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STITCH-RAG: Spatio-Temporal Influence Tracing over Topic Hypergraphs for Multi-Hop Retrieval-Augmented Generation
Haodong Yang, Mengzhu Chen, Jia Cai
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Abstract
Abstract: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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- Source: https://arxiv.org/abs/2609.34127v1
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STITCH-RAG: Spatio-Temporal Influence Tracing over Topic Hypergraphs for Multi-Hop Retrieval-Augmented Generation Haodong Yang Mengzhu Chen Jia Cai †thanks: Corresponding author Abstract 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. School of Statistics And Data Science, Guangdong University of Finance &\& Economics Guangzhou, China haodongyang@student.gdufe.edu.cn, mengzhuchen@student.gdufe.edu.cn, jiacai1999@gdufe.edu.cn 1 Introduction Standard dense-retrieval RAG partitions documents into fixed-size chunks and ranks them by query similarity. This representation can miss multi-hop chains that cross chunk or document boundaries. Structured RAG adds entity and relation indexes, but the published representations considered here do not jointly retain two forms of context. First, an unlabeled pairwise projection without a generating-topic identifier discards the topic that produced a multi-entity co-occurrence. This limitation does not apply to pairwise graphs augmented with relation labels, provenance, event identifiers, or equivalent higher-order attributes. Second, fully merging repeated entity mentions can erase chunk-specific roles, whereas treating every mention independently removes an explicit cross-chunk identity link. Both choices introduce retrieval noise when evidence depends on topic context and local entity state. Figure 1: Representation trade-offs for an example query about the birthplace of Film X’s director. (a) Chunk-based RAG can return locally similar but disconnected passages. (b) The illustrated unlabeled pairwise/full-merge representation retains the path through Alice Smith, but its single static entity node mixes the evidence-bearing birthplace context with unrelated contexts such as awards. The panel depicts one unlabeled full-merge representation, not all pairwise graphs. (c) STITCH-RAG preserves the two local Alice Smith states and links them by name equivalence, allowing query-conditioned propagation through topic hyperedges and across chunk-specific entity states. Figure 1 illustrates these representation trade-offs. In the controlled unlabeled pairwise/full-merge example, the graph retains a route from Film X to Canada, but a single Alice Smith node cannot distinguish the birthplace-bearing context from the award context. STITCH-RAG instead represents topic-level co-participation with hyperedges and retains chunk-specific entity states as separate nodes. An LLM extracts topic summaries as hyperedges and context-aware entity descriptions as nodes. The semi-merged hypergraph preserves those descriptions and links mentions with identical normalized canonical names. This link is a name-equivalence heuristic, not a ground-truth entity linker. Throughout the paper, spatial denotes topical co-participation within a hyperedge, whereas temporal denotes proximity in deterministic preprocessing indices. Across documents, this quantity is an index-proximity heuristic rather than a reading order, chronology, event time, or causal relation. At retrieval time, dense similarity activates entity nodes. Spatial bridging transfers influence to co-participants in the same topic hyperedge, whereas index-proximity bridging transfers influence across name-equivalent states through bounded frequency-adaptive decay and query-relevance gating. The resulting continuous scores are projected onto chunks and used as priors for localized approximate Personalized PageRank (PPR), replacing binary entity-match initialization with graded, context-aware diffusion. On HotpotQA, 2WikiMultiHopQA, and Mix, STITCH-RAG attains the highest reported Contain-Acc and LLM-Acc point estimates under the stated protocol. Recall@8 is compared only where standardized retrieval outputs are available. LLM-judged metrics remain auxiliary (Section 4.1). The novelty claim concerns the coupling of topic-preserving hyperedges, context-specific entity states, operational name-equivalence links, and continuous PPR initialization in one retrieval pipeline. No single component is claimed to be new in isolation. The main contributions are as follows: • A semi-merged hypergraph with a controlled recoverability characterization. The construction preserves per-chunk entity descriptions as distinct nodes while exposing canonical-name equivalence through an operational name-equivalence map. Proposition 2 shows that, among the three controlled representations considered here, semi-merging alone retains both properties required by the stated state-specific propagation rule. The controlled merge diagnostic reports a higher LLM-Acc point estimate for the implemented semi-merge variant than for the two implemented alternatives. Because retrieval metrics, structural compression, and run-level variances are unavailable for these variants, this is supporting, not conclusive, evidence. • Topic-space and index-proximity influence bridging with frequency-adaptive decay. STIBP operates before PPR through topic-hyperedge propagation and deterministic chunk-index linkage across name-equivalent entity states. The bounded decay f(Δt)=exp(−tanh(αΔt))f( t)= (- (α t)) uses α=nu/n¯α=n_u/ n to attenuate index-distant links more strongly for frequent names. Theorem 1 provides a one-sided bound for contributions propagated from one activated source. It neither models chronology nor characterizes the final scores after max aggregation over multiple sources. • Continuous influence priors with a conditional evidence-mass characterization. Existing PPR-based methods (Zhuang et al. 2025; Gutiérrez et al. 2024) commonly use binary entity-match initialization. STITCH-RAG instead derives a non-negative, normalized chunk prior from graded STIBP scores. Proposition 3 gives an exact PPR evidence-mass identity and a sufficient alignment condition under which this prior assigns more evidence mass than a binary prior. The strict binary-only diagnostic in Table 3 is not used to verify this condition because binary seed coverage, empty-match behavior, and prior-support size are not measured separately. The propositions and theorem characterize the chosen representation, decay, and PPR prior. They clarify the design assumptions but do not constitute end-to-end superiority guarantees. 2 Related Work Structured RAG methods differ primarily in index representation and query-signal propagation. Under their published representations, the methods compared here do not jointly retain topic-level co-participation, per-occurrence descriptions, and operational name-equivalence links. STITCH-RAG couples these properties to construct graded localized-PPR priors. It does not claim novelty for each component in isolation. Graph-based RAG. GraphRAG, LightRAG, NodeRAG, and LinearRAG instantiate entity–relation, dual-layer, heterogeneous, and name-matched PPR indexes, respectively (Edge et al. 2024; Guo et al. 2024; Xu et al. 2025; Zhuang et al. 2025). For an unlabeled pairwise projection, the generating-topic identity is unavailable at retrieval time (Proposition 1). This scope excludes provenance-enriched pairwise graphs. SubGraphRAG and GFM-RAG (Li et al. 2025; Luo et al. 2025b) prioritize local precision, whereas HippoRAG variants (Gutiérrez et al. 2024; Gutiérrez et al. 2025) apply global PPR with binary matching. STITCH-RAG preserves topic identity and linked local states, then uses their graded influence as the PPR prior (Proposition 3). Hypergraph-based RAG. HyperGraphRAG, Cog-RAG, and CogniRAG use relational, thematic, and causal hyperedges (Luo et al. 2025a; Hu et al. 2026a; He 2026). In the controlled merge constructions, full merging removes local states and no merging removes ϕφ, whereas semi-merging retains both ϕφ and ψ. Hyper-RAG, Cog-RAG, and IGMiRAG trade traversal, filtering, or routing cost against coverage (Feng et al. 2026; Hou et al. 2026). STITCH-RAG instead propagates only within the activated subgraph. Unlike the trained precedence model in OKH-RAG (Wu et al. 2026), its index-proximity decay is training-free and targets complex multi-hop queries, where structured retrieval is most useful (Xiang et al. 2025). Complementary directions. Adaptive routing, long-context retrieval, and granularity selection address complementary design choices (Yan et al. 2024; Jeong et al. 2024; Asai et al. 2024; Li et al. 2024a; Li et al. 2024b; Wu et al. 2024; Chen et al. 2024; Sarthi et al. 2024; Kim et al. 2024). STITCH-RAG targets boundary fragmentation in large or dynamic knowledge bases, where one-time indexing can be amortized across repeated queries (Ovadia et al. 2024; Balaguer et al. 2024). Appendix E provides detailed comparisons. 