GeoRARE: Certified Rarity Profiles for Structural Causal Effects

Rare treatment–context regimes create two distinct problems: deciding how much they matter and determining what the data can establish about them. GeoRARE defines a two-dimensional rarity-indexed structural causal profile $(d,r)\mapsto {\Theta }_{\Psi }(d,r)$ that separately indexes treatment and context rarity. Sampling allocation governs information; reference weights govern the scientific question. One law-confidence event certifies the entire profile and its signed contrasts, with width controlled by unresolved reference mass. A finite sample upper bound and a rare-cell lower bound identify the same local information scale, up to constants and logarithmic terms. Consequently, profile statements can be certified before all individual structural signatures are resolved. Categorical certification experiments, a stochastic oscillator, signed profile reversals, and an ACIC-covariate benchmark examine this distinction and its extension under measured confounding. The same rarity family also provides a secondary targeting interpretation as an interpretable training-priority family under finite-sample, regularization, and capacity trade-offs; the experiments show no universal predictive advantage. The contribution is a rarity-indexed structural causal profile whose entire surface and signed contrasts can be certified simultaneously, together with upper and lower results that characterize its information limits.