  The finding of bulk quantum oscillations in the bulk Kondo insulator SmB$_6$,
which has been proposed to be a correlated topological insulator, proved a
considerable surprise. The subsequent measurement of bulk quantum oscillations
in other correlated insulators including YbB$_{12}$ have lent support to our
discovery of a class of unconventional insulators that are host to bulk quantum
oscillations, of which SmB$_6$ was the first example. Here we perform a series
of experiments to examine evidence for the intrinsic character of bulk quantum
oscillations in floating zone-grown single crystals of SmB$_6$ that have been
the subject of our quantum oscillation studies thus far. We present results of
experiments including chemical composition analysis, magnetisation, thermal
conductivity, electrical transport, and heat capacity on floating zone-grown
single crystals of SmB$_6$, and a series of quantum oscillation experiments as
a function of magnetic field, temperature, and magnetic field-orientation on
single crystals of floating-zone grown SmB$_6$, LaB$_6$, and elemental
Aluminium. Results of these experimental studies establish the intrinsic origin
of quantum oscillations from the bulk of pristine floating zone-grown single
crystals of SmB$_6$. The origin of the underlying bulk Fermi surface that bears
close similarity with the unhybridised Fermi surface in metallic hexaborides
despite the bulk insulating character of SmB$_6$ is thus at the heart of a
theoretical mystery.
