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Is anyone else working through this paper: A theory of generalized Donaldson-Thomas invariants, by Dominic Joyce, Yinan Song? I am trying to verifying example 6.2 (m=2 for simplicity) using only the definitions, namely:

$$J^{2\alpha}(\tau) = -1/4,$$

(where $\alpha$ satisfies $M^{\alpha}_{\mathrm{ss}} = M^{\alpha}_{\mathrm{st}}$ and that $\mathrm{Ext}^1(E, E)=0$ for any $E \in M^{\alpha}_{\mathrm{ss}}$ and finally that the only object of $M^{m\alpha}_{\mathrm{ss}}$ is $E ^{\oplus m}$).

I keep getting -3/4. Has anyone else attempted to make such a computation? Did you get the answer you are supposed to get?

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    $\begingroup$ Guided by the generous assistance of Dominic Joyce and Jonathan Wise, I have verified that J^{2\alpha}(\tau) = -1/4. I continue to work on proving the corresponding statement for a general m, using only the definitions. $\endgroup$
    – David Steinberg
    Commented Nov 17, 2009 at 2:39

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