LMC X-4 data from 2024–2026 show no clear cycle phase shift between 4–10 and 15–50 keV when known outburst dates are excluded

We test the energy dependence of the long X-ray cycle of LMC X-4 from 1 June 2024 through 19 October 2026. We use frozen public MAXI scan and Swift/BAT pointing data. We exclude five-day intervals on each side of five reported outburst dates of the nearby source 1A 0538–66. A four-harmonic fit at a period of 30.3187 days uses 8,593 MAXI scans at 4–10 keV and 7,632 BAT pointings at 15–50 keV. The fundamental phase difference, softer minus harder, is +0.0017 cycles. The 95% interval is −0.0181 to +0.0208 cycles from 10,000 paired time-cluster bootstrap draws. A full-profile correlation gives −0.0017 cycles, with interval −0.0231 to +0.0190. We also test daily products, other date exclusions, and fit choices. Changes to the weights and cluster widths are included. We also test dates with data in all bands. These recent phase intervals include zero. The 2–4 versus 4–10 keV fundamental phase is less precise and is not resolved. These results add a later constraint to the published record. They do not directly repeat the earlier 2–10 keV segmented centroid test. The evidence does not resolve an average phase shift between 4–10 and 15–50 keV under the tested model. Source confusion, calibration errors, and shifts that vary with time can remain. The package preserves input bytes, provenance, source code, results, figures, and offline repeat instructions.

LMC X-4 · X-ray binaries · superorbital modulation · MAXI · Swift BAT · phase timing · public data