Clean grids do not make fair machines: energy geography and the Sustainable AI Trilemma

The index is organized in three dimensions. Each dimension is scored by a modified TOPSIS: metrics are min-max normalized (cost metrics inverted so that higher always means better), weighted equally within the dimension, and aggregated into a proximity coefficient in the unit interval, relative to the sample. The three dimensions are reported separately; no single global score is used.The environmental sub-index uses five operational metrics (E1, E2, E4, E5, E6); the technological sub-index uses seven (T2 to T8); the social sub-index uses all eight (S1 to S8). The metrics excluded from each dimension, and the reasons, are documented in Section 3.3 and Supplementary Material S6 of the article: E3, E7 and E8 lie outside the operational boundary and carry data defects; T1 (peak operations per watt) discriminates the accelerator rather than the model, because four of the five systems share the same die, and including it inflates one model's score through an accelerator artifact (the script prints this effect for transparency).The counterfactual holds model architecture, accelerator count, workload and governance constant, so the technological and social inputs do not change; only the site-dependent environmental parameters do. The counterfactual is introduced as a sixth alternative, which renormalizes the environmental ideal solutions, so the environmental gain is reported within the six-alternative sample.