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We present an improved parametric model for neutrino emission from core-collapse supernovae that directly connects neutrino luminosity and average energy to stellar properties during emission. Our model incorporates two critical physical processes: convection within the proto-neutron star and the evolution of the neutrinosphere radius during the early emission phase. Using simulated datasets of supernova neutrino events in the Super-Kamiokande detector, we assess the sensitivity to astrophysical properties in the event of a future detection. We show that the neutrino mass ordering plays a crucial role in determining which parameters can be constrained by the observed neutrino data.

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