In process mining, computational processing of sequential data allows the discovery and analysis of processes followed by organisations. These can be either explicitly understood processes, captured in documents or rules, or implicit process paths known in more informal or emergent ways. This paper examines a long-lived institution of historical interest, the Qing (1644-1911) Chinese civil service, using data assembled by historians on civil officials during the 19th century. Mapping the promotion process by following paths of officials through civil service postings helps illuminate the everyday operation of the institution and the society around it. Two distinctive features of this data set are that it records states, not events, and careers often include holding multiple concurrent roles. The combination is a poor match for existing process discovery techniques. We describe this structure as a state snapshot log, and present a new discovery technique, the State Snapshot miner, for constructing stochastic Petri net models from such logs. A case study shows its use in analysing promotion paths for elite graduates in the Qing civil service.