → DRIFT → AUTOCORR → SILENCE we classify time-series behaviour according to which null assumption fails first. Key Finding Applying this framework to SORCE/TIM Total Solar Irradiance (2003–2020), we find: Window Length Class Interpretation 27 d DEGENERACY Period unstable 54–81 d AUTOCORR Rotation signature stable 108–182 d SILENCE No null assumption violated ≥365 d DEGENERACY Activity cycle destabilizes period The "silence band" at ~108–182 days is a new, data-driven discovery absent in synthetic validation. Significance The Sun is a diagnostic boundary case, transitioning across multiple regimes as window length changes The framework is explicitly falsifiable and transferable to other astrophysical contexts This establishes null-model selection as a physical diagnostic tool Contents manuscript/ — LaTeX source (MNRAS Letters format) figures/ — Phase diagrams (synthetic validation + real data) code/ — Python analysis pipeline data/ — Results table (CSV) Citation Takagi, T. (2026). Solar phase transitions in null-model diagnostics: window-dependent regimes in total solar irradiance. Zenodo. https://doi.org/10.5281/zenodo.18309608 Author Takayuki TakagiIndependent Researcher, Higashimatsuyama, Saitama, JapanORCID: 0009-0003-5188-2314