  The Kondo lattice model plays a key role in our understanding of quantum
materials, but a lack of small parameters has posed a long-standing problem. We
present a 3 dimensional S= 1/2 Kondo lattice model describing a spin liquid
within an electron sea. Strong correlations in the spin liquid are treated
exactly, enabling a controlled analytical approach. Like a Peierls or BCS
phase, a logarithmically divergent susceptibility leads to an instability into
a new phase at arbitrarily small Kondo coupling. Our solution captures a
plethora of emergent phenomena, including odd-frequency pairing, pair density
wave formation and order fractionalization. The ground-state state is a pair
density wave with a fractionalized charge e, S = 1/2 order parameter, formed
between electrons and Majorana fermions.
