A fixed 2154.58-day cycle lowers Vela X-1 forecast scores for 2021–2026 under Gaussian random walk models

We test whether a fixed 2154.58-day cycle improves later forecasts of the spin frequency of Vela X-1. This period comes from prior work on a longer record. We use a public Fermi GBM snapshot from 22 October 2026. One detected frequency nearest each 60-day bin center gives 78 training records before July 2021 and 33 test records through October 2026. Both models have Gaussian frequency random walk noise and drift. The second model adds a sine and cosine at the fixed period. All parameters are estimated from training data. The cycle lowers the later joint log predictive score by 0.733 and raises frequency RMSE from 1.143 to 1.339 microHz. All planned controls give the same direction of change. In 2,000 random walk simulations with both models refitted, the central 95% of score differences is -2.107 to 1.389. The observed loss is therefore small under this simulated reference. A separate noise check gives early-to-late diffusion changes that depend on the sampling grid. Constant Gaussian diffusion is not established. The tested fixed cycle gives no forecast gain, but this test does not exclude a changing or weak cycle. The package preserves source data, provenance, code, figures, forecasts, simulations, and reproduction instructions.

Vela X-1 · Fermi GBM · accreting pulsar · spin frequency · torque noise · random walk · forecast validation · periodic signal · public astronomical data