Recent measurements of primary and secondary CR spectra, their arrival
directions, and our improved knowledge of the magnetic field geometry
around the heliosphere allow us to set a bound on the distance beyond
which a puzzling 10-TeV ``bump'' \emph{cannot} originate. The sharpness
of the spectral breaks associated with the bump, the abrupt change
of the CR intensity across the local magnetic equator ($90^{\circ}$ pitch
angle), and the similarity between the primary and secondary CR spectral
patterns point to a local reacceleration of the bump particles out
of the background CRs. We argue that a nearby shock may generate such
a bump by increasing the rigidity of the preexisting CRs below 50
TV by a mere factor of \ensuremath{\sim}1.5. Reaccelerated particles
below \ensuremath{\sim}0.5 TV are convected with the interstellar
medium flow and do not reach the Sun, thus creating the bump. This
single universal process is responsible for the observed spectra of
all CR species in the rigidity range below 100 TV. We propose that
one viable candidate is the system of shocks associated with $\epsilon$ Eridani star at 3.2 pc of
the Sun, which is well aligned with the direction of the local magnetic
field. Other shocks, such as old supernova shells, may produce a similar
effect. We provide a simple formula that reproduces the spectra of
all CR species with only three parameters uniquely
derived from the CR proton data. We show how our formalism predicts helium
and carbon spectra and the B/C ratio.