Core-collapse supernovae are among the most magnificent events in the
observable universe. They produce many of the chemical elements necessary for
life to exist and their remnants -- neutron stars and black holes -- are
interesting astrophysical objects in their own right. However, despite
millennia of observations and almost a century of astrophysical study, the
explosion mechanism of core-collapse supernovae is not yet well understood.
Hyper-Kamiokande is a next-generation neutrino detector that will be able to
observe the neutrino flux from the next galactic core-collapse supernova in
unprecedented detail. We focus on the first 500 ms of the neutrino burst,
corresponding to the accretion phase, and use a newly-developed, high-precision
supernova event generator to simulate Hyper-Kamiokande's response to five
different supernova models. We show that Hyper-Kamiokande will be able to
distinguish between these models with high accuracy for a supernova at a
distance of up to 100 kpc. Once the next galactic supernova happens, this
ability will be a powerful tool for guiding simulations towards a precise
reproduction of the explosion mechanism observed in nature.