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Meet, Compare, or Abstain: LatWeave for Deterministic Multi-Hop Question Answering on Knowledge Lattices

Yuze Ren, Shaoheng Fan, Tao Wang, Yabo Yan, Han Han

Year: 2026Venue: arXiv preprintArea: cs.CLType: PreprintEmbeddings: 76

Intelligence

Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 96%

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Summary

The paper introduces LatWeave, a deterministic multi-hop question answering system that organizes knowledge into a multidimensional knowledge lattice. Unlike probabilistic LLM or RAG systems, LatWeave uses three deterministic operators—meet (constraint intersection), compare (lattice-order comparison), and abstain (structural refusal)—to generate auditable, zero-hallucination answers. LLMs are restricted to one-shot extraction and query planning, while the answer generation path is zero-LLM and zero-training. The system is evaluated on benchmarks like MetaQA, 2WikiMultihopQA, MuSiQue, HotpotQA, and IIRC, demonstrating near-lossless performance on complete knowledge and structural abstention on incomplete data.

Entities (14)

LatWeave · system · 100%2WikiMultihopQA · benchmark · 99%HotPotQA · benchmark · 99%IIRC · benchmark · 99%MetaQA · benchmark · 99%MuSiQue · benchmark · 99%Knowledge Lattice · data-structure · 98%Abstain · operator · 95%Compare · operator · 95%Meet · operator · 95%Yuze Ren · person · 95%ZenSmart Technology · organization · 95%LLM · technology · 90%RAG · technology · 90%

Relation Signals (12)

LatWeave → evaluatedon → MuSiQue

confidence 99% · on open-text deep composition (MuSiQue) ... we report degradation

LatWeave → evaluatedon → IIRC

confidence 99% · when information is incomplete (IIRC) we achieve structural abstention

LatWeave → evaluatedon → HotPotQA

confidence 99% · and extraction-coverage gaps (HotpotQA) we report degradation

LatWeave → evaluatedon → MetaQA

confidence 99% · characterize the operating envelope of this paradigm on six public benchmarks: when knowledge is complete (MetaQA...)

LatWeave → evaluatedon → 2WikiMultihopQA

confidence 99% · on templated multi-hop home ground (2WikiMultihopQA held-out n=1,258) EM 0.865

Yuze Ren → affiliatedwith → ZenSmart Technology

confidence 95% · Yuze Ren ZenSmart Technology (Beijing) Co., Ltd., China

LatWeave → usesoperator → Abstain

confidence 95% · compiles multi-hop QA into three deterministic operators -- abstain (structural abstention)

LatWeave → usesoperator → Compare

confidence 95% · compiles multi-hop QA into three deterministic operators -- compare (lattice-order comparison)

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Abstract

Abstract:Probabilistic question-answering systems -- whether large language models (LLMs) themselves, retrieval-augmented generation (RAG), or trained multi-hop retrievers -- conflate "what is known" and "how to reason" into a single probabilistic computation: hallucination cannot be eradicated, evidence chains cannot be audited, and the system answers even when it does not know. We present LatWeave, which organizes knowledge into a multidimensional knowledge lattice and compiles multi-hop QA into three deterministic operators -- meet (constraint intersection), compare (lattice-order comparison), and abstain (structural abstention); LLMs appear only on the construction side (one-shot extraction) and the query-planning side, while the answer-generation path is zero-LLM, zero-task-training, and auditable end to end -- so that question answering over Web-published knowledge becomes reproducible item by item. Rather than claiming across-the-board SOTA, we characterize the operating envelope of this paradigm on six public benchmarks: when knowledge is complete (MetaQA, 39,093 questions) meet chains are near-lossless over three hops (any-hit 0.9975, on par with fully supervised KBQA); on templated multi-hop home ground (2WikiMultihopQA held-out n=1,258) EM 0.865, well above published structure-augmented RAG reproductions; on open-text deep composition (MuSiQue) and extraction-coverage gaps (HotpotQA) we report degradation honestly and attribute it to causes outside the lattice-algebra layer; and when information is incomplete (IIRC) we achieve structural abstention with abstain accuracy 0.971 and leak rate 0.029. Within the operating envelope, deterministic execution pays no performance penalty, and every step on the answer path can be recomputed -- precisely the source of end-to-end auditability.

