  The hypothesis that the entire cosmic ray spectrum, from $\lesssim1\,{\rm
GeV}$ to $\gtrsim100\,{\rm EeV}$ energy, can be accounted for by diffusive
shock acceleration on increasingly large scales is critically examined.
Specifically, it is conjectured that Galactic cosmic rays, up to $\sim3\,{\rm
PeV}$, are mostly produced by local supernova remnants, from which they escape
upstream. These cosmic rays initiate a powerful magnetocentrifugal wind,
removing disk mass and angular momentum before passing through the Galactic
Wind Termination Shock at a radius $\sim200\,{\rm kpc}$, where they can be
re-accelerated to account for observed cosmic rays up to $\sim30\,{\rm PeV}$.
The cosmic rays transmitted downstream from more powerful termination shocks
associated with other galaxies can be further accelerated at Intergalactic
Accretion Shocks to the highest energies observed. In this interpretation, the
highest rigidity observed particles are protons; the highest energy particles
are heavy nuclei, such as iron. A universal "bootstrap" prescription, coupling
the energy density of the magnetic turbulence to that of the resonant cosmic
rays, is proposed, initially for the highest energy particles escaping far
ahead of the shock front and then scattering, successively, lower energy
particles downstream. Observable implications of this general scheme relate to
the spectrum, composition and sky distribution of Ultra-High-Energy Cosmic
Rays, the extragalactic radio background, the Galactic halo magnetic field and
Pevatrons.
