One tuned pass matches four relay legs at a third of the iterations: memory-strength selection in Relay-BP on bivariate bicycle codes

Relay belief propagation exposes a memory strength gamma_0 that the user supplies rather than the algorithm deriving: relay-bp 0.2.2 sets it to 0.1 in its constructor, and its README worked example uses 0.65. We swept gamma_0 over eight values on two bivariate bicycle codes under circuit-level noise at p = 3e-3 at four relay legs, 15,000 shots per point on [[144,12,12]] and 30,000 on [[72,12,6]], with all decoding performed by relay-bp 0.2.2 itself. On [[144,12,12]], gamma_0 = 0.1 gives 1,383 logical failures against 276 at 0.30, a factor of 5.01 (95% interval 4.40 to 5.70), and 0.65 gives 880, a factor of 3.19 (2.79 to 3.65); on [[72,12,6]] the minimum of the same grid sits at 0.20 rather than 0.30, so the position of the minimum is code-dependent. On [[288,12,18]], a code added to our library only for this test, 0.30 against 0.65 gives 226 failures in 4,000 shots against 908, a factor of 4.02 (3.47 to 4.65), with 4.03 and 4.05 in two further runs on a second machine, and the advantage falls as relay legs are added, reaching 1.74 (1.38 to 2.21) at 32 legs and 2.13 (1.57 to 2.89) at 64 legs in runs whose shots per arm were fixed before they began. With gamma_0 held at 0.30 and every relay leg pinned to a single strength, 0.30 against 0.65 is 1.07 at both four and sixteen legs, while leaving the relay legs at the package's default draw interval beats pinning them at 0.30 by 5.06 at sixteen legs, so the tuned value earns its factor at the entry point and not at the relay legs. Measured in belief-propagation iterations rather than wall-clock, a single tuned first-ensemble pass reaches the accuracy of four untuned relay legs while using about a third of the iterations at every baseline tested; the accuracy advantage over those four legs is itself baseline-dependent, from 2.55 against the constructor default 0.10 to a marginal 1.17 against a stronger baseline of 0.15 chosen as the most conservative comparison, while the near-threefold iteration saving is stable across all of them. This is parameter selection on a published decoder, not a new decoding algorithm; the package documentation already states that the memory parameters must be tuned. No systematic prior-art review has been carried out and no novelty or priority is claimed.