3 Method 3.1 Overview and Design Rationale STITCH-RAG implements a compress-then-amplify retrieval pipeline (Figure 2). During compression, documents are transformed into a semi-merged topic hypergraph ℋ=(,ℰ,ϕ,ψ)H=(V,E,φ,ψ) whose hyperedges are topic summaries and whose nodes are context-aware entity descriptions for individual chunks. During amplification, spatio-temporal influence bridging propagation (STIBP) identifies relevant entity-state pathways, and localized approximate Personalized PageRank (PPR) diffuses the resulting continuous scores over a chunk-level graph. Figure 2: Framework of STITCH-RAG: (1) document chunking; (2) semi-merged topic hypergraph construction, with topic-summary hyperedges and entity-description nodes linked by ϕφ; (3) STIBP through spatial and temporal channels; (4) influence-guided chunk scoring as a continuous PPR teleportation prior; and (5) top-k chunk retrieval for answer generation. Semi-merging is required because temporal bridging uses ϕφ, whereas query-conditioned activation requires local descriptions ψ. Proposition 2 formalizes this requirement for the controlled constructions. STIBP scores entity states on the hypergraph, and PPR diffuses those scores over the induced chunk graph. Table 3 tests their roles through controlled replacements. 3.2 Hypergraph Construction Phase Given document collection D, we produce chunks C=ckk=1NCC=\c_k\_k=1^N_C with at most cmaxc_ tokens each. An LLM with prompt pextp_ext processes each ckc_k to extract tuples gk,r=(ek,r,Vek,r)g_k,r=(e_k,r,V_e_k,r), where ek,re_k,r is a topic-summary hyperedge and Vek,rV_e_k,r is its entity set: =gk,r∣gk,r∈LLM(ck∣pext),ck∈C.G=\g_k,r g_k,r (c_k p_ext),\;c_k∈ C\. Each node v=(vname,vdes)v=(v^name,v^des) stores a canonical name and a chunk-specific description. The heuristic ϕ:→Σφ:V→ groups identical normalized names, while ψ:→ψ:V records local context; members of each group are ordered by deterministic preprocessing index. Chunks remain the retrieval targets. A topic hyperedge with m entities uses m incidence links rather than (m2) m2 pairwise links and retains its generating-topic identity (Proposition 1). Structural Advantage over Pairwise Projection For ℋ=(,ℰ)H=(V,E), the projection Π(ℋ) (H) connects u≠vu≠ v whenever u,v∈eu,v∈ e for some e. It discards the identity of the generating hyperedge. Proposition 1 therefore concerns retrieval from this unlabeled, provenance-free input, not pairwise graphs whose attributes recover the grouping (Appendix D). Proposition 1 (Non-identifiability of Pairwise Topic Projection). There exist two topic hypergraphs ℋ1H_1 and ℋ2H_2 such that Π(ℋ1)=Π(ℋ2) (H_1)= (H_2), but query-conditioned spatial propagation over ℋ1H_1 and ℋ2H_2 assigns different influence scores to the same target entities. Therefore, any retrieval rule whose input is limited to Π(ℋ) (H), without labels, provenance, or attributes that recover the generating hyperedges, cannot in general reproduce topic-selective propagation over those hyperedges. Recoverability Benefit of Semi-Merging The controlled constructions differ only in their exposure of ϕφ and retention of ψ (Definitions 2–3). For the propagation rule below, only semi-merging retains both; the result is a controlled recoverability comparison rather than a universal claim. Proposition 2 (Recoverability Separation of Semi-Merged Entity States). Let q be a query and let G=v1,…,vmG=\v_1,…,v_m\ be a name-equivalence group with ϕ(vi)=ϕ(vj)φ(v_i)=φ(v_j) for all i,ji,j. Suppose vs∈Gv_s∈ G satisfies Aq(vs)>δA_q(v_s)>δ, and vr∈Gv_r∈ G lies in a ground-truth evidence chunk with Aq(vr)≤δA_q(v_r)≤δ. Assume vrv_r is not reachable from vsv_s through any activated topic hyperedge, so that its only structural path from vsv_s is through name-equivalence temporal linkage. If Sq(evr)>0S_q(e_v_r)>0 and sim(q,cvr)>0sim(q,c_v_r)>0, then vrv_r receives no temporal influence under the no-merge construction ℋNH_N, which treats each mention as an independent node with no cross-chunk ϕφ; cannot be assigned state-specific influence under the full-merge construction ℋFH_F, which collapses each name-equivalence group into a single node; and receives strictly positive temporal influence under the semi-merged ℋH. 3.3 Retrieval Phase Given query q, retrieval has four stages: (1) dense-similarity activation of entity nodes and topic hyperedges; (2) STIBP over spatial and temporal channels to obtain graded entity-level influence; (3) projection of entity influence onto chunks with name-equivalence group-size weighting; and (4) localized PPR on the ϕφ-induced chunk graph, using the projected influence as a continuous teleportation prior. Initial Node and Hyperedge Activation We embed the query and entity descriptions with the same model and assign Aq(v)=sim(q,vdes),sim(q,vdes)>δ,0,otherwise,A_q(v)= casessim(q,v^des),&sim(q,v^des)>δ,\\ 0,&otherwise, cases with δ=0.5δ=0.5. Hyperedges use the unthresholded Sq(e)=sim(q,e)S_q(e)=sim(q,e) because spatial gating already attenuates low-relevance topics. Spatio-Temporal Influence Bridging Propagation STIBP maintains Aq(v)A_q(v), aspace(v)a^space(v), and atime(v)a^time(v) per node; within each propagated channel, it retains the maximum source value. Spatial bridging. For activated u∈eu∈ e and each v∈Ve∖uv∈ V_e \u\: aspace(v)=Aq(u)⋅Sq(e).a^space(v)=A_q(u)· S_q(e). This update requires both source activation and topic relevance. Temporal (index-proximity) bridging. For the name-equivalence group Vu∗=v∈∣ϕ(v)=ϕ(u)V_u^*=\v φ(v)=φ(u)\ of activated u, set α=nu/n¯α=n_u/ n where nu=|Vu∗|n_u=|V_u^*| and n¯ n is the corpus-wide average group size. Here tvt_v denotes the deterministic preprocessing index; across documents, the resulting distance is order-dependent index proximity rather than chronology. For each v∈Vu∗∖uv∈ V_u^* \u\ with Δt=|tu−tv| t=|t_u-t_v|, define the contribution proposed by source u as autime(v)=Aq(u)⋅Sq(ev)⋅exp(−tanh(αΔt))⋅sim(q,cv).a^time_u(v)=A_q(u)· S_q(e_v)· (- (α t))·sim(q,c_v). Here eve_v denotes a hyperedge containing v. When v belongs to several hyperedges, Sq(ev)S_q(e_v) stands for maxe∋vSq(e) _e vS_q(e), matching the max-aggregation rule above. With q=u:Aq(u)>0A_q=\u:A_q(u)>0\, the stored temporal channel is atime(v)=max(0,maxu∈q:u≠v,ϕ(u)=ϕ(v)autime(v)).a^time(v)= \! (0, _ subarraycu _q:\,u≠ v,\\ φ(u)=φ(v) subarraya^time_u(v) ). The decay function f(Δt)=exp(−tanh(αΔt))f( t)= (- (α t)) lies in (e−1,1](e^-1,1]: it retains nonzero mass for distant evidence while attenuating it. Because α∝nuα n_u, distant states of frequent names receive stronger attenuation (Table 9, Appendix C). The final entity influence aggregates all three channels: a(v)=mean(Aq(v),aspace(v),atime(v)).a(v)=mean (A_q(v),\,a^space(v),\,a^time(v) ). Mean aggregation weights the three channels equally and induces the same ranking as summation because every node has all three channels. Per-Source Analysis of Frequency-adaptive STIBP The following per-source result characterizes bounded decay under explicit signal–noise assumptions. It is not an end-to-end retrieval guarantee. Theorem 1 (Per-Source Lower-Bound Separation under