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Decomposition Buys Integrity, Not Yield

arXiv · AI, language, vision and robotics · article · Sep 15, 2026 · UTC

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 $2.4 \times 10^{-15}$ on 20,000 random irregular trees. If $r(b)=Cb^{-δ}$, a depth-$k$ tree over $N$ findings yields $C^k N^{1-δ}$: task size and archite

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