Multi-hop retrieval-augmented generation requires a retriever to connect evidence distributed across documents while preserving a concise, faithful generation context. Existing indexes leave two complementary gaps: chunk-based RAG can break cross-passage evidence chains, whereas an unlabeled pairwise projection without generating-topic provenance cannot jointly preserve topic-level co-participation and per-occurrence entity descriptions. We propose STITCH-RAG, a hypergraph-based framework with three coupled components. First, a semi-merged topic hypergraph encodes multi-entity co-participation as topic-summary hyperedges while retaining per-chunk entity states linked by canonical-name equivalence. Second, spatio-temporal influence bridging propagation (STIBP) combines topic-space propagation with deterministic chunk-index linkage across name-equivalent states under frequency-adaptive decay. Third, continuous STIBP scores replace binary entity-match seeds in localized Personalized PageRank (PPR). We characterize the condition under which this prior assigns more PPR mass to ground-truth evidence than a binary prior. Under the reported protocol, STITCH-RAG attains the highest reported Contain-Acc and LLM-Acc point estimates among the compared methods on HotpotQA and 2WikiMultiHopQA, and higher Recall@8 than the methods included in the standardized retrieval comparison. Results on the mixed-domain benchmark remain auxiliary preference-based evidence because only LLM-judged accuracy is available.

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