Frequency-Adaptive Temporal Decay). Let u be an activated entity state with Aq(u)=a>0A_q(u)=a>0 and name-equivalence group Vu∗V_u^*. For each v∈Vu∗∖uv∈ V_u^* \u\, let Δv=|tu−tv| _v=|t_u-t_v| and gv=Sq(ev)sim(q,cv)g_v=S_q(e_v)sim(q,c_v). Let ℛR and N be nonempty disjoint subsets of Vu∗∖uV_u^* \u\ satisfying gr≥βg_r≥β for all r∈ℛr , 0<gn≤ϵ0<g_n≤ε and Δn≥τ _n≥τ for all n∈n , with β>ϵ>0β>ε>0 and τ>0τ>0. With α=nu/n¯α=n_u/ n, where nu=|Vu∗|n_u=|V_u^*|: maxr∈ℛautime(r)∑n∈autime(n)≥β||ϵexp(tanh(ατ)−1). _r a^time_u(r) _n a^time_u(n)≥ β|N|ε ( (ατ)-1 ). For fixed ℛR, N, β, ϵε, τ, and n¯ n, the right-hand side is non-decreasing in α. The bound excludes final max aggregation and end-to-end retrieval. It also permits over-suppression of distant relevant states. Chunk Score Projection and Localized Approximate PPR STIBP scores are projected onto chunks and diffused on a ϕφ-derived chunk graph without further LLM calls. Let CqC_q contain direct ANN candidates and chunks incident to nonzero-influence states; projection and PPR are restricted to this query-induced set. Entity influence is projected onto chunks by Score(c)=∑v∈(c)a(v)⋅ln(1+Nv), Score(c)= _v (c)a(v)· (1+N_v), where Nv=|w∈∣ϕ(w)=ϕ(v)|N_v=|\w φ(w)=φ(v)\|. We form the non-negative prior score I~(c)=λmax0,sim(q,c)+ln(1+Score(c)), I(c)=λ \0,sim(q,c)\+ (1+ Score(c)), and normalize it over CqC_q as pST(c)=I~(c)/∑z∈CqI~(z),if ∑zI~(z)>0,1/|Cq|,otherwise.p_ST(c)= cases I(c)/ _z∈ C_q I(z),&if _z I(z)>0,\\ 1/|C_q|,&otherwise. cases The uniform fallback handles an all-zero query; λ=0.3λ=0.3 is selected as described in Section 4.4. The chunk graph connects chunks sharing a name-equivalent entity: ℬ(c)=c′∣c′≠c,∃u∈(c),v∈(c′):ϕ(u)=ϕ(v).B(c)=\c c ≠ c,\;∃ u (c),v (c ):φ(u)=φ(v)\. Let P be the column-normalized transition matrix, with Pc′c′=1P_c c =1 for dangling chunks. With d=0.85d=0.85, the PPR iteration is π(t)=(1−d)pST+dPπ(t−1),π(0)=pST,π^(t)=(1-d)p_ST+dPπ^(t-1), π^(0)=p_ST, We iterate until maxc|π(t)(c)−π(t−1)(c)|<10−6 _c|π^(t)(c)-π^(t-1)(c)|<10^-6 and pass the top-k chunks ranked by π(T)π^(T) to the generator. The following identity supports the design. Its sufficient alignment condition is not independently verified. Proposition 3 (Discounted Evidence-Mass Identity under Prior Alignment). Let pSTp_ST be the normalized chunk prior induced by STIBP and let pBp_B be a normalized binary entity-match prior. For a ground-truth evidence set ℛR, define its discounted evidence-reachability footprint as hℛ=(1−d)∑ℓ=0∞dℓ(Pℓ)⊤ℛ,h_R=(1-d) _ =0^∞d (P ) 1_R, where P is the column-stochastic transition matrix of the query-induced chunk graph. The evidence-mass difference is exactly Mℛ(pST)−Mℛ(pB)=hℛ⊤(pST−pB).M_R(p_ST)-M_R(p_B)=h_R (p_ST-p_B). Consequently, if hℛ⊤(pST−pB)≥γ>0h_R (p_ST-p_B)≥γ>0, then Mℛ(pST)≥Mℛ(pB)+γ,M_R(p_ST)≥ M_R(p_B)+γ, where Mℛ(p)=ℛ⊤π(p)M_R(p)=1_R π(p) denotes the PPR evidence mass assigned to ℛR under prior p. Here hℛ(c)h_R(c) is the discounted forward-walk reachability from c to the evidence set. The binary diagnostic does not verify the alignment condition because reachability, seed coverage, empty matches, and support size are unmeasured (Appendix D). Symbolic indexing requires O(NC+NV+NE+M+∑gnglogng)O(N_C+N_V+N_E+M+ _gn_g n_g) time and linear storage. After candidate formation, STIBP and PPR scale with activated structures; Appendix B.1 gives the full online-complexity expression. 4 Experiments We evaluate STITCH-RAG along four axes: end-to-end answer accuracy (RQ1), answer quality beyond correctness (RQ2), module-level causality (RQ3), and computational efficiency (RQ4). 4.1 Experimental Setup Datasets We use three datasets covering structured multi-hop QA and open-ended domain-specific questions. For HotpotQA (Yang et al. 2018) and 2WikiMultiHopQA (Ho et al. 2020), we follow the HippoRAG (Gutiérrez et al. 2024) protocol and draw a stratified sample of 1,000 questions per dataset (composition in Appendix A). The sampled questions are fixed across methods. We report three repeated end-to-end runs, not three resampled datasets; at temperature zero, residual variation can arise from API and extraction-service nondeterminism. Mix contains 512 open-ended questions and serves as an exploratory cross-domain evaluation. Because Mix lacks supporting-fact annotations and reports only LLM-Acc, it is not an independent objective test of generalization. Baselines The baselines span the main RAG design choices: zero-shot generation and dense-retrieval RAG as lower bounds; LightRAG (Guo et al. 2024) for relation extraction; LinearRAG (Zhuang et al. 2025) as the closest structural predecessor, using PPR with binary entity-match initialization over a flat entity graph; HippoRAG (Gutiérrez et al. 2024) for PPR-based graph memory; and Cog-RAG (Hu et al. 2026a) and Hyper-RAG (Feng et al. 2026) as recent hypergraph-based methods. Metrics We report three end-to-end metrics: Contain-Acc, which tests whether the generated answer contains the reference substring; LLM-Acc, in which Qwen-Max judges answers generated by Qwen3.5-flash; and EM, in which a distilled answer must exactly match the reference. Because Qwen-Max and Qwen3.5-flash belong to the same model family, LLM-Acc can reflect same-family judge preference. Contain-Acc and EM do not use an LLM judge and therefore serve as controls. We treat Contain-Acc, EM, and Recall@8 as primary objective evidence on HotpotQA and 2Wiki, and treat LLM-Acc and pairwise quality dimensions as auxiliary preference-based evaluations. For retrieval, we report passage-level Recall@8(q)=|Gq∩Rq8|/|Gq|Recall@8(q)=|G_q∩ R_q^8|/|G_q| using supporting-fact annotations. This metric tests whether answer-quality differences are consistent with retrieval coverage, but does not isolate retrieval as the causal source. Mix lacks such annotations, so no retrieval metric is reported for it. Implementation Details All methods use text-embedding-v4 with 1024 dimensions and Qwen3.5-flash at temperature zero. On a 200-question HotpotQA development subset, replacing the original embeddings of LightRAG and LinearRAG changes LLM-Acc by at most 0.4 and 0.2 points, respectively. This check limits embedding sensitivity for these two baselines on that subset, but does not establish the same property for every baseline. STITCH-RAG uses k=8k=8, δ=0.5δ=0.5, and d=0.85d=0.85, selected on the same held-out set and fixed across datasets. All experiments run through the Alibaba Cloud API; every repeated run uses the same evaluation questions. 4.2 Generation Accuracy (RQ1) Table 1: Answer accuracy on HotpotQA, 2Wiki, and Mix. Best result per column bolded. Only STITCH-RAG was repeated end to end; its entries average three runs on the same fixed question samples, with all run-level standard deviations below 0.004. Baseline run-level variances are unavailable. The table therefore ranks reported point estimates but does not establish statistical superiority. Method HotpotQA 2Wiki Mix Contain-Acc LLM-Acc EM Contain-Acc LLM-Acc EM LLM-Acc Zero-shot 0.422 0.451 0.300 0.505 0.398 0.345 0.269 Standard-RAG 0.700 0.702 0.460 0.689 0.617 0.467 0.669 HippoRAG 0.690 0.835 0.609 0.555 0.575 0.476 0.823 Cog-RAG 0.822 0.843 0.562 0.768 0.700 0.554 0.831 Hyper-RAG 0.735 0.808 0.511 0.785 0.745 0.541 0.808 LightRAG 0.861 0.877 0.600 0.821 0.674 0.518 0.877 LinearRAG 0.745 0.887 0.649 0.810 0.850 0.688 0.762 STITCH-RAG 0.900 0.895 0.654 0.877 0.861 0.670 0.884 STITCH-RAG ranks first in Contain-Acc and LLM-Acc on every dataset in Table 1. Relative to the strongest per-dataset baseline, the Contain-Acc/LLM-Acc margins are 3.9/0.8 points on HotpotQA and 5.6/1.1 points on 2Wiki. The Mix LLM-Acc margin is 0.7 points. LinearRAG is the closest structural comparison, and STITCH-RAG exceeds it by 15.5 and 6.7 Contain-Acc points on HotpotQA and 2Wiki, respectively. These aggregate differences do not isolate the responsible component. LinearRAG has higher 2Wiki EM (0.688 versus 0.670); without answer-length statistics or error analysis, we report this as a limitation rather than attribute it to response verbosity. Contain-Acc and Recall@8 provide the strongest objective evidence. EM is mixed, and the smaller LLM-Acc margins remain auxiliary. Table 2: Passage-level Recall@8 on HotpotQA and 2Wiki, defined as |Gq∩Rq8|/|Gq||G_q∩ R_q^8|/|G_q| where GqG_q is the ground-truth supporting chunk set and Rq8R_q^8 is the top-8 retrieved set. Mix is excluded because supporting-fact annotations are unavailable. Only methods with publicly available retrieval outputs under the standardized embedding protocol are included. Method HotpotQA 2Wiki Standard-RAG 0.612 0.587 LightRAG 0.741 0.693 LinearRAG 0.723 0.712 STITCH-RAG 0.798 0.769 Among methods with standardized retrieval outputs, STITCH-RAG exceeds LinearRAG in Recall@8 by 7.5 points on HotpotQA and 5.7 points on 2Wiki. This pattern is consistent with broader retrieval coverage, but the comparison omits methods without standardized outputs and does not show that retrieval alone causes the answer-accuracy gains. The margins also match the mechanism in Proposition 3, though the experiment does not verify its alignment condition because γ is not measured per query. 