Toward extracting $\gamma$ from $B \to DK$ without binning

$B^\pm \to DK^\pm$ transitions are known to provide theoretically clean information about the CKM angle $\gamma$, with the most precise available methods exploiting the cascade decay of the neutral $D$ into $CP$ self-conjugate states. Such analyses currently require binning in the $D$ decay Dalitz plot, while a recently proposed method replaces this binning with the truncation of a Fourier series expansion. In this paper, we present a proof of principle of a novel alternative to these two methods, in which no approximations at the level of the data representation are required. In particular, our new strategy makes no assumptions about the amplitude and strong phase variation over the Dalitz plot. This comes at the cost of a degree of ambiguity in the choice of test statistic quantifying the compatibility of the data with a given value of $\gamma$, with improved choices of test statistic yielding higher sensitivity. While our current proof-of-principle implementation does not demonstrate optimal sensitivity to $\gamma$, its conceptually novel approach opens the door to new strategies for $\gamma$ extraction. More studies are required to see if these can be competitive with the existing methods.