S2G-HAMC: Forecast-Calibrated Context Adaptation for Frozen Time-Series Foundation Models

Time-series foundation models (TSFMs) can forecast without task-specific retraining. However, every frozen forecaster still depends on the numerical context it receives. Deployment observations may not align with all coordinates in that context. The system must therefore map timestamped observations to a canonical context. We introduce S2G-HAMC, a forecast-calibrated context-adaptation framework for frozen TSFMs. Its S2G-Adapter builds a support-aware canonical context. It learns two calibration scalars on synthetic signals by using forecast loss from the frozen forecaster. It does not fit real benchmark targets. HAMC is a fixed robustness module. It evaluates nearby S2G context views and combines their forecasts across the prediction horizon. It does not change the backbone or add trainable parameters. S2G-HAMC improves 35/36 backbone–dataset pairs across 12 real-world datasets and three frozen forecasting families. Its mean Weighted Quantile Loss (WQL) gains are 7.62–8.60% over the corresponding validation-selected Linear interface. S2G alone yields 7.39–8.24% mean gains, and the complete system has a larger mean gain than S2G alone on all three backbones. The S2G-HAMC gain also increases as observation retention falls from 0.40 to 0.10. At the sparsest level, the gains reach 9.61–15.15%. With all adaptation choices fixed, the framework also improves quantile loss in 22/24 cells across three previously unused domains. These results show that S2G-HAMC can adapt frozen TSFMs through their numerical context. Across 12 datasets with 80% missing histories, the proposed adapter achieves the best mean Weighted Quantile Loss (WQL) rank among eight frozen/pretrained forecasting models and ranks first on 6 of 12 datasets. The same frozen adapter further transfers to held-out domains without retuning. These results demonstrate that explicitly modeling sampling geometry provides an effective forecast-oriented context interface for robust probabilistic forecasting under severe observation sparsity.