A half-cycle window shift changes whether a two-harmonic mean loop interval contains zero for 4U 1820-30 in 2009–2026 MAXI data

We test whether paired MAXI 2–4 and 10–20 keV fluxes of 4U 1820-30 trace a mean signed loop. The primary analysis uses 37 complete 167.43-day windows, with two Fourier harmonics and equal weights in each band. We calculate the exact closed area from the coefficients. We divide each area by 2 pi times the product of the fitted variable root mean square values. The mean normalized area is -0.0222. Its whole-cycle 95% bootstrap interval is -0.1175 to +0.0898. A planned half-cycle shift of the data windows gives a mean of -0.0670 and an interval that excludes zero. The original windows and other period, harmonic, and weight checks do not give a stable exclusion. Thus the weak mean-loop test depends on the data windows. This result does not establish the absence of source hysteresis. We give paired residual-block simulations for zero-delay and delayed curves at the actual observation times. We verify the area formula with an independent polygon integral, a regression check, and a fixed-window phase rotation. A newer source download gives identical accepted primary areas. The result applies to these native daily flux products, finite curves, and cycle resampling assumptions. It does not choose a physical cause for the long brightness cycle. The package preserves two input snapshots, provenance, the local analysis plan, per-cycle coefficients, all control results, simulation draws, figures, code, and repeat instructions.

4U 1820-30 · MAXI · X-ray binary · spectral hysteresis · signed loop area · superorbital cycle · paired energy bands · public data