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The Kondo lattice model plays a key role in our understanding of quantummaterials, but a lack of small parameters has posed a long-standing problem. Wepresent a 3 dimensional S= 1/2 Kondo lattice model describing a spin liquidwithin an electron sea. Strong correlations in the spin liquid are treatedexactly, enabling a controlled analytical approach. Like a Peierls or BCSphase, a logarithmically divergent susceptibility leads to an instability intoa new phase at arbitrarily small Kondo coupling. Our solution captures aplethora of emergent phenomena, including odd-frequency pairing, pair densitywave formation and order fractionalization. The ground-state state is a pairdensity wave with a fractionalized charge e, S = 1/2 order parameter, formedbetween electrons and Majorana fermions.

A solvable 3D Kondo lattice exhibiting odd-frequency pairing and order fractionalization