Formal Result: Append-Only Multi-Agent Transcripts Collapse to Finite-State, and Two Pop-Enabled Channels Reach Universality

arXiv 2607.29496·low signalXBlueskyLinkedInCopy link

Modeling fixed finite-precision causal Transformers whose transcripts are partitioned into bounded-block channels, the paper proves that the standard append-only layer realizes exactly the deterministic finite-state transductions — and that this holds for any fixed finite agent population under a monotone protocol that appends, routes, and copies visible blocks. In other words, orchestrating more append-only agents buys no expressive power. Adding a pop operation that deletes the newest block makes a channel a stack, transferring the classical hierarchy: deterministic context-free for one channel and recursively enumerable for two or more, so two pop-enabled transcripts — in one agent or across two — suffice for universality.