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Meet, Compare, or Abstain: LatWeave for Deterministic Multi-Hop Question Answering on Knowledge Lattices Yuze Ren ZenSmart Technology (Beijing) Co., Ltd., China renyuze@zhongshuruizhi.com Shaoheng Fan ZenSmart Technology (Beijing) Co., Ltd., China fanshaoheng@zhongshuruizhi.com Tao Wang ZenSmart Technology (Beijing) Co., Ltd., China wangtao@zhongshuruizhi.com Yabo Yan ZenSmart Technology (Beijing) Co., Ltd., China yanyabo@zhongshuruizhi.com Han Han ∗ ZenSmart Technology (Beijing) Co., Ltd., China hanhan1@zhongshuruizhi.com Abstract Probabilistic question-answering systems—whether large language models (LLMs) themselves, retrieval-augmented generation (RAG), or trained multi-hop retrievers—conflate “what is known” and “how to reason” into a single probabilistic computation: hallucination can- not be eradicated, evidence chains cannot be audited, and the system answers even when it does not know. We present LatWeave, which organizes knowledge into a multidimensional knowledge lattice and compiles multi-hop QA into three deterministic operators— meet (constraint intersection), compare (lattice-order comparison), and abstain (structural abstention); LLMs appear only on the con- struction side (one-shot extraction) and the query-planning side, while the answer-generation path is zero-LLM, zero-task-training, and auditable end to end—so that question answering over Web- published knowledge becomes reproducible item by item. Rather than claiming across-the-board SOTA, we characterize the oper- ating envelope of this paradigm on six public benchmarks: when knowledge is complete (MetaQA, 39,093 questions) meet chains are near-lossless over three hops (any-hit 0.9975, on par with fully supervised KBQA); on templated multi-hop home ground (2Wiki- MultihopQA held-out푛=1,258) EM 0.865, well above published structure-augmented RAG reproductions; on open-text deep com- position (MuSiQue) and extraction-coverage gaps (HotpotQA) we report degradation honestly and attribute it to causes outside the lattice-algebra layer; and when information is incomplete (IIRC) we achieve structural abstention with abstain accuracy 0.971 and leak rate 0.029. Within the operating envelope, deterministic execution pays no performance penalty, and every step on the answer path can be recomputed—precisely the source of end-to-end auditability. Keywords constraint meet; lattice-order comparison; structural abstention; knowledge lattice; multi-hop question answering; deterministic reasoning; retrieval-augmented generation 1 Introduction Modern question answering systems have nearly converged on a hybrid architecture: keyword retrieval guarantees exact matches, semantic retrieval handles recall, and GraphRAG-style methods further introduce structured retrieval into the pipeline, explicitly ∗ Corresponding author. connecting the correlations that remain isolated between semantic chunks. Engineering mechanisms such as chunk IDs have given the evidence chain a traceable form in production for the first time. Yet two structural problems remain unsolved. The first is hallucination: provenance annotations can trace which snippets an answer con- sulted, but not whether the answer is logically entailed by them—the final step from snippets to answer is still taken in probability space, and distortion, extrapolation, and outright fabrication all occur at this step. This is not an engineering oversight: hallucination is a mathematical inevitability of probability-based generation—any calibrated language model must hallucinate [20]. The second is answering anyway by design: when neither retrieval nor the graph contains facts supporting an answer, the system has no structural mechanism to stop itself. The two problems trace back to the same root: engineering-level auditability—the sources are traceable, but the reasoning from evi- dence to conclusion is a black box. This paper argues for mechanism- level auditability: the answer itself is a meet chain unfolded step by step, each step a verifiable lattice-algebra operation that any exam- iner can replay and check independently. A clarification of scope: this paper does not claim that deterministic methods outperform probabilistic ones across all multi-hop tasks; what we characterize is where they approach losslessness, where they structurally degrade, and how they abstain honestly when the paradigm degrades—its operating envelope. Mapping this envelope out is itself one of the contributions of this paper. Our approach can be summarized in one sentence: the LLM is restricted to a “builder + query translator,” and answers are pro- duced deterministically by three operators on the lattice. Meet (con- straint intersection) compiles the question into a set of dimension constraints and takes their greatest lower bound (GLB) on the product lattice; the hit instances form the answer, each carrying its source_text, so the evidence can be audited item by item. Compare (lattice-order comparison) performs comparison and set operations along the lattice order—Boolean tests, complete answer-set return, and lattice-order adjudication of “which is more푋.” Abstain (struc- tural refusal): when constraints conflict or the fact is absent from the lattice, the system refuses structurally—a direct consequence of lattice semantics, not a low-confidence fallback. Figure 1 gives the two-stage overview: at build time (offline, one-off ) an LLM extracts typed predicates from question-blind documents and constructs the lattice; at query time an LLM planner compiles the question arXiv:2609.27225v1 [cs.CL] 23 Sep 2026 Yuze Ren, Shaoheng Fan, Tao Wang, Yabo Yan, and Han Han into a typed plan that the three operators execute deterministically. LLM participation is confined to the builder and planner roles—the answer path makes zero LLM calls and requires zero