When Present Climate Agreement Does Not Imply Future Agreement: Minimum Observations for Separating Incompatible Climate Futures

Climate models can agree with the same present-day evidence yet imply materially different futures because forcing, ocean heat uptake, warming patterns, and cloud feedback can compensate over the historical record. We ask a deliberately operational question: what is the least observational information needed to rule out every presently admissible climate world whose future is incompatible with another? We formulate future-targeted discrimination as an incompatibility-graph problem in which worlds are joined when their 100-year warming differs by at least 0.5 K, and observations cover edges only when they separate the corresponding worlds at a specified resolution. We implement the formulation in a reproducible pattern-aware two-layer benchmark and solve it exactly. Historical constraints retain 69 admissible worlds forming 1,044 future-incompatible pairs. At zero observational uncertainty, no scalar diagnostic is sufficient; the exact minimum is two observations, combining deep-ocean temperature with cloud-pattern sensitivity. Under finite uncertainty, the minimum rises to three observations by additionally requiring an SST-pattern diagnostic. At twice the nominal stress-test uncertainty, no available diagnostic subset guarantees separation. The 2 → 3 → ∞ transition shows that observational precision changes the information needed to exclude divergent futures. This methodological result links climate equifinality, decision-relevant divergence, and experiment design.