Communication is made possible by common ground---the unspoken knowledge that people share and presuppose of one another, whether that be online or offline. In his conception of common ground, Clark (1996) distinguishes between personal and communal common ground, and asserts that the latter is graded: the more community affiliations two people share, the more common ground they share as well. Social media research has invoked this mechanism to explain how users connect, but it has gone largely untested because community memberships are rarely visible and, where they are, they are coupled to user interactions in a way that leads to conflating effects. To circumvent these challenges, this study repurposes Bluesky starter packs (SPs) as user-curated community affiliation labels. Across 191,648 pairs of users, we show that shared lexical repertoire---our proxy for common ground---grows monotonically with the number of SPs that users share, with users sharing a single pack being roughly twice as similar as equally connected strangers. A semantic renormalization of SP co-membership shows furthermore that it is more so the number of topically \emph{distinct} communities, rather than the raw count, in which common ground is graded. Finally, we show that community co-membership adds to common ground independently of proximity in the Bluesky follow network. These results lead to the conclusion that community membership is a measurable, separable, and semantically structured carrier of common ground. Reading it as such makes common ground observable before an exchange rather than inferred from it, and thus opens the door for large-scale observational approaches to a set of questions that have so far only been posed in the laboratory.

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