Transcript-Managed Transformers: Monotone Multi-Agent Collapse and Universality with Two Pop-Enabled Transcripts

We study transcript management for fixed, finite-precision causal Transformers. A transcript is partitioned into channels of bounded blocks. Each transition consults a fixed visible suffix and may append one block, leaving the model, weights, and token protocol unchanged. The operation P_c:=\PopContext(c) deletes the newest block on channel c and exposes its predecessor. We model the layer by the Transcript-Managed Transducer \TMTn{k}: one finite controller, k channels, and per-round actions from stay, push, and pop under a caller-driven status map. Fixed visible windows encode as finite symbols. The pop-free Restricted Transcript-Managed Transducer \RTMTn{k} is the standard append-only layer and, for every fixed k, realizes exactly the deterministic finite-state transductions. The same holds for every fixed finite agent population under a monotone protocol that appends, routes, and copies visible blocks. Admitting {P_c}_{c=1}^k restores pop. Newest-first, a pop-enabled channel is a stack; compiling to the Hopcroft--Ullman presentation transfers the classical hierarchy: \DCFL for k=1 and \RE for every k\ge2. Orchestrated one-channel agents match one controller with k channels, so two pop-enabled transcripts---in one agent or two---suffice for universality. Simulation costs and invariance to fixed block size and visible radius are stated. The bounds fix precision, alphabets, blocks, visibility, controller state, and population; growing exact context, hidden-block access, writable stores, and unbounded Spawn add further state.