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tokens: 14.0, is notable. If O vi arises primarily at interfaces between cool clouds and a hot, volume-filling phase, the lack of O vi absorption suggests partial covering of such structures in the relevant galaxy halo(s) and intragroup medium. For the stronger of the two H 2 -bearing velocity components, the excitation state of the molecules may be due to UV pumping by an ambient radiation field that is elevated above that observed in the solar neighborhood by a factor of α = 10–100. This field may be produced by shocks arising from collisions between cool clouds or at the interface between these clouds and the hot, ambient medium, or may imply the presence of undetected star formation obscured by dust or the glare of the QSO (see point III below). In this picture, the observed rise in b value with J level can be attributed to stratification in the cloud, in which J > 1 levels are primarily populated closer to the surface of the cloud and thus in more diffuse and spatially extended gas than the lower rotational levels (e.g., Abgrall et al. 1992 ; Balashev et al. 2009 ). The galaxy redshift survey presents an unprecedented opportunity to explore the origin and physical conditions of an H 2 -bearing DLA in the context of its galactic environment. Nine galaxies are detected within d = 600 pkpc and Δ ν g = 300 km s −1 of the absorber, and here we discuss the possible association of the diffuse molecular gas and the relevant galaxies. I. Association with a massive, early-type galaxy at d = 41 pkpc . Several lines of evidence favor an association between the H 2 -bearing DLA and the massive elliptical galaxy, G41. In addition to having the smallest projected distance ( d = 41 pkpc) and a modest velocity offset (Δ ν g = −57 km s −1 ), this galaxy is also the most massive system observed at the redshift of the DLA and represents almost 70% of the stellar mass of the small group comprising this galaxy and its four closest neighbors. Furthermore, as discussed in Section 4.3 , the chemical abundance pattern suggests Fe enhancement consistent with significant contributions from Type Ia SNe. This chemical signature is commonly seen in the inner halos of massive quiescent galaxies ( d ≲ 100 pkpc), in contrast to their outer halos and star-forming systems (e.g., Zahedy et al. 2017 ). The observed subsolar metallicity at d ≈ 40 pkpc is not in tension with the supersolar stellar metallicities often observed at the centers of massive quiescent galaxies, due to the stellar metallicity gradients observed in these systems (e.g., Spolaor et al. 2010 ) and the significant scatter seen within single luminous red galaxy halos suggesting a range of gas cloud origins and poor gas mixing (Zahedy et al. 2019 ). Given the observed projected distance, d = 41 pkpc, the absorber could be associated with either the outer ISM or true CGM of this massive galaxy. Significant amounts of neutral atomic and molecular gas have been observed in early-type galaxies at low and intermediate