4.3 Answer Quality Comparison (RQ2) We apply the LightRAG pairwise protocol as an auxiliary preference-based evaluation of comprehensiveness, diversity, and empowerment. STITCH-RAG exceeds the 50% win-rate line on most dataset–dimension pairs (Figure 3, Appendix C), with the largest margins in comprehensiveness and diversity on HotpotQA and 2Wiki, consistent with the Recall@8 results in Table 2. On Mix, LightRAG remains competitive in selected dimensions, plausibly because explicit relation extraction can better encode structured domain knowledge when topic-hyperedge boundaries are less distinct. Both rely on an LLM judge and remain exploratory. 4.4 Ablation Study (RQ3) Table 3: Ablation of STITCH-RAG (three-run LLM-Acc average). The upper block removes STIBP/PPR or uses dense retrieval; the lower block removes one STIBP channel or replaces continuous priors with binary initialization. Variant HotpotQA LLM-Acc 2Wiki LLM-Acc Mix LLM-Acc Full STITCH-RAG 0.895 0.861 0.884 w/o STIBP 0.823 0.707 0.800 w/o PPR 0.825 0.793 0.854 w/o all (dense retrieval) 0.761 0.684 0.672 w/o spatial bridging 0.838 0.742 0.814 w/o index-proximity bridging 0.840 0.748 0.815 Strict binary-only initialization diagnostic 0.459 0.365 0.469 Table 4: Efficiency and LLM-Acc on Mix. Indexing costs are one-time; query-stage tokens include answer generation and method-specific query-time LLM calls under identical hardware and API conditions. Method Time (s) Token Consumption LLM-Acc Indexing Retrieval Idx. Prompt Idx. Completion Query Prompt Query Completion HippoRAG 1706.91 39.56 1382281 1321272 55845.91 3774.76 0.823 Cog-RAG 19109.94 126.88 3082137 7988713 36840.47 13246.30 0.831 Hyper-RAG 70414.64 52.20 4652473 7264711 18557.08 5521.35 0.808 LightRAG 89882.40 75.87 6588007 8685853 29795.00 8148.52 0.877 LinearRAG 633.37 23.00 0 0 6395.72 261.50 0.762 STITCH-RAG 10384.41 31.12 1229660 14196127 4054.52 2558.72 0.884 Table 3 provides controlled evidence that STIBP and PPR contribute non-redundant gains: removing STIBP/PPR reduces HotpotQA LLM-Acc by 7.2/7.0 points and 2Wiki LLM-Acc by 15.4/6.8 points. The larger STIBP loss on 2Wiki is consistent with stronger cross-chunk entity-tracking demands. Under the fixed pipeline, semi-merging achieves higher point estimates than both controlled merge alternatives (Appendix C), although this diagnostic does not establish general optimality. The lower block shows that both bridging channels and frequency-adaptive decay are beneficial; adaptive decay reaches 0.884 on Mix, compared with 0.853 and 0.846 for fixed and logarithmic scaling. Each variant retains the remaining pipeline components and changes only the stated operation. Appendix C details the binary-initialization diagnostic and its controls, while Appendix A provides the extraction prompt and phase-level visualization. Hyperparameter Sensitivity Analysis We select δ=0.5δ=0.5, λ=0.3λ=0.3, and k=8k=8 on the HotpotQA development set and transfer them unchanged to 2Wiki and Mix. Appendix B.3 reports the complete sweeps; among the tested decay rules, adaptive α attains the highest reported Mix LLM-Acc. 4.5 Efficiency Analysis (RQ4) Table 4 pairs STITCH-RAG’s top Mix LLM-Acc with the second-lowest structural-retrieval latency. Its added cost occurs during one-time indexing of context-aware entity descriptions, whereas structural retrieval issues no LLM API calls. Appendix B.1 gives the component-level cost decomposition. 5 Conclusion STITCH-RAG couples topic-preserving hyperedges, semi-merged local entity states, frequency-adaptive STIBP, and continuous-prior PPR. Proposition 1 applies only to provenance-discarding pairwise inputs, and Proposition 2 compares three controlled merge constructions. The decay and PPR results characterize the proposed mechanisms; they are not end-to-end optimality guarantees. Under the reported protocol, STITCH-RAG attains the highest Contain-Acc and LLM-Acc point estimates in Table 1 and the highest Recall@8 in Table 2. The merge and binary diagnostics remain inconclusive because baseline variance and per-query alignment are unmeasured, 2Wiki EM is below LinearRAG, and the merge comparison does not establish a compression–relevance optimum. 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Huang Linearrag: linear graph retrieval augmented generation on large-scale corpora. arXiv preprint arXiv:2510.10114. Cited by: 3rd item, §2, §4.1, §E.1. Reproducibility Checklist This paper: • Includes a conceptual outline and/or pseudocode description of AI methods introduced (yes/partial/no/NA) yes • Clearly delineates statements that are opinions, hypothesis, and speculation from objective facts and results (yes/no) yes • Provides well-marked pedagogical references for less-familiar readers to gain background necessary to replicate the paper (yes/no) yes Does this paper make theoretical contributions? (yes/no) yes If yes, please complete the list below. • All assumptions and restrictions are stated clearly and formally. (yes/partial/no) yes • All novel claims are stated formally (e.g., in theorem statements). (yes/partial/no) yes • Proofs of all novel claims are included. (yes/partial/no) yes • Proof sketches or intuitions are given for complex and/or novel results. (yes/partial/no) yes • Appropriate citations to theoretical tools used are given. (yes/partial/no) yes • All theoretical claims are demonstrated empirically to hold. (yes/partial/no/NA) partial • All experimental code used to eliminate or disprove claims is included. (yes/no/NA) yes Does this paper rely on one or more datasets? (yes/no) yes If yes, please complete the list below. • A motivation is given for why the experiments are conducted on the selected datasets (yes/partial/no/NA) yes • All novel datasets introduced in this paper are included in a data appendix. (yes/partial/no/NA) yes • All novel datasets introduced in this paper will be made publicly available upon publication of the paper with a license that allows free usage for research purposes. (yes/partial/no/NA) yes • All datasets drawn from the existing literature (potentially including authors’ own previously published work) are accompanied by appropriate citations. (yes/no/NA) yes • All datasets drawn from the existing literature (potentially including authors’ own previously published work) are publicly available. (yes/partial/no/NA) yes • All datasets that are not publicly available are described in detail, with explanation why publicly available alternatives are not scientifically satisficing. (yes/partial/no/NA) NA Does this paper include computational experiments? (yes/no) yes If yes, please complete the list below. • This paper states the number and range of values tried per (hyper-) parameter during development of the paper, along with the criterion used for selecting the final parameter setting. (yes/partial/no/NA) yes • Any code required for pre-processing data is included in the appendix. (yes/partial/no) no • All source code required for conducting and analyzing the experiments is included in a code