Math and science reasoning benchmarks rely on pass@k, the fraction of sampled chains that reach gold, as the canonical per-example difficulty signal. We show this proxy has a persistent blind spot on its hardest stratum: on the eight free-form math cells we test (GSM8K and MATH across four open-weight models), 10.3-22.9% of the examples that no sampling seed solves in six tries are instead solved at matched compute by a six-chain deterministic regime. These are greedy decoding plus five cheap residual-stream perturbations applied via activation grafting, while greedy alone solves at most 6% on these math cells. Recovery scales with the additional budget, across perturbations whose mechanistic distinctness we verify across all twelve cells (cross-kind fix-set Jaccard ≤ 0.47 in every setup. Activation grafting is used as an intervention on internal representations, not a decoding method; we use it purely as a diagnostic and diversification tool, and our recovered items show that the pass@k=0 stratum is structurally identifiable in the residual stream rather than that the unmodified model reaches them under ordinary inference.

Time series captioning, the task of describing time series in natural language, requires numeric and temporal reasoning, trend interpretation, and contextual understanding. Existing benchmarks, however, often rely on fully synthetic or generic captions, and typically neglect metadata and visual representations. We introduce CaTS-Bench, a comprehensive benchmark for Context-aware Time Series reasoning across 11 diverse domains, centered on a gold-standard evaluation set of 1746 human-rewritten captions that measure how effectively models translate numeric trends into immediately interpretable narratives. To address the scarcity of human-annotated data, we also propose a scalable pipeline for generating high-fidelity synthetic captions, the quality of which we validate. We evaluate leading Vision-Language Models on our benchmark, revealing that even proprietary models struggle to capture numeric nuances in temporal descriptions, while finetuning open-source models on synthetic data yields substantial performance gains. Finally, we release a diagnostic suite of 910 multiple-choice questions and use tailored numeric metrics to gauge time-series-specific reasoning capabilities, establishing CaTS-Bench as a reliable foundation for grounded, multimodal text generation in numeric domains.