qector-bp-osdlisted

# QECTOR BP-OSD Source of authority: v1.0.0 reference manual, chapters 8, 9. ## Where BP-OSD applies BP-OSD is the only decoder defined for **arbitrary GF(2) parity-check matrices** (manual 11.1). The matching decoders reject any code with a qubit of degree > 2; the Union-Find rejection is the explicit contract, not a bug (manual 20.8). BP-OSD handles: - qLDPC codes (bicycle, bivariate-bicycle, hypergraph-product). - Color codes (`codes.color_code`). - Any code with hyperedges (weight > 2 mechanisms). - Codes fed by a DEM with mechanisms that cannot be collapsed to graph edges. ## The belief-propagation update (manual 8.1) Let `gamma_q = LLR_prior(q) + sum_{c in N(q)} m_{c->q}` be the posterior LLR of qubit `q`. The check-node update is the **box-plus kernel** in the log domain: phi(x) = -ln(tanh(x/2)) = ln coth(x/2) for x > 0 phi(0) = +inf phi(x) -> 0 for large x Three schedules are supported: | Schedule | Formula | Notes | | ------------------ | -------------------------------------------------------- | ---------------------------------------- | | Exact sum-product | `m_{c->q} = sgn * phi( sum_{q'} phi(|m_{q'->c}|) )` | default; numerically stable | | Min-sum | `m_{c->q} = sgn * min_{q'} |m_{q'->c}|` | classical approximation, opt-in | | Relay (layered) | same kernel; checks processed sequential