appendix. (yes/partial/no) no • All source code required for conducting and analyzing the experiments will be made publicly available upon publication of the paper with a license that allows free usage for research purposes. (yes/partial/no) yes • All source code implementing new methods have comments detailing the implementation, with references to the paper where each step comes from. (yes/partial/no) yes • If an algorithm depends on randomness, then the method used for setting seeds is described in a way sufficient to allow replication of results. (yes/partial/no/NA) NA • This paper specifies the computing infrastructure used for running experiments (hardware and software), including GPU/CPU models; amount of memory; operating system; names and versions of relevant software libraries and frameworks. (yes/partial/no) partial • This paper formally describes evaluation metrics used and explains the motivation for choosing these metrics. (yes/partial/no) yes • This paper states the number of algorithm runs used to compute each reported result. (yes/no) no • Analysis of experiments goes beyond single-dimensional summaries of performance (e.g., average; median) to include measures of variation, confidence, or other distributional information. (yes/no) yes • The significance of any improvement or decrease in performance is judged using appropriate statistical tests (e.g., Wilcoxon signed-rank). (yes/partial/no) no • This paper lists all final (hyper-)parameters used for each model/algorithm in the paper’s experiments. (yes/partial/no/NA) yes Appendices A Reproducibility and Implementation Details Dataset sample composition. The stratified 1,000-question samples contain approximately 520 bridge and 480 comparison questions in HotpotQA, and approximately 280 comparison, 250 inference, 240 compositional, and 230 bridge questions in 2Wiki. Mix is reported only in aggregate, so its results are exploratory. A complete release should document domain counts, corpus and chunk sizes, question and reference-answer provenance, construction and deduplication procedures, train/test isolation checks, and data licenses. Reproducibility of baselines. For LightRAG11 1 https://github.com/HKUDS/LightRAG, Cog-RAG22 2 https://github.com/haoohu/Cog-RAG, Hyper-RAG33 3 https://github.com/iMoonLab/Hyper-RAG, and LinearRAG44 4 https://github.com/DEEP-PolyU/LinearRAG, we use the authors’ released implementations and replace only the embedding model with text-embedding-v4 to standardize vector representations. Baseline verification protocol. For Cog-RAG and Hyper-RAG, we first reproduce the reported results under the original evaluation settings, including the default embedding models and generation backbones. All reproduced metrics fall within 1.5 percentage points of the reported values; the remaining deviations may reflect API-version or random-seed differences. We then rerun every baseline under the standardized protocol in Section 4.1. Reviewer access and verification. The supplementary material provides frozen code snapshots with written sharing permission, checksummed Docker images with pinned dependencies, retrieved chunks and generated answers for all 1,000 questions on each dataset, and a comparison log for the reproduction check. The anonymous repository includes wrapper scripts, evaluation scripts, and VERIFICATION.md with checksums and expected metric outputs. Complete extraction prompt pextp_ext. The prompt below extracts topic summaries and chunk-conditioned entity descriptions. It is applied independently to each chunk and receives no cross-chunk context. Listing 1: Extraction prompt pextp_ext ⬇ 1 ---Goal--- 2 Extract the knowledge expressed in the task text. Divide the text into self-contained knowledge segments. For each segment, return: 3 - reference: the supporting text span. 4 - knowledge: one self-contained sentence describing the segment. 5 - entities: an object mapping each entity’s complete name to its context-specific description. 6 Notes: 7 - Do not omit information stated in the original text. 8 - Each knowledge sentence must be understandable without additional context. 9 - Return only valid JSON that can be parsed by JSON.parse(). 10 - If an entity description is absent or only repeats the name, use an empty string (""). 11 - Ground every description in the task text. 12 - Use the complete entity name as the key and include that complete name in its non-empty description. 13 14 ---Output JSON format--- 15 Return one or more objects in a JSON array following this structure: 16 [ 17 18 "reference": "Original supporting text", 19 "knowledge": "A self-contained knowledge statement.", 20 "entities": 21 "Entity 1": "Entity 1 is described in the task text.", 22 "Entity 2": "Entity 2 is described in the task text." 23 24 25 ] 26 27 ###################### 28 Task text: 29 content 30 Output: Each extracted knowledge segment creates one topic-summary hyperedge ek,re_k,r, whose text is the segment’s knowledge sentence. Each entry in its entities field creates an incident entity-state node v=(vname,vdes)v=(v^name,v^des). Extraction convention summary. The extraction procedure uses three conventions. First, entity boundaries follow the maximal-noun-phrase rule: New York City is one entity rather than three tokens. Second, each topic represents one coherent claim or narrative thread; a chunk covering a person’s early career and later achievements should yield two topic segments. Third, entity descriptions are grounded in the current chunk, so repeated entities receive role-specific local descriptions. B Algorithmic Details Algorithm 1 STITCH-RAG: Retrieval Pipeline 0: Query q; semi-merged hypergraph ℋ=(,ℰ,ϕ,ψ)H=(V,E,φ,ψ); chunk set C; parameters δ, λ, d, k; ANN candidate budgets KV,KE,KCK_V,K_E,K_C 0: Top-k retrieved chunks CqkC_q^k 1: (Vq0,Eq0,Cq0)←ANN(q,,ℰ,C,KV,KE,KC)(V_q^0,E_q^0,C_q^0) (q;V,E,C,K_V,K_E,K_C) 2: for each entity node v∈Vq0v∈V_q^0 do 3: Aq(v)←sim(q,vdes)⋅[sim(q,vdes)>δ]A_q(v) (q,v^des)·1[sim(q,v^des)>δ] 4: end for 5: for each hyperedge e∈Eq0∪e:e∋v,v∈Vq0e∈E_q^0∪\e:e v,\ v∈ V_q^0\ do 6: Sq(e)←sim(q,e)S_q(e) (q,e) 7: end for 8: Initialize aspace(v)←0a^space(v)← 0, atime(v)←0a^time(v)← 0 for all v 9: for each activated node u with Aq(u)>0A_q(u)>0 do 10: for each hyperedge e∋ue u do 11: for each v∈Ve∖uv∈ V_e \u\ do 12: aspace(v)←max(aspace(v),Aq(u)⋅Sq(e))a^space(v)← (a^space(v),\;A_q(u)· S_q(e) ) 13: end for 14: end for 15: Vu∗←v∈∣ϕ(v)=ϕ(u)V_u^*←\v φ(v)=φ(u)\ name-equivalence group 16: α←|Vu∗|/n¯α←|V_u^*|/ n frequency-adaptive decay rate 17: for each v∈Vu∗∖uv∈ V_u^* \u\ do 18: Δt←|tu−tv| t←|t_u-t_v| 19: atime(v)←max(atime(v),Aq(u)⋅Sq(ev)⋅exp(−tanh(αΔt))⋅sim(q,cv))a^time(v)← (a^time(v),\;A_q(u)· S_q(e_v)· (- (α t))·sim(q,c_v) ) 20: end for 21: end for 22: a(v)←mean(Aq(v),aspace(v),atime(v))a(v) (A_q(v),\,a^space(v),\,a^time(v) ) for all v 23: Cq←Cq0∪cv:a(v)>0C_q← C_q^0∪\c_v:a(v)>0\ 24: for each chunk c∈Cqc∈C_q do 25: Score(c)←∑v∈(c)a(v)⋅ln(1+Nv) Score(c)← _v (c)a(v)· (1+N_v) 26: I~(c)←λmax0,sim(q,c)+ln(1+Score(c)) I(c)←λ \0,sim(q,c)\+ (1+ Score(c)) 27: end for 28: pST(c)←I~(c)/∑z∈CqI~(z)p_ST(c)← I(c)/ _z∈ C_q I(z) if the sum is positive; otherwise pST(c)←1/|Cq|p_ST(c)← 1/|C_q| 29: Build chunk graph: ℬ(c)←c′∣∃u∈(c),v∈(c′) s.t. ϕ(u)=ϕ(v)B(c)←\c ∃\,u (c),\,v (c ) s.t. φ(u)=φ(v)\ 30: Column-normalize the adjacency as P; set Pcc=1P_c=1 when ℬ(c)=∅B(c)= 31: π(0)←pSTπ^(0)← p_ST 32: repeat 33: for each chunk c∈Cqc∈ C_q do 34: π(t)(c)←(1−d)pST(c)+d∑c′∈CqPcc′π(t−1)(c′)π^(t)(c)←(1-d)p_ST(c)+d _c ∈ C_qP_c π^(t-1)(c ) 35: end for 36: until maxc|π(t)(c)−π(t−1)(c)|<10−6 _c|π^(t)(c)-π^(t-1)(c)|<10^-6 37: Cqk←top-kC_q^k -k chunks by π(T)(c)π^(T)(c) 38: return CqkC_q^k Algorithm 2 STITCH-RAG: Offline Hypergraph Construction 0: Document collection D; max chunk size cmaxc_ ; extraction prompt pextp_ext 0: Semi-merged hypergraph ℋ=(,ℰ,ϕ,ψ)H=(V,E,φ,ψ) 1: Split D into chunks C=ckk=1NCC=\c_k\_k=1^N_C with |ck|≤cmax|c_k|≤ c_ 2: for each chunk ck∈Cc_k∈ C do 3: gk,rr←LLM(ck∣pext)\g_k,r\_r (c_k p_ext) extract (topic, entities) tuples 4: for each tuple gk,r=(ek,r,Vek,r)g_k,r=(e_k,r,V_e_k,r) do 