task training— and every answer is an auditable meet chain. Our contributions are fourfold: • Mechanism. A formalization and system realization of the knowledge lattice with the meet/compare/abstain opera- tors; the answer path contains zero LLM calls and zero task training (§3–4). •Upper-bound evidence. With complete or templated knowl- edge, deterministic retrieval is near-lossless: MetaQA any- hit 0.9975 (zero training, on par with fully supervised KBQA) and 2Wiki held-out EM 0.865 (§6). • Boundary evidence and attribution. Degradation on three boundary benchmarks (MuSiQue / HotpotQA / FRAMES) is attributed layer by layer to causes outside lattice algebra, consolidating into a unified failure classification (§7). •Abstention as a first-class capability. A two-scale evalu- ation framework (recall×precision), corroborated on IIRC by structural abstention: abstain accuracy 0.971, leak rate 0.029, zero drift on the tuning pool (§8). The lineage of this work is also worth stating: LatWeave builds on an earlier rule-centric knowledge base system developed within our group, where partial ordering on a classification lattice served solely for applicability gating, not yet a retrieval algebra; we general- ize that gating into a full multi-dimensional product-lattice algebra. The step from “partial ordering used only for gating” to “the lattice is the retrieval space” is precisely where the core contribution of this paper lies. 2 Related Work Today’s QA systems have evolved along four technical lines, each solving a different problem: neural multi-hop retrievers achieve multi-hop recall but depend on model training; RAG and GraphRAG mitigate knowledge staleness and chunk isolation, yet hallucination cannot be eliminated and evidence chains remain hard to audit; KBQA and semantic parsing deliver precise answers, but are bound to a predefined schema and a trained parser; selective prediction lets a system refuse when it does not know, but the refusal rests on a confidence threshold whose calibration drifts with the task distribution. Only this work achieves zero training, deterministic answers, mechanism-level auditability, and structural abstention at the same time—these four properties have never before appeared in a single system (Appendix Table 9). 2.1 Multi-Hop Question Answering HotpotQA [44], 2WikiMultihopQA [16], MuSiQue [38], IIRC [8], and FRAMES [23] together define the difficulty spectrum of multi- hop QA—from templated two-hop questions to adversarial deep composition, and from complete to incomplete information. Main- stream solvers (MDR [42], IRCoT [39], Beam Retrieval [45], Ho- pRAG [28]) are probabilistic or training-dependent—a different precondition from our zero-training setting. 2.2 Retrieval-Augmented and Graph-Augmented LLMs RAG [24] and its refinements (Self-RAG [2] learns when retrieval pays off; FLARE [19] re-retrieves proactively mid-generation) use semantic-similarity retrieval to mitigate hallucination; GraphRAG [6], LightRAG [12], HippoRAG 2 [13], ToG [37], RoG [29], and KAG [25] further introduce graph structure into retrieval, mining the associa- tions between semantic chunks. This line strengthens “retrieval,” yet answers are still LLM-generated—the hallucination and auditability problems remain exactly as before. 2.3 KBQA and Semantic Parsing KBQA systems reason deterministically with fully verifiable inference— KV-Mem [30], GraftNet [36], SRN [31], PullNet [35], EmbedKGQA [33], NSM [15], and RoG [29]—but each depends on two prerequisites: a ready-made knowledge graph and a trained parser. Our method carries neither: a one-shot LLM extraction builds the lattice directly from text, keeping auditability with no model-training requirement. On the query side, the most recent publicly available work is LLM-Plan by Shrestha and Kim [34]: an LLM plans only a relation sequence that a deterministic BFS executes over a knowledge graph. LatWeave differs structurally: meet intersects per-dimension value constraints where LLM-Plan’s relation traversal carries none; we provide compare semantics and structural abstention where LLM- Plan has neither; and we characterize a six-benchmark operating envelope, while LLM-Plan is evaluated on a single benchmark. The item-by-item numeric comparison appears in Section 6.2. 2.4 Abstention, Selective Prediction, and Hallucination Selective prediction supplies the theoretical frame for “abstain when unsure” [7,11], carried into QA [21] and VQA [40]; TruthfulQA [27] and hallucination surveys [18] chart the cost of never abstaining. Yet existing abstention is almost entirely probabilistic confidence thresholding, whose risk–coverage trade-off drifts with the task— softmax-score rejection attains under 7.5% coverage at 1% risk, and a learned selector attains only about 15.6% [40]. Our abstain is structural: a fact absent from the lattice entails abstention, with no threshold to tune and a leak rate that is empirically near zero (Section 8). 2.5 Concurrent Work and Positioning Concurrent W 2026 work approaches different facets of the same problem: S-Path-RAG [9] trains a differentiable path scorer and injects cross-attention into the LLM; CompactRAG [43] cuts the LLM-call and token cost of multi-hop QA to two calls per question, yet those calls still synthesize the final answer; RoE [14] unifies retrieval and generation via SFT- and RL-trained graph exploration; HyperRAG [26] upgrades retrieval to n-ary hypergraphs with an LLM-guided beam. We differ from all four on the same two poles: zero training, and an answer path that never enters the LLM. 3 The Knowledge Lattice Model This section pins down the lattice as a mathematical object that a re- viewer can verify, and defines the three operators—meet (constraint Meet, Compare, or Abstain: LatWeave for Deterministic Multi-Hop Question Answering on Knowledge Lattices BUILD TIME · offline, one-offQUERY TIME · online, per question extraction noise is absorbed here (dedup, normalization, whitelist) it never reaches the answer path answer path: zero LLM · zero task training every answer is an auditable meet chain corpus (question-blind) documents LLM extraction one-off · hybrid sliding window dedup · normalize · whitelist no text no fact KNOWLEDGE LATTICE multi-dim product lattice of instances every predicate carries its source_text question (natural language) LLM planner temp 0.0 deterministic core: meet, compare, abstain answer + evidence chain retrieval space typed plan abstain on conflict or absent fact LLM (frozen)LLM Figure 1: LatWeave in two stages. Build time (offline, one-off): an LLM extracts typed predicates from question-blind documents (dedup, normalization and a dimension whitelist absorb extraction uncertainty before it can enter the lattice), yielding a product lattice whose instances each carry theirsource_text. Query time (online, per question): an LLM planner compiles the question into a typed plan, and a deterministic core executes the three operators —meet, compare, abstain. The LLM is confined to the two orange boxes (extraction and planning); the answer path carries zero LLM calls and zero task training, so every answer is an auditable meet chain. intersection), compare (lattice-order comparison) and abstain (struc- tural refusal)—as algebraic operations with explicit semantics; the four classical results the system puts to work, and the engineering question each answers, are given at the end of Section 3.1. 3.1 Posets, Dimensions, and Product Lattices Start with a miniature example (Figure 2). Take two dimensions: species, a biological taxonomy (under animal sit mammal, bird, and fish, and under mammal sit whale, dog, and bat), and habitat, whose values include aquatic, terrestrial and amphibious. An instance— one particular whale—is bound to the product-lattice coordinate (whale, aquatic). The query “aquatic mammals” then amounts to a single meet: whale is a descendant of mammal on the first dimen- sion and aquatic matches the second, so the whale is returned. If instead we ask for “terrestrial whales,” the two constraints conflict, so the system abstains deterministically rather than guessing. The structure is no toy: the same product-lattice slice already runs over our group’soil and gas production corpus. Three standard notions—poset (a reflexive, antisymmetric, tran- sitive relation⊑on a set푃), lattice (a poset in which every pair 푎,푏has a greatest lower bound푎 ∧ 푏and a least upper bound 푎 ∨ 푏), and product lattice (componentwise order, meet and join over퐿 1 ×·× 퐿 푘 )—freeze the intuition’s left half (see, e.g., [4]); the two definitions and one convention below are our own, attach- ing dimensions and instances to the product lattice and covering instances that miss a dimension. Definition 4 (Dimension). Each knowledge dimension퐿 푖 is a rooted directed acyclic graph: its nodes are dimension values (including synonym sets and numeric intervals), its edges encode the “more general→ more specific” order, and its root is⊤. Definition 5 (Instance). An instance is bound to a coordinate of the product lattice; its predicate set(푑 푖 ,푣 푖 ,휏 푖 )gives, for each dimension, a value and a confidence. Every predicate must carry its source_text—an anti-hallucination rule: an assertion without supporting evidence text is not admitted into the lattice. Convention (embedding of missing components). When an instance misses a dimension, that component is read as⊤(the most general value) and violates no order check. A “query” is then stated precisely as a meet on the product lattice—the subject of the next subsection. Four classical results are put to work by the system, each answer- ing one engineering question. (1) Is the lattice legitimate? Birkhoff ’s distributivity identity푥 ∧ (푦 ∨ 푧)= (푥 ∧ 푦) ∨ (푥 ∧ 푧)turns the naive푀 3 /푁 5 witness search into a per-triple check (푂(푛 3 )with bitset meet/join tables) [4]; dimensions containing ambiguous sub- lattices never go live. (2) Can we afford meet? On-demand Dedekind– MacNeille completion computes GLBs by bitset intersection plus ex- tremum extraction, replacing the 2 |푃| enumeration. (3) How is cross- dimension structure discovered? Formal Concept Analysis (FCA) identifies attributes shared across dimensions and supports cross- reference expansion [10,41]. (4) Are the dimensions independent? The Dilworth width, obtained via Kőnig bipartite matching, assesses the mutual independence of dimensions [5]. 3.2 Three Deterministic Operators and the Capability Boundary meet (constraint intersection). The semantics of a constraint set 퐶=(푑 푖 ,푉 푖 )is per-dimension GLB followed by coordinate com- position in the product lattice: for every constrained dimension we intersect the descendant sets of the candidate values and extract the greatest element; a dimension with no common lower bound is a conflict in that dimension. A conflict is not an exception but a first-class output of the lattice semantics—it is the legitimate trigger of abstain. compare (lattice-order comparison). One operator, four instantia- tions on the lattice order: (1) Boolean comparison of two entities along the same dimension (2Wiki comparison questions); (2) order- based selection of an extremum among candidates (bridge_comparison’s “which is more푋”); (3) complete-set return—meet returns the full answer set rather than a top-1 ranking (the primary MetaQA metric, Table 4); (4) Boolean boundary—when the compared objects are not in the lattice, compare degrades to abstain (IIRC binary questions, Table 13). The four forms share one algebraic basis: instantiations of a single operator, not four patched-together features. Yuze Ren, Shaoheng Fan, Tao Wang, Yabo Yan, and Han Han (a) Dimension taxonomies species habitat (b) Instance = point instance: a whale