A High-Precision Statistical Analysis of the SN1987A Neutrino Temporal Distribution
The interpretation of the SN1987A neutrino data remains limited by significant absolute timing uncertainties across independent detectors and a long-standing tension in the angular distributions. This work presents a high-precision statistical framework that resolves these issues by formalizing the mathematical distinction between intrinsic and relative timing offsets (ITOs and RTOs). By performing a simultaneous $\chi^2$-alignment of the Kamiokande-II and Baksan data with the IMB clock, we systematically incorporate non-Gaussian statistical correlations, reducing the temporal uncertainty by two orders of magnitude to the sub-second level. The $\chi^2$-analysis shows that Baksan's absolute timestamps require an advancement of $30.4\,$s, while those of Kamiokande-II require a delay of about $6.4\,$s. Establishing this unified, high-precision timeline is critical to test the physical nature of the first Kamiokande-II event (K1), specifically whether its distinct angular features signal the onset of the prompt neutronization burst. Previous literature often assumes that K1 originated from inverse beta decay (IBD) on qualitative grounds. By contrast, our multidimensional likelihood analysis incorporates energy, direction, and MSW flavor-conversion effects to provide the first quantitative constraint on its origin. We find a likelihood ratio of 3-6 in favor of an accretion-phase $\bar{\nu}_e$ origin over a neutronization-burst origin, thereby turning a traditional assumption into a statistically bounded physical inference. This framework provides the most stringent constraints to date on the chronology of SN1987A and establishes a precise methodology for future multimessenger observations of Galactic supernovae.