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The origin of the matter-antimatter asymmetry apparently obligates the lawsof physics to include some mechanism of baryon number ($\mathcal{B}$)violation. Searches for interactions violating $\mathcal{B}$ andbaryon-minus-lepton number $\mathcal{(B-L)}$ represent a rich and underutilizedopportunity. These are complementary to the existing, broad program of searchesfor $\mathcal{L}$-violating modes such as neutrinoless double $\beta$-decaywhich could provide deeper understandings of the plausibility of leptogenesis,or $\mathcal{B}$-violating, $\mathcal{(B-L)}$-conserving processes such asproton decay. In particular, a low-scale, post-sphaleron violation mechanism of$\mathcal{(B-L)}$ could provide a \textit{testable} form of baryogenesis.Though theoretically compelling, searches for such $\mathcal{(B-L)}$-violatingprocesses like $\Delta\mathcal{B}=2$ dinucleon decay and $n\rightarrow\bar{n}$remain relatively underexplored experimentally compared to other rareprocesses. By taking advantage of upcoming facilities such as the DeepUnderground Neutrino Experiment and the European Spallation Source, this gapcan be addressed with new intranuclear and free searches for neutrontransformations with very high sensitivity, perhaps greater than three ordersof magnitude higher than previous experimental searches. This proceedingsreports on recent theoretical and experimental advances and sensitivities ofnext-generation searches for neutron transformations were detailed as part ofthe Amherst Center for Fundamental Interactions Workshop, "TheoreticalInnovations for Future Experiments Regarding Baryon Number Violation," directlycoordinated with the Rare Processes and Precision Measurements Frontier.

$|\Delta \mathcal{B}| =2$: A State of the Field, and Looking Forward--A brief status report of theoretical and experimental physics opportunities