src: field observation note badges ①② = nodes occupied in the taxonomies (left) (c) One meet, three steps Any (root) animal mammalbirdfish whaledogbat Any (root) aquaticterrestrialamphibious whale aquatic ① query q = ( species: mammal, habitat: aquatic ) ② per-dimension descendant check: whale ∈ ↓mammal ✓ aquatic = aquatic ✓ ③ meet(q, whale) feasible → whale returned contrast: q′ = ( species: whale, habitat: terrestrial ) ↓terrestrial ∩ aquatic = ∅ → conflict ⊥ → abstain (deterministic) species habitat 1 2 1 2 Figure 2: A product-lattice slice (species×habitat mini-example): (a) value hierarchies of the two dimensions; (b) an instance as a point in the product lattice; (c) one meet in three deterministic steps—a hit requires the descendant check on every dimension, and a conflict on any dimension entails abstain. abstain (structural abstention). A monotone abstention seman- tics: if the constraints conflict, or no lattice point satisfies all con- straints (the hit set is empty), the system abstains. The tighter the constraints, the weaker the answerability—never the reverse. Capability boundary (declared a priori). Any question that derives new values on top of lattice values (arithmetic, derived counts) belongs to external operator modules, which this paper neither implements nor counts in the in-scope numbers. This declaration licenses the FRAMES capability strata (Appendix A) and the IIRC value-type accounting (Table 13). Three short propositions follow, each with a one-sentence proof idea (the full arguments are immediately checkable). Proposition 1 (determinism): the same lattice and the same query yield the same result, because GLB and lattice-order comparison are functions with no random source. Proposition 2 (auditability): every answer unfolds into a meet chain, and every instance on the chain car- ries itssource_text; auditing means checking the algebra and the evidence text step by step. Proposition 3 (monotone abstention): tight- ening the constraints (adding a dimension or taking a more specific value) never turns an abstain into an answer, because tightening shrinks the satisfying set monotonically and an empty set stays empty. 3.3 Relation to FCA and Knowledge Graphs We borrow lattice semantics from FCA, but our objects are multi- attribute instances rather than formal concepts; we borrow entity- relation structure from knowledge graphs (KGs), but keep dimen- sional coordinates and the lattice order, making meet/compare native operations rather than bolted-on traversals. FCA answers “which objects share which attributes”, whereas we answer “given constraints, which lattice points satisfy them; and when none do, is it a conflict or a gap”. 4 LatWeave: System Design This section presents the system design of LatWeave. At con- struction time (Section 4.1) open text is woven into a knowledge lattice; at query time (Section 4.2) deterministic three-state execu- tion runs on the lattice; Section 4.3 closes with implementation and efficiency notes. The LLM appears in exactly two places—extraction at construction time and planning at query time—and its uncer- tainty is kept off the answer path. Engineering details are limited to feasibility numbers; the rest goes to the appendix. 4.1 Construction: From Text to Lattice Construction turns open text into a knowledge lattice; the core is hybrid extraction. Short documents go through the whole-doc mode, where the full text is fed to the LLM once; long documents go through a physical sliding window cut by character position (win- dow size derived from the model’s context size, consecutive chunks overlapping 200–500 characters), so that no content is lost during chunking. Extracted facts then pass a strict grid-point hash dedup: a fact repeated by the LLM—same lattice coordinates, same source evidence—enters the lattice only once. The last step is whitelist- guided extraction with dimension normalization: the prompt carries a table of preferred dimensions whose canonical names are used when they match semantically, uncovered relations may be named freely, and a variant table normalizes synonymous variants after- ward; LLM-invented dimensions are thereby mostly long-tail and low-frequency. The motivation is empirical: in MuSiQue construc- tion, free naming once shattered the single relation “educated at” into 1,017 dimension names. 4.2 Query Time: Planning and Deterministic Three-State Execution Query time has two parts: the LLM planner compiles the question into a typed plan, and deterministic execution runs that plan on the lattice and returns one of three states. The planner is a replaceable semantic-parsing front end (temperature 0.0; plans are cacheable and reproducible), and its loss can be measured separately from lattice competence by an oracle-plan ceiling experiment (Section 7). For “physicists born in Vienna who won the Nobel Prize in Physics” the compiled plan is a conjunction of three dimension meets, and the executor intersects them to obtain the complete answer set (a meet hit); if the constraints conflict or the hit set is empty, it abstains—the refusal comes directly from on-lattice execution, with no external fallback of any kind; compare returns a Boolean, an extremum, or a complete-set verdict. Union semantics applies to Meet, Compare, or Abstain: LatWeave for Deterministic Multi-Hop Question Answering on Knowledge Lattices Table 1: Datasets, structure, and role in this paper’s argument. DatasetSize usedStructureRole MetaQA [46]test푛=39,0931/2/3-hop:9,947/ 14,872 / 14,274 Control: complete knowledge⇒lat- tice algebra lossless 2WikiMultihopQA [16] held-out푛= 1,258 4 question typesMainexperiment: templatedmulti- hop, end-to-end HotpotQA [44] held-out푛= 741 bridge 592 / compari- son 149 Boundary 1: fact- coverage gap MuSiQue [38]held-out푛= 242 2/3/4-hop: 125/76/41Boundary 2: longer- chain degradation IIRC [8] held-out푛= 130 span 59/ value 23/ bi- nary 13/ none 35 Refusal experiment: abstain under in- completeness FRAMES [23]dev 742 + held- out 82 factuality×multi-hopCompounded stress test: coverage× grounding the meet path only, because complete-set semantics must not be diluted by unions. All experiments in this paper evaluate exactly this three-state execution. The executor itself is three lines of logic: per-dimension descendant-set intersection, extremum extraction, and conflict return when a dimension has no common lower bound. 