Phase-Locked Partition-Invariance Breaking as a Signature of Externally Imposed Stellar Activity: ER Vulpeculae

Phase-Locked Partition-Invariance Breaking as a Signature of Externally Imposed Stellar Activity: ER Vulpeculae Summary This paper introduces the N/E/P protocol—a three-axis operational test for distinguishing externally imposed ("imposed") from internally generated ("immanent") stellar activity patterns: (N) Null-robust: Breaking persists under shuffle/shift null transformations (E) Epoch-robust: Pattern stable across multi-year observations (P) Phase-locked: Asymmetry fixed to orbital period, not internal cycles Key Results Using archival Ca II H&K spectroscopy (Shkolnik et al. 2005) and Doppler imaging (Xiang et al. 2014) of the RS CVn binary ER Vulpeculae (P_orb = 0.698 d), we demonstrate: Axis Criterion Result Status (N) Null-robust p < 0.01 p = 0.0016 ✓ (E) Epoch-robust CV < 20% CV = 9% ✓ (P) Phase-locked offset < 0.1 offset = 0.02 ✓ ER Vul satisfies all three conditions, constituting the first quantitative demonstration of the "imposed" activity signature in stellar chromospheric data. Significance Operational definition: Classification based solely on observable signatures, without assumptions about dynamo mechanisms Falsifiable criteria: Clear thresholds for each axis enable independent verification Look-elsewhere correction: Statistical rigor addressing multiple testing concerns Files Included Takagi_2026_ER_Vul_standalone.pdf — Full paper (PDF) Takagi_2026_ER_Vul_MNRASL.tex — LaTeX source (MNRAS format) Takagi_2026_ER_Vul_standalone.tex — LaTeX source (standalone) publication_figure.pdf/png — Figure 1 (4-panel) publication_analysis.py — Analysis code (Python) shkolnik2005_observations.csv — Digitized data Citation Takagi, T. (2026). Phase-Locked Partition-Invariance Breaking as a Signature of Externally Imposed Stellar Activity: ER Vulpeculae. Zenodo. https://doi.org/10.5281/zenodo.18300523 Author Takayuki TakagiIndependent Researcher, Higashimatsuyama, Saitama, JapanORCID: 0009-0003-5188-2314Email: lemissio@gmail.com Keywords stars: activity · stars: chromospheres · binaries: close · stars: individual (ER Vul) · methods: statistical · partition-invariance · N/E/P protocol License CC BY 4.0 This preprint establishes priority for the N/E/P protocol. A journal submission to MNRAS Letters is in preparation.