5: Add hyperedge ek,re_k,r to ℰE with topic summary text 6: for each entity (vname,vdes)∈Vek,r(v^name,v^des)∈ V_e_k,r do 7: Create node v with ϕ(v)←vnameφ(v)← v^name, ψ(v)←vdesψ(v)← v^des 8: Add v to V; record incidence (v,ek,r)(v,e_k,r) and chunk membership (v,ck)(v,c_k) 9: end for 10: end for 11: end for 12: Group nodes by canonical name: Gs=v∣ϕ(v)=ss∈Σ\G_s=\v φ(v)=s\\_s∈ 13: Sort nodes within each group by the deterministic preprocessing index tvt_v 14: Embed all entity descriptions vdes\v^des\, topic summaries e\e\, and chunks ck\c_k\ 15: return ℋ=(,ℰ,ϕ,ψ)H=(V,E,φ,ψ) B.1 Complexity Analysis Let NCN_C, NV=||N_V=|V|, NE=|ℰ|N_E=|E|, and M=∑e∈ℰ|e|M= _e |e| denote the numbers of chunks, entity-state nodes, topic hyperedges, and entity–hyperedge incidence links. The symbolic complexities exclude LLM inference and embedding execution, which are model-dependent and not assumed to be shared across systems. Table 4 reports measured time and token consumption separately. Offline indexing. Topic incidence storage requires O(M)O(M) links; ϕφ-based grouping requires O(NV)O(N_V) hash operations; within-group sorting by chunk index requires O(∑gnglogng)O( _gn_g n_g) where ngn_g is the size of group g. The total symbolic indexing cost is O(NC+NV+NE+M+∑gnglogng),O\! (N_C+N_V+N_E+M+ _gn_g n_g ), and storage is O(NC+NV+NE+M)O(N_C+N_V+N_E+M). All indexing costs are incurred once. Online retrieval. Let AqA_q, ℰqE_q, and BqB_q denote the activated entity-state set, incident topic hyperedges, and edge set of the query-induced chunk graph. Let Tcand(NV,NE,NC)T_cand(N_V,N_E,N_C) denote candidate-generation cost over node, hyperedge, and chunk vector indexes. Under exact search, it is O((NV+NE+NC)demb)O((N_V+N_E+N_C)d_emb); ANN cost depends on the selected index and approximation parameters. Spatial propagation costs O(∑e∈ℰq|e|)O( _e _q|e|), temporal propagation costs O(∑u∈Aq|Vu∗|)O( _u∈ A_q|V_u^*|) without materializing pairwise links, and localized PPR costs O(T|Bq|)O(T|B_q|) for T iterations. The total online cost is O(CLOSE O\! ( Tcand(NV,NE,NC)+∑e∈ℰq|e| T_cand(N_V,N_E,N_C)+ _e _q|e| +∑u∈Aq|Vu∗|+T|Bq|). + _u∈ A_q|V_u^*|+T|B_q| ). Candidate generation remains corpus-dependent, whereas propagation depends on the activated subgraph. Table 4 reports measured latency rather than extrapolating end-to-end scaling from propagation terms alone. B.2 Qualitative Compression–Context Interpretation of Semi-Merging The three controlled merge strategies trade compact identity representation against local-context retention. Full merging collapses name-equivalent mentions and removes per-chunk descriptions. No merging retains each local description but exposes no cross-chunk name-equivalence relation. Semi-merging retains distinct local states while exposing their operational name equivalence to retrieval. This interpretation motivates the representation design but is not an information-bottleneck result: the paper neither defines nor estimates mutual information for the three constructions. Table 8 is an answer-level controlled comparison and does not directly measure compression or retained task information. B.3 Complete Hyperparameter Sensitivity Results Tables 5 and 6 report post-hoc transfer sensitivity of the activation threshold δ and balance parameter λ on Mix. Bold values were chosen on the HotpotQA development set, not on Mix. Table 7 reports the top-k sweep on that 200-question development set. Each sweep fixes all other hyperparameters and the retrieval pipeline at their defaults (k=8k=8, d=0.85d=0.85, adaptive α=nu/n¯α=n_u/ n). Table 5: Post-hoc Mix LLM-Acc sensitivity to δ. The bold row denotes the value preselected on HotpotQA, not a value selected on Mix. All other hyperparameters are fixed. δ Mix 0.3 0.861 0.4 0.815 0.5 0.884 0.6 0.838 0.7 0.861 Table 6: Post-hoc Mix LLM-Acc sensitivity to λ. The bold row denotes the value preselected on HotpotQA, not a value selected on Mix. All other hyperparameters are fixed. λ Mix 0.1 0.823 0.3 0.884 0.5 0.846 0.7 0.846 0.9 0.861 Table 7: LLM-Acc under varying top-k retrieval count on the 200-question HotpotQA development set. The bold column denotes the selected value. All other hyperparameters are fixed at their defaults. k 5 6 7 8 9 10 LLM-Acc 0.823 0.853 0.861 0.884 0.869 0.876 C Additional Experimental Results This appendix contains the phase-level ablation visualization, pairwise answer-quality comparison, merge-strategy diagnostic, and temporal-decay comparison cited in the main text. Figure 3: Pairwise answer-quality win rates of STITCH-RAG against five baselines on HotpotQA, 2Wiki, and Mix, judged by Qwen-Max on comprehensiveness (coverage of relevant details), diversity (variety of useful perspectives), and empowerment (utility for informed judgment). The dashed circle marks the 50% win-rate line. Values outside it favor STITCH-RAG. Table 8: LLM-Acc point estimates for one implementation of each merge strategy under a fixed retrieval pipeline. The diagnostic does not evaluate run-level variance, retrieval recall, graph compression, statistical significance, or all possible implementations of the three strategies. Strategy HotpotQA 2Wiki Mix Full-Merge 0.873 0.839 0.807 Semi-Merge 0.895 0.861 0.884 No-Merge 0.879 0.844 0.831 Table 9: LLM-Acc on Mix under three temporal decay functions, with all other pipeline components held fixed (same hypergraph, same PPR initialization, same α=nu/n¯α=n_u/ n). Decay Function LLM-Acc exp(−αΔt) (-α t) (pure exponential) 0.853 σ(−αΔt+b)σ(-α t+b) (sigmoid gate) 0.815 exp(−tanh(αΔt)) (- (α t)) (ours) 0.884 D Proofs of Main Results This appendix states the definitions used by Propositions 1 and 2, then provides all proofs. Definition 1 (Pairwise Topic Projection). Given a topic hypergraph ℋ=(,ℰ)H=(V,E), its pairwise projection is the graph Π(ℋ) (H) =(,ℰ2), =(V,E_2), ℰ2 _2 =u,v∣u≠v,∃e∈ℰs.t.u,v∈e. = \\u,v\ u≠ v,\;∃ e \ s.t.\ u,v∈ e \. The projection retains pairwise co-occurrence but discards the identity of the topic hyperedge that generated each pair. Definition 2 (Semi-Merged Hypergraph). Let ℋ=(,ℰ,ϕ,ψ)H=(V,E,φ,ψ) denote a semi-merged hypergraph, where V is the set of entity nodes, ℰE is the set of hyperedges, ϕ:→Σφ:V→ maps each node to an entity name in name space Σ , and ψ:→ψ:V maps each node to a context-specific description in description space D. Two nodes vi,vj∈v_i,v_j satisfy ϕ(vi)=ϕ(vj)φ(v_i)=φ(v_j) when their normalized canonical-name strings are identical. This operational relation approximates, but does not guarantee, real-world co-reference: aliases can produce false splits, whereas homonyms can produce false links. The equivalence classes under ϕφ are called name-equivalence groups. Definition 3 (Full-Merge and No-Merge Hypergraphs). A full-merge hypergraph ℋFH_F collapses all nodes within each name-equivalence group into a single node and discards per-chunk descriptions. A no-merge hypergraph ℋNH_N treats every extracted entity mention as an independent node with no cross-chunk identity linkage; equivalently, ℋNH_N does not define a map ϕφ across chunks. Proof of Proposition 1. We construct two topic hypergraphs with identical pairwise projections and exhibit a query under which topic-selective spatial propagation produces different influence assignments, establishing the non-identifiability claim. Let the entity set be =a,b,c,dV=\a,b,c,d\. Consider two hypergraphs: ℋ1=(,a,b,c,a,b,d,a,c,d,b,c,d)H_1= (V,\\a,b,c\,\a,b,d\,\a,c,d\,\b,c,d\\ ) and ℋ2=(,a,b,c,d).H_2= (V,\\a,b,c,d\\ ). Every pair from a,b,c,d\a,b,c,d\ co-occurs in at least one hyperedge of ℋ1H_1 (each triple contains all (32)=3 32=3 pairs, and the four triples together cover all (42)=6 42=6 pairs), and every pair co-occurs in the single hyperedge of ℋ2H_2. Hence both hypergraphs project to the complete graph on four vertices: Π(ℋ1)=Π(ℋ2)=K4. (H_1)= (H_2)=K_4. Fix a query q that is semantically relevant only to the topic a,b,c\a,b,c\, and let Aq(a)=1A_q(a)=1 be the only activated source node. In ℋ1H_1, assign topic relevance scores Sq(a,b,c)=1,Sq(e)=0for all other e∈ℰ1.S_q(\a,b,c\)=1, S_q(e)=0 all other e _1. The spatial