4.3 Implementation and Efficiency This section gives feasibility evidence: the system runs at real- istic scale, and it is fast. Scale: the 2Wiki dataset holds 1.2M in- stances, built from the full dev corpus of 125,760 passages. Efficiency: lexicon-scan construction takes 235 ms; retrieval executes at p50 below 18.7 ms and p95 below 50 ms; planning for the 1,258 held- out questions replays from cache in about 1 s. Against GraphRAG- style systems: their indexing requires multiple LLM passes over the whole corpus plus maintained embeddings, and an LLM still sits in the query loop—the gap is architectural, not something that engineering-level tuning can close. 5 Experimental Setup 5.1 Datasets and Their Roles We evaluate LatWeave’s retrieval on six public datasets, each serv- ing one role in our argument (Table 1). MetaQA is the control: with knowledge complete, it verifies that the lattice algebra itself loses nothing. 2WikiMultihopQA is the main experiment. HotpotQA and MuSiQue are the two boundary experiments, exposing respec- tively the fact-coverage gap of open-domain extraction and the degradation as chains lengthen (2→4 hops). IIRC examines refusal under incomplete information. FRAMES is a compounded stress test (Appendix A): fact-coverage gap× query grounding. 5.2 Split Rules and Leakage Control All text benchmarks share one split rule: a stratified 90/10 dev/held- out division (seed 88). Lattice construction is strictly question- blind—only paragraphs or KB triples are read, never questions or answers. Configurations are frozen on dev, and the held-out split is evaluated exactly once. MetaQA keeps its official test split (39,093 questions); its configuration is frozen on the official dev split with a 9-shot planner prompt (exemplars drawn only from the train split, so no test information leaks). Held-out drift is zero: 2Wiki 0.886 vs. 0.865; IIRC precision measure 0.9682 vs. 0.9437. Table 2: 2WikiMultihopQA main results (held-out푛=1,258). MethodEMF1*Resolved Keyword baseline0.0830.11173.2% Naive RAG (TF-IDF + LLM)0.1980.205100% GraphRAG [6]0.514 ‡ 0.586 ‡ — HippoRAG 2 [13]0.650 ‡ 0.710 ‡ — IRCoT [39]0.530.65— HopRAG [28]0.620.69— Beam Retrieval [45]— OPEN-RAG [17]— Self-RAG [2]— LatWeave (held-out)0.865 0.87292.2% (tune pool푛=10,179, refer- ence) 0.886—92.9% ‡ Published values [22] carry protocol differences (1k-question subset, restricted corpus, Llama-3.3-70B reader): a paradigm reference, not a same-condition comparison. Beam Retrieval, OPEN-RAG, and Self-RAG are trained methods, listed for positioning without numbers. Table 3: 2WikiMultihopQA per-type breakdown (held-out 푛= 1,258). Question typeShareEMΔ vs. overall bridge_comparison21.9%0.975+11.0p comparison24.2%0.888+2.3p compositional41.7%0.815 −5.0p inference12.3%0.794 −7.1p Overall100%0.865— 5.3 Baselines and Condition Labeling Baselines fall into two blocks. The zero-training block runs on the same corpus and the same scoring function as ours: a keyword baseline, Naive RAG (TF-IDF retrieval plus an LLM reader), and LatWeave. The reference block reports published values with proto- col differences footnoted (GraphRAG 0.514 ‡ , HippoRAG 2 0.650 ‡ , IRCoT 0.53, HopRAG 0.62, and the supervised family on MetaQA); it serves as a paradigm reference only, and we draw no same-condition win/loss verdicts from it. 5.4 Metrics Our metric family is organized around three abilities: answering correctly (EM / F1), answering completely (any-hit / complete-set recall), and refusing honestly (Faithfulness / dual measures / leak rate). EM and F1 come from a single scoring function: prediction and gold pass through the same text normalization; EM tests exact equality of the normalized strings, and F1 is token-level overlap. Since EM=1 forces F1=1.0, our F1 convention is equivalent toF1 ∗ := max(F1 raw , EM) . Every LLM call is pinned to temperature 0.0 and seed 88; the FRAMES capability classes are assigned by a frozen mechanical decision table whose rules read only the question and the gold answer—never the model output (Appendix B). 6 Main Results: Meet at Its Best 6.1 2WikiMultihopQA: The Main Battlefield The breakdown brings the compare family to numbers for the first time: bridge_comparison (0.975) and comparison (0.888) lead, and these two are precisely the compare operator’s home ground Yuze Ren, Shaoheng Fan, Tao Wang, Yabo Yan, and Han Han Table 4: MetaQA test main results (푛=39,093, single final run, frozen 9-shot configuration). Hop 푛any-hitrecall (complete)EM (strict)set-F1 1-hop9,9470.99900.99870.94470.9798 2-hop14,8720.99830.99830.62390.9448 3-hop14,2740.99550.99540.53040.9369 All39,093 0.9975 0.99730.67140.9508 (Section 3.2) — lattice-order side selection and Boolean comparison, where lattice comparability yields the answer directly with no generation. On held-out (푛=1,258) LatWeave reaches EM 0.865, F1* 0.872, and resolved 92.2%, and on the resolved questions EM climbs to 0.938: on the questions it answers, the system is 93.8% precise. The relative gains over the same-protocol Naive RAG rerun (0.198) and the strongest published graph-RAG value (HippoRAG 2, 0.650) are 337% and 33% respectively. The tune pool (푛=10,179, disjoint from held-out) gives EM 0.886, 2.1p above held-out — tuning did not overfit the held-out set. Ablation (Appendix Table 10) shows that from the dev-only baseline 0.731 