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Question: Three campaign studies found that NOAA DOISST v2.1 lost day-to-day SST variance in steps at satellite input changes, which causes most of its reported persistence rise. Do the same changes also cause steps in the spatial structure of DOISST, and do they cause false trends in front and gradient statistics? Approach: For each day of 1982-2025 we calculated, on the 0.25-degree grid from 50S to 50N, the mean SST gradient G, the sub-75-km spatial variance V3 and the share of strong fronts F3, for the ocean and 12 regions. We tested steps at documented and known dates against placebo dates, grouped per-pixel steps by background gradient, compared DOISST with MUR SST v4.1 on 294 identical days and points, and fitted 1982-2025 trends with and without step terms. Results: On 2007-01-01 (Pathfinder to Navy AVHRR), V3 increased by a factor of 2.2 in the Gulf Stream and by 1.4 to 1.9 in the Kuroshio, Agulhas and Brazil-Malvinas, and decreased by 26-28% in the subtropical gyres. A blind change-point search put the break in the 10-day block containing 2007-01-01 in all four western boundary currents. At 2007-01-01 and 2021-11-01 (ACSPO input), V3 fell by 36-55% in the four lowest deciles of background gradient and rose by 16-28% in the highest decile. Undocumented steps on 1985-01-15 and 2020-06-28 lowered V3 everywhere. MUR did not show these steps: the ln ratio DOISST/MUR of V3 stepped by +0.74 +/- 0.15 in the Gulf Stream and -0.28 +/- 0.09 in the N Pacific gyre at 2007, by +0.48 +/- 0.08 (Agulhas) and -0.56 +/- 0.11 (S Pacific gyre) at 2021, and by -0.25 +/- 0.05 over the full ocean at 2020. The raw DOISST trends were +12.1 +/- 1.9% per decade for the 50S-50N strong-front share, +4.0 to +5.5% per decade for G in the Gulf Stream, Agulhas and Brazil-Malvinas, and -7.4% per decade for G in the N Pacific gyre. With the three documented steps in the model, none of these trends stayed positive and significant; with six steps, a small rise of strong fronts remained (+3.6 +/- 1.5% per decade). Conclusion: The input changes changed the spatial structure of DOISST in steps: sharper strong fronts and a smoother quiet ocean. DOISST front intensification in western boundary currents, the rise of global strong-front area and the smoothing of the gyres are mostly product artifacts. Limitations: MUR has its own input changes and covers three step dates; step-adjusted trends remove any real change at the step dates; regions and front thresholds are fixed choices.