A fixed 313.6-day curve reduces observed mean squared error by 6.8% for 604 selected Cygnus X-1 days in 2018–2026 after secular fits

We test whether an earlier long-period hard X-ray curve carries into later public Cygnus X-1 data. We fit a sine and cosine at the published 313.6-day period to 1341 Swift/BAT daily rates in 2006–2010. We keep these two coefficients fixed for 604 later days selected with surrounding MAXI data. Each sample has its own mean, plus constants and slopes in 1000-day blocks. Thus the test is conditional on later secular fits, rather than an absolute flux forecast. The fixed curve reduces observed mean squared error by 6.819%. Its signed scale is 0.776. With 120-day residual-score blocks, the joint 95% multiplier range for scale is 0.364–1.389. The range for gain is −0.00234 to 0.00804 in squared fractional-flux units. All eight tested block choices give a positive scale range and a gain range that includes zero. The evidence shows positive fitted correspondence, but does not establish improved expected squared error. Log flux and added annual terms give central gains of 5.32% and 4.07%. All tested individual time-block omissions keep the central gain positive. A broader BAT state label gives one negative gain under an alternative secular fit. The earlier BAT data also remain subject to an archive warning about count overflow. These results do not establish a continuous physical clock or disc precession. An independent selection and dense solve reproduce the central result. The package preserves source tables, hashes, code, figures, planned and added checks, and reproduction instructions.

Cygnus X-1 · Swift BAT · MAXI · superorbital variation · X-ray binaries · waveform transfer · hard state · time series · reproducible data