The mean of two minima keeps offsets from odd harmonics in ten TESS sector fits of KIC 9832227

The mean of two eclipse minima can keep shifts from odd Fourier harmonics. We derive the leading second-order term about a minimum of the flux averaged over half an orbit. We test it in ten public TESS light curves of KIC 9832227 from 2019 to 2024. For simultaneous fits with eight harmonics, the paired mean differs from the even-curve minimum by -5.09 to +5.91 seconds. The second-order term predicts each offset to within 0.016 second. The size and sign depend on harmonic order: the tested fits with 4 to 12 harmonics span -12.15 to +12.04 seconds. Conditional cluster intervals do not include this model uncertainty. We test the real time samples with no noise. A fit that omits odd harmonics shifts the known even minimum by up to 5.19 seconds. A joint fit followed by the half-orbit flux average removes the defined odd component exactly. It does not remove even changes or give a known conjunction time. A sinusoidal control also shows a common timing term at twice the frequency of the odd-component longitude. This is a model result, not a measured stellar period or evidence for a new companion. The package preserves source FITS files, provenance, code, coefficients, resampling draws, figures, and offline reproduction instructions.

KIC 9832227 · TIC 63205800 · TESS · eclipse timing · Fourier harmonics · contact binaries · time series · public data