Uniform interval models give only two static Vela X-1 orbit contrasts at fixed period and reference frequency with a free spin level (2008–2026 GBM)

All 2,208 search intervals in the 2008–2026 Fermi/GBM Vela X-1 frequency record repeat three exact orbital phase windows. We test what orbit corrections these summary data can identify. With uniform interval weights, fixed period, fixed reference frequency, and a free spin level, four static corrections have only two independent contrasts. Nine distinct nonlinear Kepler orbits give the same window contrasts. This shows a specific limit on orbit inference from these interval models. Linear rate fits also change with assumed interval weights, fit dates, and period constraints. At fixed period, the full record gives a point-model orbit rotation rate of +0.361 +/- 0.102 degrees per year. A broad positive kernel with the same mean time gives +0.623 +/- 0.173. Fits before 2022 give negative central rates. With period correction and rotation both free, the full-record point rate is -0.311 +/- 0.361 degrees per year. The two corrections have correlation +0.959. All errors apply within the selected linear response and Gaussian random walk model. Exact Kepler checks give linear-expansion errors of 0.004–0.007 microhertz RMS, so the rates are sensitivity diagnostics. Added rotation and period terms give lower later forecast scores than two phase offsets. The released summary does not specify the effective interval weights. The cause of the phase pattern remains open. We preserve the data, source code, provenance, all model results, numerical checks, and figures.

Vela X-1 · Fermi GBM · pulsar timing · apsidal advance · binary orbit · interval weights · parameter identifiability · frequency random walk · reproducible research