When More Data Is Not Enough: Identifying and Repairing Support Gaps in Mechanism-Resolved Forecasting

Accurate marginal prediction does not necessarily determine the predictive law for a specified combination of factors. We quantify this ambiguity with the Support-Induced Composition Radius (SICR), the minimax information radius of target laws compatible with the population training experiment. Positive SICR gives an architecture-independent lower bound on worst-case target excess log loss at every sample size. Within a specified interaction family, we prove that SICR vanishes exactly when the target interaction feature lies in the training row span, under composition-wise context overlap and anchored reference and atomic effects. This characterization yields target-span acquisition (TSA), a greedy rule that selects compositions to reduce the target residual outside the training span. Controlled experiments show a persistent error plateau when sampling from the same support and its removal when the span is expanded. Across 200 six-factor design tasks, three TSA additions reduce the mean normalized squared target residual to 0.0023, compared with 0.5057 for regularized D-optimal design. In a retrospective UCI Bike Sharing audit, TSA reduces target RMSLE averaged across four predictors by 11.4% relative to the best non-targeted policy at 200 added records. An omitted-interaction stress test evaluates the certificate's sensitivity to the chosen interaction basis. Together, these results provide a target-specific workflow for diagnosing support gaps, choosing informative additions, and checking the structural assumptions behind extrapolation.