Fair Decoder Baselines and Rigorous Finite-Size Scaling for Bivariate Bicycle Codes on the Quantum Erasure Channel

Fair threshold estimation for bivariate bicycle (BB) codes on the quantum erasure channel runs into two recurring problems: decoder-baseline unfairness and the conflation of finite-size pseudo-thresholds with true asymptotic thresholds. We run both uninformed and erasure-aware minimum-weight perfect matching (MWPM) surface code baselines alongside BP-OSD decoding of BB codes. With standard depolarizing-weight MWPM and no erasure information, performance matches random guessing on the erasure channel in our tested regime - so prior work that compares against this baseline is really comparing decoders, not codes. Using 200{,}000 shots per point and bootstrap confidence intervals, we sweep five BB code sizes from N=144 to N=1296. Pseudo-thresholds WER = 0.10 run from p^* = 0.370 to 0.471; finite-size scaling (FSS) gives an asymptotic threshold p^*_infty approx 0.488, within 2.4% of the zero-rate limit and without maximum-likelihood decoding. On the fair baseline, BB at N=1296 has a modest edge in threshold over the surface code at twice the qubit count, and a 12times lower normalized overhead - the latter is where the practical advantage sits. All runs are reproducible from recorded seeds and package versions.