Zero-Incoherence Capacity of Interactive Encoding Systems: Achievability, Converse, and Side Information Bounds

arXiv:2602.23520v1 Announce Type: new
Abstract: We introduce the zero-incoherence capacity for interactive multi-location encoding systems: the maximum encoding rate that guarantees exactly zero probability of disagreement among replicated encodings. Our main information-theoretic results are compact and self-contained: an exact capacity theorem ($C_0=1$), a tight side-information lower bound for resolution ($geqlog_2 k$ bits for $k$-way incoherence), and a rate–complexity separation (modification cost $O(1)$ at capacity vs $Omega(n)$ above).
The paper frames encoding locations as terminals in a multi-terminal source-coding model. Derivation (automatic deterministic dependence) is interpreted as perfect correlation that reduces effective rate; only complete derivation (one independent source) achieves zero incoherence. We give concise achievability and converse proofs in IT style, formalize the confusability/incoherence graph connection, and present an explicit mutual-information argument for the side-information bound.
Theoretical contributions are supplemented by constructive instantiations (programming-language patterns and a software case study). For TIT submission we move detailed language evaluation, extended code examples, and the full Lean proof corpus to supplementary material; the main text contains brief instantiations only. Core theorems (capacity, realizability, bounds) are machine-checked in Lean 4; entropy arguments apply standard Fano-inequality techniques.