With random walk noise, 30-day unweighted BAT means lower later frequency RMSE for 4U 1907+09 at a 2019 split and raise it at a 2018 split

Does the measured hard X-ray rate help reconstruct later spin frequencies of 4U 1907+09? We audit two public Fermi/GBM products and retain 64 unique timing intervals from 2011 to 2025. We fit drift and drift plus the time integral of Swift/BAT rate. Both models include Gaussian random walk noise in frequency. With 30-day unweighted rate means and a 2019 split, the later root mean square error falls from 0.713 to 0.438 microHz, a 38.5% gain. A 2018 split raises the error by 32.9%. Inverse-variance rate means also remove the 2019 gain. BAT lowers the error in 8 of 18 overlapping input checks and raises it in 10. In the full fit, the likelihood ratio falls from 56.49 with independent excess noise to 3.48 with random walk noise. Under fitted drift-only random walk nulls, 78 of 1000 simulations reach that likelihood ratio and 159 of 1000 reach the main later-error gain. The tests use observed later BAT rates and are retrospective. They do not establish a stable rate-spin relation or a new torque reversal. The package preserves raw inputs, row audits, all tested settings, figures, code, null draws, and independent numerical checks.

4U 1907+09 · Fermi GBM · Swift BAT · accreting pulsar · spin frequency · random walk noise · torque · held-out data · reproducible research