BAT brightness reduced spin-change loss against a constant normal model in 15 OAO 1657−415 30-day windows from 2022 to 2025

We tested whether hard X-ray brightness helps to predict the spin-frequency derivative of OAO 1657-415. We used public Fermi/GBM frequencies and Swift/BAT daily rates saved on 23 October 2026 UTC. Fixed 30-day windows used coverage cuts without a cut on spin-change sign or size. We fitted four normal models to 59 windows before 2022. We tested constant, brightness-dependent mean, brightness-dependent scatter, and combined models on 15 accepted windows from April 2022 to November 2025. The mean model reduced signed squared error from 5.9813 to 3.6679 in units of (10^-12 Hz/s)^2, a 39% gain. Mean log loss fell by 0.2026 nats per test window. Its 95% interval was [-0.3097, -0.0855] from paired 120-day calendar blocks with fixed fits. An added check that refitted the models gave [-0.3750, -0.0336]. Adding a scatter term to the mean model gave a smaller loss gain. Its primary interval included zero. The test did not clearly separate the mean-only and scatter-only models. All eight control point estimates favored the mean model over the constant model, but two control intervals included zero. A truncated-normal example shows how changing scatter can create opposite trends after cuts on large positive and negative changes. This example is not a fitted physical explanation. The test is retrospective, and prior later-data correlations were known. It uses brightness measured in the same window and requires detected pulses. No primary window in 2026 passed the coverage cuts. The package preserves source data, provenance, code, all window decisions, results, figures, and independent numerical checks.

OAO 1657-415 · Fermi GBM · Swift BAT · spin-frequency derivative · X-ray binaries · torque reversal · prediction · selection effects · reproducible astronomy