Target-Coherent Risk Envelopes: Sharp Completion Bounds for Overlapping Forecast Adaptation

Rolling multi-horizon forecasters issue new predictions before earlier targets are observed. Forecasts from different origins can therefore refer to the same absolute target. Standard itemwise worst-case evaluation treats these repeated predictions as if their shared label could vary independently, allowing mutually incompatible outcomes and overstating the remaining excess of issued corrections. We introduce the Target-Coherent Forecast-Space Risk Envelope (TC-FSRE), a safety layer that groups pending loss terms by absolute target and optimizes over one legal label for each group. Under the stated completion model, this construction gives the sharp bound for a fixed pending set. For normalized absolute loss, we further characterize exactly when the itemwise bound is conservative: the gap is positive when corrections sharing a target require conflicting labels to attain their separate worst cases. Online, TC-FSRE projects each proposed correction onto the feasible action interval. If adaptation is later disabled, previously issued corrections remain within the cumulative-excess constraint as their labels arrive. Across 11 FreTS-H192 and PatchTST-H720 dataset–backbone units, target-coherent evaluation reduced the same-action bound by 77.23% on average and increased mean issued action by 0.18184. All 72 certificate paths remained valid in matched tests with TAFAS, DSOF, and COSA candidates. The guarantee concerns cumulative excess under the specified loss and completion model; candidate forecast quality remains a separate empirical question.