Retrieval-Augmented Generation (RAG) grounds large language model outputs in external evidence, but remains challenged on multi-hop question answering that requires long reasoning. Recent works scale RAG at inference time along two complementary dimensions: sequential depth for iterative refinement and parallel width for coverage expansion. However, naive scaling causes context contamination and scaling inefficiency, leading to diminishing or negative returns despite increased computation. To address these limitations, we propose SPARC-RAG, a framework that coordinates joint depth–width scaling around a unified context management mechanism—a shared global context state on which specialized control agents regulate parallel exploration and sequential stopping. To optimize scaling behavior, we further introduce a lightweight fine-tuning method with process-level verifiable preferences, which improves the efficiency of sequential scaling and effectiveness of parallel scaling. Across five single- and multi-hop QA benchmarks, SPARC-RAG outperforms the strongest reproduced baseline by an average of 3.8 F1 points at 7B and 9.8 at 32B, with the largest gains on challenging multi-hop tasks.

Temporal Knowledge Graphs (TKGs) represent dynamic facts as timestamped relations between entities. While Large Language Models (LLMs) show promise for TKG completion, current approaches typically apply generic pipelines (neighborhood sampling, supervised fine-tuning, uncalibrated inference) without task-specific adaptation to temporal relational reasoning. Through systematic analysis under unified evaluation, we reveal three key failure modes: (1) retrieval strategies miss multi-hop dependencies when target entities are not directly observed in history, (2) standard fine-tuning reinforces memorization over relational generalization, and (3) uncalibrated generation produces contextually implausible entities. We present RECIPE-TKG, a parameter-efficient framework that addresses each limitation through principled, task-specific design: rule-based multi-hop sampling for structural grounding, contrastive fine-tuning to shape relational compatibility, and test-time semantic filtering for contextual alignment. Experiments on four benchmarks show that RECIPE-TKG outperforms prior LLM-based methods across input regimes, achieving up to 22.4% relative improvement in Hits@10, with particularly strong gains when historical evidence is sparse or indirect.