qector-orchestrationlisted

# QECTOR Orchestration Source of authority: v1.0.0 reference manual, chapter 11. ## The two questions The routing layer answers two questions: 1. **Validity**: which decoder family is valid for a problem? 2. **Execution**: which execution backend should run it? The validity answer is **structural**: a problem with any qubit of degree > 2 is non-graphlike, so matching decoders are not eligible and BP-OSD is forced regardless of how the problem was labelled. ## The recommend_decoder policy (manual 11.1) Inputs: `(code family, distance, qubit count, batch size, priority)`. Output: a decoder name. For graphlike problems: - **accuracy priority** -> exact `Blossom` for small / moderate codes, region-growing `SparseBlossom` for large ones. - **speed priority** -> `FastUnionFind` (or the GPU batch path for huge batches). - **balanced priority** -> interpolate by batch size and code size. For non-graphlike problems: always route to `BPOSDDecoder`. ## Theorem 14 (dispatch faithfulness, manual 11.1) > Let `Auto(s) = D_{k(s)}(s)` be the dispatch of syndrome `s` to > the decoder selected by the policy `k(s)`. If every backend `D_i` > is syndrome-faithful for the problems it is eligible to decode, > and the policy only selects eligible backends, then `Auto(s)` > satisfies `H c = s` whenever any eligible backend can satisfy > it. The dispatch selects `k(s)` among eligible backends; no syndrome alteration occurs before dispatch; by hypothesis the selected backend returns `c`