to the frozen configuration the largest single increment comes from train-set transfer (+9.5p), with alias normalization (+2.0p) and rule-based re-extraction (+1.0p) accounting for the rest. 6.2MetaQA: The Representation-Independence Controlled Comparison MetaQA is a templated QA dataset: every question is template- generated and every answer is drawn strictly from the knowledge graph, so on the same questions any hit-rate gap between the knowledge-graph and knowledge-lattice representations is fully at- tributable to the representation form itself. The most recent publicly available work on the same benchmark is LLM-Plan by Shrestha and Kim [34], evaluated on the identical 39,093-question test split (Table 5). The 2Wiki results above rest on LLM open extraction, so a natural objection is whether the performance comes from the extrac- tion or from the lattice algebra itself. MetaQA is a purely structured KBQA benchmark (134,741 triples / 43,234 entities / 9 relations) whose triples map to lattice points with zero LLM—dimensions are the relations (9 forward + 9 inverse + 1 subject anchor), instances the subject- and object-side entities (269,482)—so the same engine runs losslessly when the knowledge source is swapped from text to KB, turning “the lattice is a general knowledge representation, not a byproduct of LLM extraction” into a falsifiable claim. KB cover- age and seed-entity linkage are both 100% (measured), so the only source of loss is question parsing. The evaluation setup mirrors the 2Wiki experiment: question- blind construction (minutes onkb.txt); configuration frozen on dev (9-shot, temp 0.0 / seed 88); test evaluated once. Parsing costs one LLM call per question (parse_fail = 0); query execution is a pure meet-algebra chain with zero LLM. Three observations. (i) With no training, LatWeave reaches hits comparable to those of fully supervised methods: 1-hop (0.9990) and 3-hop (0.9955) match or exceed the best published values, while 2-hop (0.9983) comes within 0.07p of the best (0.999). (i) The hop- decay profiles are categorically different: KV-Mem degrades sharply Table 5: MetaQA test vs. published KBQA methods (super- vised rows: Hits@1 verified from source papers, converted to decimals). The Shrestha–Kim row reports Hit Rate—verbatim the any-hit measure, hence directly comparable to our any- hit row; their pooled micro-F1 is not cross-compared with our per-question set-F1 0.9508. Method1-hop2-hop3-hopParadigm (trained) KV-Mem [30]0.9620.8270.489Memory networks (yes) GraftNet [36]0.9700.9480.777Subgraph retrieval (yes) SRN [31]0.9700.9510.752Neuralreasoning (yes) PullNet [35]0.9700.9990.914Graph retrieval (yes) EmbedKGQA [33]0.9750.9880.948KGE (yes) NSM [15]0.9710.9990.989State machine (yes) RoG [29]—0.848 LLM+graph (1k fine- tune) LLM-Plan + BFS [34] 0.9990.9990.970LLM plan + BFS (no task training) LatWeave(any- hit) 0.9990 0.9983 0.9955 Lattice meet (zero training) LatWeave (recall, complete) 0.99870.99830.9954 gold⊆ returned set with depth (0.962→0.489), even the strongest NSM shows visible 3- hop decay (0.999→0.989), whereas LatWeave is almost flat across three hops (total span 0.0035)—hop depth is not a difficulty variable for the lattice algebra. (i) Every supervised baseline needs large- scale training (96k–330k questions), while LatWeave only reads the KB. Dev/test are highly symmetric (per-hop any-hit deviation ≤ 8× 10 −4 ); empty= 69 (0.18%). Completeness is the compare family’s second home ground: meet returns the full answer set deterministically, so completeness is a direct product of the semantics—ranking-style methods, which treat “gold enters the top-푘candidates” as the hit endpoint, cannot structurally promise it. Our any-hit measure — 1 iff ˆ 퐴∩ 퐴 ∗ ≠∅—is the Hits@1 of the same returned set under an optimal internal ordering, hence an upper bound on Hits@1; with set-F1 0.9508 the actual gap is negligible. Tightness matters equally: on the single- answer subset (|퐴 ∗ |=1,푛=14,834) any-hit and ranked Hits@1 are strictly equivalent, measured 0.9974. Appendix Table 11 shows that recall (complete)—1 iff퐴 ∗ ⊆ ˆ 퐴— is≥0.996 in every answer-set-size bucket. Strict answer-set EM ( ˆ 퐴≡ 퐴 ∗ ) is 0.6714 and decays with answer-set size (0.833 at|퐴 ∗ |=1, 0.379 at|퐴 ∗ | ≥11)—an artifact of set strictness: over 99% of EM misses still intersect the gold set, no under-answering miss exists, and all misses come from one or two extra or wrong entities. The MetaQA control arm yields a direct production-route corol- lary: domains that already hold structured knowledge (KG / data- base / table) should map it straight to a lattice and skip LLM ex- traction entirely—zero training, zero fine-tuning, any-hit 0.9975, sub-50 ms retrieval, zero LLM. Three premises are stated honestly: question parsing remains the only source of loss; fan-out value selection still needs deterministic post-processing or a human in the loop; and the lattice inherits the KG’s missing edges and dirty triples losslessly—input quality is the ceiling. Meet, Compare, or Abstain: LatWeave for Deterministic Multi-Hop Question Answering on Knowledge Lattices 1-hop2-hop3-hop4-hop 0.0 0.2 0.4 0.6 0.8 1.0 any-hit / EM 0.999 0.998 0.996 0.965 0.944 0.364 0.048 00 0.144 0.132 0.122 MetaQA—LatWeave MetaQA—RAG MuSiQue—LatWeave MuSiQue—RAG Figure 3: Hop decay in two contrasts. MetaQA (complete KB, any-hit): lattice meet chains are nearly lossless over three hops (0.9990 / 0.9983 / 0.9955), while the same-corpus RAG baseline (hits@1) decays to 0.364 at 3-hop. MuSiQue (open- text extraction, EM): lattice retrieval collapses to zero on multi-hop text composition (0.048 / 0 / 0), while RAG stays flat at a low 0.12–0.14 (insensitive to hop count). 