bridging formula aspace(v)=Aq(a)⋅Sq(e)a^space(v)=A_q(a)· S_q(e) for each v∈Ve∖av∈ V_e \a\ gives aspace(b)=1,aspace(c)=1,aspace(d)=0,a^space(b)=1, a^space(c)=1, a^space(d)=0, since d does not appear in any hyperedge e with Sq(e)>0S_q(e)>0 under ℋ1H_1. In ℋ2H_2, the only available hyperedge is a,b,c,d\a,b,c,d\. Two exhaustive cases arise. If Sq(a,b,c,d)>0S_q(\a,b,c,d\)>0, spatial bridging from a assigns the same positive score Aq(a)⋅Sq(a,b,c,d)A_q(a)· S_q(\a,b,c,d\) to each of b, c, and d, so d receives positive influence. If Sq(a,b,c,d)=0S_q(\a,b,c,d\)=0, no influence propagates at all, so b and c receive zero influence. In neither case can ℋ2H_2 reproduce the selective outcome aspace(b)>0a^space(b)>0, aspace(c)>0a^space(c)>0, aspace(d)=0a^space(d)=0. Since Π(ℋ1)=Π(ℋ2) (H_1)= (H_2), any retrieval rule whose input is restricted to Π(ℋ) (H) must produce identical outputs on ℋ1H_1 and ℋ2H_2, yet the propagation outcomes differ for the query q constructed above. Therefore, no retrieval rule defined solely on the pairwise projection can, in general, reproduce topic-selective propagation over hyperedges. ∎ Proof of Proposition 2. We verify the influence received by vrv_r under each of the three constructions, holding q, G, and all activation scores fixed throughout. The assumptions in force are: Aq(vs)>δA_q(v_s)>δ; Aq(vr)≤δA_q(v_r)≤δ, so after thresholding Aq(vr)=0A_q(v_r)=0; vrv_r is not reachable from vsv_s through any activated topic hyperedge; Sq(evr)>0S_q(e_v_r)>0 for some hyperedge evre_v_r containing vrv_r; and sim(q,cvr)>0sim(q,c_v_r)>0. No-merge hypergraph ℋNH_N. In ℋNH_N, the map ϕφ is not defined across chunks, so every entity mention is an independent node. The corresponding name-equivalence group of vsv_s under the no-merge construction reduces to the singleton Vvs∗=vsV_v_s^*=\v_s\, so the temporal bridging loop does not visit vrv_r. By hypothesis, vrv_r is not reachable from vsv_s through any activated topic hyperedge, so aℋNspace(vr)=0a^space_H_N(v_r)=0. Combined with Aq(vr)=0A_q(v_r)=0, the mean aggregation gives aℋN(vr)=0a_H_N(v_r)=0. The evidence chunk cvrc_v_r therefore receives zero projected influence from vrv_r and is structurally unreachable from vsv_s under ℋNH_N. Full-merge hypergraph ℋFH_F. All nodes in G are collapsed into a single representative v¯=merge(v1,…,vm) v=merge(v_1,…,v_m) with aggregated description v¯des v^des and membership in the union of all original hyperedges and chunks. Two cases arise. (2a) If Aq(v¯)=sim(q,v¯des)>δA_q( v)=sim(q, v^des)>δ, then v¯ v is activated. Every chunk containing any original member of G receives the same influence through v¯ v, because the per-chunk descriptions ψ(vi)ψ(v_i) have been discarded and replaced by the single aggregated description. The projected score of cvrc_v_r under ℋFH_F therefore equals the projected score of any other chunk cvjc_v_j containing a member of G, regardless of whether vjv_j is evidence-bearing. The retrieval algorithm cannot preferentially assign state-specific influence to cvrc_v_r over cvjc_v_j using entity-state information. (2b) If Aq(v¯)≤δA_q( v)≤δ, then v¯ v is not activated and no chunk in G’s scope receives entity-level influence. This arises when the aggregated description v¯des v^des averages over both query-relevant and query-irrelevant mentions of the entity, diluting the cosine similarity below the activation threshold δ even though vsv_s would have been activated had its per-chunk description been retained. In either case, ℋFH_F cannot assign state-specific positive influence to vrv_r: in (2a) influence is distributed uniformly across all G-members, and in (2b) it is zero. Semi-merged hypergraph ℋH. In ℋH, nodes vsv_s and vrv_r retain distinct descriptions ψ(vs)ψ(v_s) and ψ(vr)ψ(v_r), while ϕφ exposes their name-equivalence relationship ϕ(vs)=ϕ(vr)φ(v_s)=φ(v_r). The name-equivalence group satisfies Vvs∗=v∈∣ϕ(v)=ϕ(vs)∋vrV_v_s^*=\v φ(v)=φ(v_s)\ v_r. Since Aq(vs)>δ>0A_q(v_s)>δ>0, node vsv_s is activated and temporal bridging iterates over Vvs∗V_v_s^*. For target vrv_r at chunk-index distance Δt=|tvs−tvr| t=|t_v_s-t_v_r| and frequency-adaptive rate α=|Vvs∗|/n¯α=|V_v_s^*|/ n, the STIBP formula gives avstime(vr) a^time_v_s(v_r) =Aq(vs)⋅Sq(evr)⋅exp(−tanh(αΔt)) =A_q(v_s)· S_q(e_v_r)· (- (α t) ) ⋅sim(q,cvr). ·sim(q,c_v_r). Here evre_v_r denotes a hyperedge containing vrv_r with Sq(evr)>0S_q(e_v_r)>0; such a hyperedge exists by assumption. If vrv_r belongs to multiple hyperedges, the max operation in STIBP ensures the stored atime(vr)a^time(v_r) is at least the source-specific value computed with this evre_v_r, so it suffices to verify positivity for one such hyperedge. Each factor is strictly positive: Aq(vs)>δ>0A_q(v_s)>δ>0 by hypothesis; Sq(evr)>0S_q(e_v_r)>0 by assumption; exp(−tanh(αΔt))>0 (- (α t))>0 because tanh(x)<1 (x)<1 for every finite x and the exponential is always positive; and sim(q,cvr)>0sim(q,c_v_r)>0 by assumption. Hence avstime(vr)>0a^time_v_s(v_r)>0 and therefore atime(vr)>0a^time(v_r)>0. Since Aq(vr)=0A_q(v_r)=0 after thresholding and aspace(vr)=0a^space(v_r)=0 by hypothesis, the mean aggregation gives a(vr) a(v_r) =mean(Aq(vr)⏟= 0,aspace(vr)⏟= 0,atime(vr)⏟> 0) =mean\! ( A_q(v_r)_=\,0,\; a^space(v_r)_=\,0,\; a^time(v_r)_>\,0 ) =13atime(vr)>0. = 13\,a^time(v_r)>0. Because a(vr)>0a(v_r)>0, chunk cvrc_v_r receives strictly positive projected influence via vrv_r and enters the PPR initialization with non-zero prior weight. Recoverability separation. Combining the three cases, aℋN(vr) a_H_N(v_r) =0, =0, aℋF(vr) a_H_F(v_r) is undifferentiated or zero, is undifferentiated or zero, aℋ(vr) a_H(v_r) >0. >0. Among these three constructions, the semi-merged hypergraph is the only one satisfying both requirements simultaneously: ϕφ exposes the name-equivalence relation needed for temporal bridging, and ψ retains the per-chunk descriptions needed for state-specific activation, completing the proof. ∎ Proof of Theorem 1. We establish a lower bound for the contributions propagated from one fixed activated source u by bounding maxr∈ℛautime(r) _r a^time_u(r) from below and ∑n∈autime(n) _n a^time_u(n) from above. Throughout, Aq(u)=a>0A_q(u)=a>0, α=|Vu∗|/n¯>0α=|V_u^*|/ n>0, and the nonempty sets ℛR and N satisfy the conditions in the theorem. Because gn>0g_n>0 for every n∈n , the denominator is positive. Lower bound for relevant targets. For any r∈ℛr , the definition of autime(r)a^time_u(r) and the assumption gr=Sq(er)sim(q,cr)≥βg_r=S_q(e_r)sim(q,c_r)≥β give autime(r) a^time_u(r) =agrexp(−tanh(αΔr)) =a\,g_r (- (α _r)) ≥aβexp(−tanh(αΔr)). ≥ aβ (- (α _r)). Since tanh(x)∈[0,1) (x)∈[0,1) for all finite x≥0x≥ 0, we have −tanh(αΔr)>−1- (α _r)>-1, so exp(−tanh(αΔr))>e−1 (- (α _r))>e^-1 for every finite Δr _r. Here Δr _r is a finite non-negative integer because chunk indices are bounded, and α>0α>0 by assumption. Therefore autime(r)≥aβe−1for all r∈ℛ,a^time_u(r)≥ aβ e^-1 all r , and in particular maxr∈ℛautime(r)≥aβe−1. _r a^time_u(r)≥ aβ e^-1. Upper bound for noisy targets. For any n∈n , the assumptions 0<gn≤ϵ0<g_n≤ε and Δn≥τ>0 _n≥τ>0 give autime(n) a^time_u(n) =agnexp(−tanh(αΔn)) =a\,g_n (- (α _n)) ≤aϵexp(−tanh(αΔn)). ≤ aε (- (α _n)). The function x↦exp(−tanh(αx))x (- (α x)) is non-increasing for x≥0x≥ 0 when α>0α>0, because tanh(αx) (α x) is non-decreasing in x. Since Δn≥τ _n≥τ, we obtain exp(−tanh(αΔn))≤exp(−tanh(ατ)) (- (α _n))≤ (- (ατ)), and hence autime(n)≤aϵexp(−tanh(ατ))for all n∈.a^time_u(n)≤ aε (- (ατ)) all n . Summing over N: ∑n∈autime(n)≤a||ϵexp(−tanh(ατ)). _n a^time_u(n)≤ a|N|ε (- (ατ)). Signal-to-noise ratio. Combining the two bounds: maxr∈ℛautime(r)∑n∈autime(n) _r a^time_u(r) _n a^time_u(n) ≥aβe−1a||ϵexp(−tanh(ατ)) ≥ aβ e^-1a|N|ε (- (ατ)) =β||ϵexp(tanh(ατ)−1). = β|N|ε ( (ατ)-1). Monotonicity in α. For fixed ℛR, N, β, ϵε, τ, and n¯ n, the function α↦tanh(ατ)α (ατ) is strictly increasing for α≥0α≥ 0. Therefore exp(tanh(ατ)−1) ( (ατ)-1) is non-decreasing in α. This statement holds with the sets and constants fixed and does not compare realized ratios across name-equivalence groups of different sizes. ∎ Proof of Proposition 3. The proof proceeds by showing that PPR evidence mass is linear in the initialization prior, then applying linearity to compare pSTp_ST and pBp_B directly. Linearity of PPR evidence mass. The PPR stationary distribution π(p)π(p) under prior p is the unique fixed point of π=(1−d)p+dPπ=(1-d)p+dPπ. Solving by Neumann series, which converges absolutely because d<1d<1 and P is column-stochastic with ‖P‖1=1\|P\|_1=1: π(p)=(1−d)∑ℓ=0∞dℓPℓp.