  In recent years, a version of enumerative geometry over arbitrary fields has
been developed and studied by Kass-Wickelgren, Levine, and others, in which the
counts obtained are not integers but quadratic forms. Aiming to understand the
relation to other "refined invariants", and especially their possible
interpretation in quantum theory, we explain how to obtain a quadratic version
of Donaldson-Thomas invariants from the motivic invariants defined in the work
of Kontsevich and Soibelman and pose some questions. We calculate these
invariants in a few simple examples that provide standard tests for these
questions, including degree zero invariants of $\mathbb A^3$ and higher-genus
Gopakumar-Vafa invariants recently studied by Liu and Ruan. The comparison with
known real and complex counts plays a central role throughout.
