This paper explores the territory that lies between best-effort Byzantine-Fault-Tolerant Conflict-free Replicated Data Types (BFT CRDTs) and totally ordered distributed ledgers. It formally characterizes a novel class of distributed objects that only requires a First In First Out (FIFO) order on the object operations from each process (taken individually). The formalization relies on Mazurkiewicz traces to define legal sequences of operations and ensure a combination of Strong Eventual Consistency (SEC) and Pipleline Consistency (PC). The paper presents a generic algorithm that implements this novel class of distributed objects in both crash- and Byzantine setting. Finally, the proposed approach is illustrated with four instances of this class of objects, namely money transfer, Petri nets, multi-sets, and concurrent work stealing dequeues.