$\mathbb Z_2$-Stable Dark Matter via Broken $\text{SU}(5)$ Gauge Bosons

I construct and analyze a dark matter sector that is neutral under the unbroken Standard Model gauge group and couples only to the broken $\text{SU}(5)$ gauge directions, the leptoquark vectors $X,Y$. An exact $\mathbb Z_2$ renders the dark matter stable. I give a gauge-covariant definition of projectors onto the unbroken Standard Model and broken ($X,Y$) subspaces, demonstrate that the covariant derivative of dark matter selects only $X,Y$, and integrate out $X,Y$ at tree level to obtain the leading effective operators. I also derive the loop-induced $\chi^2\,G^a_{\mu\nu}G^{a\mu\nu}$ coupling to gluons, prove color neutrality, and show consistency with cold dark matter phenomenology. Cosmological production proceeds via UV freeze-in or even more suppressed channels in.