  We give local axioms that uniquely characterize the crystal-like structure on
shifted tableaux developed in a previous paper by Gillespie, Levinson, and
Purbhoo. These axioms closely resemble those developed by Stembridge for type A
tableau crystals. This axiomatic characterization gives rise to a new method
for proving and understanding Schur $Q$-positive expansions in symmetric
function theory, just as the Stembridge axiomatic structure provides for
ordinary Schur positivity.
