Registered Absorption Chains and Placement Fibers for a Circular Action with an Adjacent Idempotent

We classify the registered absorption chains and literal placement fibers generated by a deterministic circular action with cyclic rotation and an adjacent idempotent collapse. Registration begins when the packet {0,1} is first created; a summary retains its ordered origin, subsequent selected absorption chain, and current placed partition. Complete chains admit a ternary encoding, and every admitted chain and placement is realized by an actual execution. We obtain exact fixed-chain fiber and total-summary counts, with exponential growth base 9/2. The objects counted are event-anchored summaries, not execution words or minimal predictive equivalence classes.