Within the academy, signals of a scholar's academic influence are made manifest in indices like the "h"-index, which rank output. In open scholarly networks, however, signals of influence are less codified, and the ways in which they are enacted and understood have yet to be articulated. Yet the influence scholars cultivate in open networked publics intersects with institutional academia in grant-required measures of "public impact", in media visibility, and in keynote and job opportunities. How do scholars within open networks judge whether another scholar's signals are credible or worthy of engagement? What counts as academic influence on a platform like "Twitter"? This paper concludes that scholars employ complex logics of influence to assess the networked profiles and behaviors of peers and unknown entities. Significantly, these logics of influence depart from the codified terms of rank and bibliometric indexing on which conventional academic influence is judged. While some are numeric--participants recognized relatively large-scale accounts as a general signal of influence--recognizability and commonality are as important as or more important than quantifiable measures or credentials. The paper suggests that the impression of capacity for meaningful contribution is key to cultivating influence and the regard of actively networked peers.