  Samarium hexaboride is an anomaly, having many exotic and seemingly mutually
incompatible properties. It was proposed to be a mixed-valent semiconductor,
and later - a topological Kondo insulator, and yet has a Fermi surface despite
being an insulator. We propose a new and unified understanding of SmB$_6$
centered on the hitherto unrecognized dynamical bonding effect: the coexistence
of two Sm-B bonding modes within SmB$_6$, corresponding to different oxidation
states of the Sm. The mixed valency arises in SmB$_6$ from thermal population
of these distinct minima enabled by motion of B. Our model simultaneously
explains the thermal valence fluctuations, appearance of magnetic Fermi
surface, excess entropy at low temperatures, pressure-induced phase
transitions, and related features in Raman spectra and their unexpected
dependence on temperature and boron isotope.
