Linear X-ray terms give no consistent gain in 2025 spin predictions for 4U 1626−67 after 2023–2024 fits

We test whether measured X-ray brightness improves later spin predictions within the known spin-down state of 4U 1626−67. We fit four linear rate models to public Fermi GBM pulse frequencies from 2023–2024. We then predict 2025 frequency changes, using measured MAXI or Swift BAT brightness. The main test uses 30-day brightness means, 54 fit frequencies, and 24 test frequencies. All measured test interval brightness means lie within their training ranges. Adding brightness to a time trend changes test increment squared error by −0.09% for MAXI and +0.67% for BAT. Positive values mean lower error. The gain changes sign under the planned analysis choices. A constant-rate control has lower main test error than the time models. The result supplies a reproducible benchmark within one spin state. It does not reject a physical brightness–torque relation. The study is retrospective. It has a short, noisy test record and assumes Brownian frequency noise for conditional uncertainty. The package preserves the public input snapshot, source credit, code, all planned scores, figures, and numerical checks.

4U 1626-67 · accreting pulsars · spin-down · Fermi GBM · MAXI GSC · Swift BAT · prediction · timing noise · public data · negative result