Orbital phase terms reduce Vela X-1 frequency forecast errors in a 2022–2026 random walk test

We test forecasts of public Fermi/GBM spin frequencies for Vela X-1. A frozen release contains 2,208 detected measurements from 2008 to 2026. We fit parameters before 2022 and score 582 later measurements. A frequency random walk gives root mean square error 0.12002 microHz. Two fitted orbital phase offsets reduce this error to 0.11241 microHz, a 6.34% decrease, and add 45.11 to the natural log score. The phase gain is positive in every later calendar year. Added 2021 and 2023 date splits give error decreases of 5.96% and 7.59%. These checks share data. The phase model is exploratory because later residual inspection led to its selection. All phase and noise parameters use only earlier data, but this is not a blind test of model selection. The original test of finite torque memory gives a smaller 1.02% error decrease. That gain nearly vanishes at lower sampling density and reverses without an added measurement error floor. Interval coverage remains below its nominal 95% value. The phase terms describe this released table; they do not identify an orbital, physical, or measurement cause. The package preserves both source FITS formats, source hashes, provenance, every forecast, all tested settings, figures, code, and reproduction instructions. Independent FITS, dense covariance, simulation, and causal forecast checks verify the calculations.

Vela X-1 · Fermi GBM · accreting pulsar · spin frequency · orbital phase · random walk · torque noise · sequential prediction · public data · reproducible research