π(p)=(1-d) _ =0^∞d P p. The series converges in ℓ1 ^1 norm because (1−d)∑ℓ=0∞dℓ‖Pℓp‖1≤(1−d)∑ℓ=0∞dℓ‖p‖1=‖p‖1<∞(1-d) _ =0^∞d \|P p\|_1≤(1-d) _ =0^∞d \|p\|_1=\|p\|_1<∞ for any normalized prior p, justifying the interchange of summation and inner product below. Therefore, Mℛ(p) M_R(p) =ℛ⊤π(p)=ℛ⊤(1−d)∑ℓ=0∞dℓPℓp =1_R π(p)=1_R (1-d) _ =0^∞d P p =(1−d)∑ℓ=0∞dℓ 1ℛ⊤Pℓp. =(1-d) _ =0^∞d \,1_R P p. For each ℓ , the scalar ℛ⊤Pℓp1_R P p equals ((Pℓ)⊤ℛ)⊤p((P ) 1_R) p because u⊤Av=(A⊤u)⊤vu Av=(A u) v for any compatible vectors and matrix. Hence, Mℛ(p)=((1−d)∑ℓ=0∞dℓ(Pℓ)⊤ℛ)⊤p=hℛ⊤p,M_R(p)= ((1-d) _ =0^∞d (P ) 1_R ) p=h_R p, where the interchange of the finite linear functional (⋅)⊤p(·) p and the absolutely convergent series is valid by the dominated convergence theorem for sums. Evidence-mass comparison. Since Mℛ(p)=hℛ⊤pM_R(p)=h_R p is linear in p, Mℛ(pST)−Mℛ(pB)=hℛ⊤(pST−pB).M_R(p_ST)-M_R(p_B)=h_R (p_ST-p_B). The condition hℛ⊤(pST−pB)≥γ>0h_R (p_ST-p_B)≥γ>0 yields immediately Mℛ(pST)≥Mℛ(pB)+γ.M_R(p_ST)≥ M_R(p_B)+γ. Interpretation of hℛh_R. The c-th entry of hℛh_R equals (1−d)∑ℓ=0∞dℓ[(Pℓ)⊤ℛ]c(1-d) _ =0^∞d [(P ) 1_R]_c, the probability that a forward walk initialized at chunk c occupies ℛR when stopped after a geometrically distributed number of transitions. The condition hℛ⊤(pST−pB)>0h_R (p_ST-p_B)>0 therefore holds whenever STIBP places more prior mass on chunks with high discounted reachability to ℛR than binary initialization does. The aggregate ablation in Table 3 is consistent with this mechanism, but it does not establish the alignment condition for every query. ∎ Prior and dangling-node convention. The retrieval procedure directly uses the non-negative normalized prior pST(c)=I~(c)/∑zI~(z)p_ST(c)= I(c)/ _z I(z) when the denominator is positive, with the same uniform fallback used in the main text otherwise. For every dangling chunk c, the self-loop Pcc=1P_c=1 makes P column stochastic. Thus the assumptions used in the proposition, the main-text iteration, and Algorithm 1 are identical; no post-hoc normalization argument is required. Geometrically stopped forward-walk reading of hℛh_R. Let a walk start at chunk c and stop at its current state with probability 1−d1-d before each transition. It stops after ℓ transitions with probability (1−d)dℓ(1-d)d . Consequently, hℛ(c)h_R(c) is exactly the probability that the walk occupies ℛR when it stops. This interpretation follows directly from the discounted occupancy series and does not require a reverse-time transition process. E Extended Related Work This appendix expands the two comparisons that determine STITCH-RAG’s design: what the index retains about a multi-entity topic and how the retriever initializes propagation. We compare published representations and algorithms; provenance-enriched variants outside those specifications are not ruled out. E.1 Representing Topic Provenance and Local Entity State GraphRAG extracts entity–relation triples and summarizes graph communities (Edge et al. 2024). LightRAG reduces this indexing burden with a dual-layer graph (Guo et al. 2024), and NodeRAG uses heterogeneous node types to retain multiple evidence granularities (Xu et al. 2025). These systems can encode rich pairwise relations. The distinction relevant here is narrower: if retrieval receives an unlabeled projection with no shared event, topic identifier, or provenance, it cannot reconstruct which n-ary group generated a pair. Proposition 1 formalizes this input-specific loss. LinearRAG avoids LLM-based relation extraction and links canonical entity names for semantic bridging and PPR (Zhuang et al. 2025). Its published index represents matching names as one graph entity, so it does not expose the chunk-specific states used by STIBP. In STITCH-RAG, ψ retains the local descriptions and ϕφ links their normalized names. Proposition 2 tests this difference with controlled full-merge, no-merge, and semi-merge constructions. HyperGraphRAG encodes n-ary relational facts, Cog-RAG uses thematic hyperedges, and CogniRAG represents causal structures (Luo et al. 2025a; Hu et al. 2026a; He 2026). STITCH-RAG adopts thematic hyperedges but does not collapse all occurrences of an entity name. OKH-RAG also models cross-occurrence structure through learned precedence and sequence inference (Wu et al. 2026); STITCH-RAG instead uses a training-free index-proximity rule gated by query relevance and frequency under ϕφ. Chunk granularity changes the number and scope of these local states. Proposition-level retrieval favors narrow evidence units (Chen et al. 2024), while RAPTOR retrieves recursively summarized clusters (Sarthi et al. 2024). AutoRAG reports that the preferred granularity depends on question complexity (Kim et al. 2024). STITCH-RAG fixes the chunking policy and bridges the resulting boundaries; it does not determine the optimal chunk size. E.2 Initializing and Controlling Graph Propagation SubGraphRAG retrieves a query-matched local subgraph (Li et al. 2025), and GFM-RAG learns graph retrieval from training data (Luo et al. 2025b). HippoRAG and HippoRAG2 use PPR for broader diffusion (Gutiérrez et al. 2024; Gutiérrez et al. 2025). Their entity-match prior is binary: every matched entity is seeded and every unmatched entity receives zero. STIBP instead derives a continuous prior from the query similarity of local entity states, their topic hyperedges, and their name-equivalent neighbors. Proposition 3 states the resulting evidence-mass identity and its sufficient alignment condition. Hyper-RAG enumerates higher-order paths with beam search (Feng et al. 2026); Cog-RAG filters themes before entity retrieval (Hu et al. 2026a); and IGMiRAG adjusts mining depth from estimated question complexity (Hou et al. 2026). ReMindRAG stores previous traversal experience in graph-edge embeddings (Hu et al. 2026b). STITCH-RAG uses no path enumeration or query-time LLM call: STIBP scores the activated hypergraph structures, and PPR is restricted to the induced chunk graph. Table 4 reports the combined retrieval latency, not the isolated cost of localization. Corrective RAG, Adaptive-RAG, Self-RAG, and StructRAG decide whether retrieval or a particular structure is needed (Yan et al. 2024; Jeong et al. 2024; Asai et al. 2024; Li et al. 2024a). That routing decision is separate from the retrieval operator evaluated here. Long-context studies likewise show that evidence placement and concentration affect multi-hop reasoning even when the source fits within the context window (Li et al. 2024b; Wu et al. 2024). These results motivate selective retrieval but do not identify a preferred graph representation. LinearRAG remains the closest end-to-end structural comparison. STITCH-RAG changes its two relevant design choices: local entity states replace the single name-matched entity representation, and continuous STIBP scores replace binary PPR seeds. STITCH-RAG exceeds LinearRAG in Contain-Acc by 15.5 points on HotpotQA and 6.7 on 2Wiki, and in Recall@8 by 7.5 and 5.7 points. These aggregate margins do not separate the effects of representation, initialization, and localization; the controlled replacements in Table 3 provide the component-level evidence available in this study. The deployment regime also matters. RAG is preferable to knowledge internalization when the corpus is large or updated independently of model training, whereas fine-tuning can remain competitive on narrow static domains (Ovadia et al. 2024; Balaguer et al. 2024). Structured retrieval is most useful for questions that require cross-passage evidence rather than direct lookup (Xiang et al. 2025). STITCH-RAG further assumes that repeated queries amortize its one-time hypergraph construction cost.