Global-scale claims about landscape-entropy regimes are highly perturbation-sensitive at the individual-tile level but surprisingly stable at the aggregate-envelope level. We demonstrate this on the Dai (2026, submitted) baseline, which partitions 209 ten-degree tiles at 0.5° resolution into three threshold-defined attribution bands — land-cover-dominant, mixed, and climate-elevated — based on the ratio of unique partial R² of land-cover and climate blocks in a per-tile nested OLS. We do not defend any specific numerical partition. Instead we report a <em>perturbation envelope</em> across seven non-overlapping perturbations: cell grain (MAUP coarsening from 0.5° to 1°, plus a 5° check), a stratified sensitivity on the high-entropy cell subset, per-tile bootstrap over 500 cell-level resampling iterations, a classification-threshold scan, a spatial-null toroidal-shift test, Hansen Global Forest Change partial corroboration at post-2000 frontier cells, and FAOSTAT national agricultural change at country level.</p> <p>Across all seven perturbations the information band ranges between 43 and 92 per cent, the mixed band between 0 and 55 per cent, and the climate-elevated band between 1 and 10 per cent. Within ±50 per cent of the reference thresholds the climate-elevated band narrows to 5–7 per cent. The narrowest envelope therefore attaches to the band that audit-naïve readers might expect to be the most contested — climate-elevated. Two independent observations explain the apparent paradox. Bootstrap resampling preserves the modal classification in 100 per cent of land-cover-dominant tiles, 89 per cent of mixed tiles, and only 73 per cent of climate-elevated tiles (four of fifteen flip to mixed). Under the spatial-null toroidal shift the median class survival is 12 per cent for information tiles, 32 per cent for mixed tiles, and 54 per cent for climate-elevated tiles. Climate-elevated <em>individual-tile labels</em> are highly sensitive to OLS sampling and substantially classifications are therefore numerically stable in aggregate proportion but the reproducible by random spatial shifts alone — diagnostic of a ratio-instability pathology in which the climate / land-cover R²-ratio diverges when the land-cover denominator approaches zero in low-LULC-variance cells. Hansen GFC corroborates only a small subset of post-2000 frontier cells (one of fifty exceeds 5 per cent within-decade pixel-level forest loss); the remainder fall in countries with documented FAOSTAT national agricultural area change between 2000 and 2018. We offer the seven-perturbation audit package as a recommended baseline for future global LULC entropy classification studies.