The fixed step forecast has lower phase error in three 2023–2026 MAXI profiles of 4U 1820−30

We test two published forecasts for the long X-ray cycle of 4U 1820−30. One assumes a past period step and a later constant period. The other assumes a smooth period decrease. Both phase curves keep the central parameters from Table 4 of Chou et al. (2025). The primary test uses three complete 342-day MAXI windows after MJD 60157. Each 2–20 keV profile uses a constant and four Fourier harmonics at a period of 167.40 days. The phase root mean square error is 0.0891 cycle for the step forecast. It is 0.1808 cycle for the forecast with a smooth period decrease. The step forecast also gives lower error under all eight harmonic and weight settings and all 12 window settings. These controls reuse the same data. In a separate test, fixed reference flux profiles predict all later rows through MJD 61314. Their mean square errors are 0.09536 for the step clock and 0.14370 for the decrease clock. A constant reference flux gives 0.10147 in the same units. The last two fitted profile minima occur 12.8 and 22.2 days after the central step forecast. The first profile has several possible minima. Changing profile shape and three complete windows limit physical inference. This result compares two fixed central forecasts. It does not establish a physical cause for the long cycle. The package preserves source tables, hashes, code, figures, controls, and instructions for reproduction.

4U 1820-30 · X-ray binaries · superorbital modulation · forecast test · MAXI · Swift BAT · phase timing · public data