How Much of the Routing Gap Is Real? Decomposing the Router-to-Oracle Gap into Reproducible Specialist Advantage and Single-Draw Label Noise

arXiv:2607.03436v1 Announce Type: new Abstract: Routing among large language models (LLMs) promises better quality at lower cost, motivated by the reported gap between learned routers and a per-instance oracle. But that oracle is computed from a single correctness label per (query, model), so under stochastic decoding it is one Bernoulli draw, not a reproducible property. We recast the question structurally: the expected per-instance oracle decomposes as $O^{\exp}=O^{\mathrm{repro}}+\Delta$, into reproducible single-commit headroom $O^{\mathrm{repro}}$ and a non-negative single-commit selectio