# Decomposition Buys Integrity, Not Yield

arXiv: https://arxiv.org/abs/2609.17464 · HTML: https://mlsanity.com/paper/2609.17464/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 15 references that are in the map.
- First posted on arXiv 15 Sep 2026.

## Builds on (most cited first, 6 of 6)

- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Why Do Multi-Agent LLM Systems Fail?](https://mlsanity.com/paper/2503.13657/) (2025)
- [Towards a Science of Scaling Agent Systems](https://mlsanity.com/paper/2512.08296/) (2025)
- [On the Resilience of LLM-Based Multi-Agent Collaboration with Faulty Agents](https://mlsanity.com/paper/2408.00989/) (2024)
- [Understanding the Information Propagation Effects of Communication Topologies in LLM-based Multi-Agent Systems](https://mlsanity.com/paper/2505.23352/) (2025)
- [Hallucination Cascade: Analyzing Error Propagation in Multi-Agent LLM Systems](https://mlsanity.com/paper/2606.07937/) (2026)

## Abstract (arXiv)

Multi-agent systems split a task across a tree of agents and justify the split with folklore: smaller contexts, cleaner separation, parallelism. We ask what the split does to how much of what the leaves discover reaches the root. Model a decomposition as a tree in which an agent handed b items keeps any one with probability r(b). If r(b)=1/b, every tree delivers exactly one finding, for every task size and every shape; we verify this to 2.4 × 10-15 on 20,000 random irregular trees. If r(b)=Cb-δ, a depth-k tree over N findings yields Ck N1-δ: task size and architecture separate, and architecture contributes only C ≤ 1 per level, so flat is optimal for yield and no arrangement of agents escapes the exponent δ. On 600 production deep-research traces δ = 0.34 [0.30, 0.38], by three identifications that do not share a failure mode. At a hop where item boundaries come from the tool rather than a text heuristic, and where b=1 occurs 550 times, C = 0.571 [0.527, 0.615] is observed rather than extrapolated, over 16,082 hops. A tier also costs alignment: on 1,012 annotated multi-agent traces one brief in sixteen goes off-target, giving μ = 0.939 and a per-tier penalty Cμ = 0.536. Depth is bought on two other axes. The root context is the only state that persists and the only one that cannot cheaply forget, and depth cuts its exposure from N items to N1/k. Depth is also cheaper: production flat agents bill as N1.39, not the N2 an append-only context predicts, and at equal spend two tiers overtake flat at 403 findings. Across every parameter we measured the model says 0.7% to 11.3% of production sessions are worth delegating, against 7.8% that do. A hazard model on 743,819 production tool calls finds that delegation does not respond to a filling context and is instead an opening move.