1\newcommand{\WPabstract}{%2Agents built on language models hand information to one another as text, summaries, structured evidence, shared-memory references or---when3they share a checkpoint---attention state (KV cache). We ask under which task, model, cache, network and reuse conditions each representation4preserves task-relevant information at the lowest end-to-end cost, and answer with a reproducible study executed by an autonomous research5operator (Claude Code) on Apple-Silicon hardware with the MLX runtime, whose caches are inspectable tensors. Twenty-two conditions (text6truncation, extractive selection, summaries, structured evidence with spans, references with metered retrieval, a lossless codec, LLMLingua-2,7native and serialized caches, packed 8/4-bit quantization, sink-plus-recent, random, SnapKV-style and PyramidKV-style eviction) are measured on8Qwen2.5-3B and Llama-3.2-3B across private-fact ledgers, LongBench QA and executable tasks, in question-blind and question-aware regimes, with9measured bytes, synchronized latency spans and peak memory (13\,280 trials; frozen protocol, cluster bootstrap, Holm-corrected tests). Further10experiments measure two-node cache transfer over a 1~GbE LAN (324 runs), relays of 1--8 handoffs with an evaluator-only fact ledger (7\,200),11fan-in with conflicting evidence (1\,600), a same-family learned KV mapper, hosted receivers (672) and a development-fitted router. Lossless12representations are interchangeable in quality and differ only in cost, whose ranking inverts between cold and reused regimes; on the measured13link, moving an 8-bit cache beats re-reading the text at every length. Lossy choices are model- and regime-dependent: 4-bit quantization is free14for Llama and fatal for Qwen; attention-based eviction keeps 78--98\,\% of private-fact accuracy with the question and 12--19\,\% without it, and15no eviction survives a code specification. At a 512-token budget prose summaries beat structured evidence (38--44 vs 12--15\,\%), relays are16nearly lossless after the first hop and invent almost nothing, and metered repair buys a few points for kilobytes of re-reading. A ridge KV mapper17transfers no content while producing coherent abstention, and an invalid cache concatenation yields plausible answers---both argue for18compatibility manifests and negative controls. The router halves amortized latency at equal quality when questions are unknown and does not help19otherwise. Cross-family cache transfer was not executed; the study is partial in that respect. Code, records, protocol, checkpoint and a20minimal reproduction (64/64 identical outputs) are released.%21}22