  We study the spectral properties of the cosmic-ray spectrum in the
interstellar medium within 1 kpc distance from the Sun. We used eight-year
exposure data of molecular clouds of the Gould Belt obtained with the Fermi/LAT
telescope to precisely measure the cosmic-ray spectrum at different locations
in the local Galaxy. We compared this measurement with the direct measurements
of the cosmic-ray flux in and around the solar system obtained by Voyager and
AMS-02 or PAMELA. We find that the average cosmic-ray spectrum in the local
Galaxy in the 1-100 GeV range is well described by a broken power-law in
rigidity with a low-energy slope of $2.33^{+0.06}_{-0.08}$ and a break at
$18^{+7}_{-4}$ GV, with a slope change by $0.59\pm 0.11$. This result is
consistent with an earlier analysis of the gamma-ray signal from the Gould Belt
clouds based on a shorter exposure of Fermi/LAT and with a different event
selection. The break at 10-20 GV is also consistent with the combined Voyager +
AMS-02 measurements in/around the solar system. The slope of the spectrum below
the break agrees with the slope of the average cosmic-ray spectrum in the inner
part of the disk of the Milky Way that was previously derived from the
Fermi/LAT gamma-ray data. We conjecture that it is this slope of 2.33 and not
the locally measured softer slope of 2.7-2.8 that is determined by the balance
between a steady-state injection of cosmic rays with a power-law slope of 2-2.1
that is due to Fermi acceleration and the energy-dependent propagation of
cosmic-ray particles through the turbulent interstellar magnetic field with a
Kolmogorov turbulence spectrum. The approximation of a continuous-in-time
injection of cosmic rays at a constant rate breaks down, which causes the
softening of the spectrum at higher energies.
