  In this paper, we present the analysis and results of a direct measurement of
the cosmic-ray proton spectrum with the CALET instrument onboard the
International Space Station, including the detailed assessment of systematic
uncertainties. The observation period used in this analysis is from October 13,
2015 to August 31, 2018 (1054 days). We have achieved the very wide energy
range necessary to carry out measurements of the spectrum from 50 GeV to 10 TeV
covering, for the first time in space, with a single instrument the whole
energy interval previously investigated in most cases in separate subranges by
magnetic spectrometers (BESS-TeV, PAMELA, and AMS-02) and calorimetric
instruments (ATIC, CREAM, and NUCLEON). The observed spectrum is consistent
with AMS-02 but extends to nearly an order of magnitude higher energy, showing
a very smooth transition of the power-law spectral index from -2.81 +- 0.03
(50--500 GeV) neglecting solar modulation effects (or -2.87 +- 0.06 including
solar modulation effects in the lower energy region) to -2.56 +- 0.04 (1--10
TeV), thereby confirming the existence of spectral hardening and providing
evidence of a deviation from a single power law by more than 3 sigma.