7 Analysis: The Operating Envelope This section turns the “operating envelope” from a position state- ment into a quantified characterization. The claim: on the three multi-hop boundary datasets (HotpotQA, MuSiQue; FRAMES in Appendix A), all losses fall outside the lattice-algebra layer, in two upstream layers—(a) open-text-to-structure conversion (coverage gaps and dimension fragmentation after whitelist governance; Sec- tions 4.1 and 7.3); (b) natural-language-to-lattice-query parsing (query grounding and chain landing-point precision). 7.1 Failure Attribution: Four Boundary Classes On the three multi-hop boundary datasets, the dominant cause of lattice-retrieval failure differs by class. On HotpotQA, the answer never enters the candidate set: 90.6% of residual broken chains lack the final-answer edge in the lattice (Appendix Table 12), and among resolved-but-wrong questions, 77% have their gold answer outside the returned set altogether; nor is the gap unrepaired— build-layer repair lifts the formerly hop-1-broken bucket from EM 0 to 17.3%, but conversion saturates and oracle injection falsifies same-mechanism repair (Section 7.3). MuSiQue’s attribution is com- positional decay across hops: 48.3% of chains break at the first hop and a single failing hop fails the whole chain (EM 0.0248). FRAMES compounds the two. IIRC adds a fourth class—the answerability boundary (Section 8.3): answers must be derived on top of lattice values (time differences, counts), which exceeds the declared deter- ministic capability (Section 3.2); or the compared subject is absent from the lattice altogether—in both cases the correct behavior is to abstain rather than guess. 7.2 Hop Decay in Two Contrasts: Complete KB vs. Open Text The dual-contrast figure (Figure 3) shows jointly that hop depth is not a difficulty variable for the lattice algebra itself; the degradation comes from the knowledge source, not the reasoning core. Cor- roborating per-hop conditional meet accuracy (Appendix Figure 5, MuSiQue tune pool푛=2,175): 0.37–0.44 at hop 1, 0.09–0.22 at hop 2, approaching zero at hop 3—each additional hop compounds Table 6: Four levels of query grounding. Level MechanismGrounding objectStatus L0Free generationnoneRejected L1Global vocabularyglobalrelation names Internalized(Hot- potQA) L2Entity menuseedentity’s lattice neighbor- hood Internalized (FRAMES) L3Per-hop replanningintermediate enti- ties Not adopted (argued below) conditional success approximately multiplicatively, and the first hop is the largest loss surface. The RAG contrast: on MuSiQue held-out, RAG reaches EM 0.1364 above the lattice’s 0.0248; on HotpotQA held-out, EM 0.4683 above 0.1687—the coverage gap puts lattice retrieval’s full-pool EM at about one third of the same-corpus generative RAG baseline. Once facts are inside, lattice retrieval itself is accurate (resolved-EM 0.4545 on HotpotQA, 0.938 on 2Wiki). MuSiQue falls into three classes by break type: operational (OP_final,푛=61, EM 0.082); honestly resolvable (QU_honest,푛=28, EM 0.0357); and structural- abstention (QU_not_honest, anchor unresolvable, empty returned by design,푛=153, EM 0)—all 6 correct answers are 2-hop verba- tim matches. On HotpotQA, comparison questions resolve at 70.1% while multi-hop meet questions resolve at only 29.6%: multi-hop meet must ground hop by hop, compounding per-hop in-lattice rates and landing-point errors multiplicatively. 7.3 Query-Grounding Levels and Loss Upper Bounds The oracle-plan upper bound separates planner loss from lattice capability in numbers: on 2Wiki, resolved-EM is 0.938 (vs. 0.865 full-pool) and on HotpotQA 0.4545 (vs. 0.1687)—given successful parsing and chaining, on-lattice execution is far above the end- to-end numbers. Appendix Table 12 puts the planner-attributable share of HotpotQA’s residual broken chains at 9.4%, and FRAMES’ oracle ceiling is only 4.9% (vs. EM 2.56%)—on neither boundary is the planner the main bottleneck, so repair investment shifts to the build layer (measured limits below). Query grounding refers to where the planner’s relation names come from when it lays out a chain—generated from thin air, chosen from a global vocabulary, or chosen from an entity’s in-lattice relation menu (Table 6). We have internalized L1 and L2 in the two boundary experiments respectively: the HotpotQA planner is injected with the global relation vocabulary; the FRAMES planner first queries which relations the seed entity actually has in the lattice and is restricted to that menu—relation names are thereby anchored to edges that genuinely exist on that entity. Yet both experiments show that L1/L2 remain insufficient, for structural reasons. The structural limitation is a circular dependency: static planning can, by construction, ground only the first hop—the intermediate entity of hop-푘(푘 ≥2) is unknown until hop-(푘−1)has executed, so its dimension menu is unavailable at planning time. The FRAMES chain-break dissection shows this directly: an intermediate entity typically already carries 64–129 dimensions in the lattice, yet the Yuze Ren, Shaoheng Fan, Tao Wang, Yabo Yan, and Han Han Table 7: Operating envelope (all numbers are frozen final values). DatasetKnowledge-source form Main bottleneckResult 2WikiMultihopQAOpen text extraction, templated questions —(home ground)EM 0.865 MetaQAKB triples mapped di- rectly Question parsing only any-hit 0.9975 HotpotQAOpen text extraction, free paragraphs Coverage gap (90.6%)EM 0.1687 MuSiQueOpen text extraction, 4-hop chains Chain deepening (48.3% hop-1 break) EM 0.0248 FRAMES(dev 푛= 742) Open text extraction, multi-hop+factuality Coverage gap+chain- design error EM 0.0256 IIRC(held-out 푛= 130) Open text extraction, incomplete informa- tion Answerability boundary Prec.mea- sure 0.9437 break-point relation (e.g.,nominate_for) is still absent—the break is a chain-design error (planning a relation the entity does not have), against which re-extraction is ineffective in principle: exactly the position L2 cannot reach and only L3 could. Why not adopt L3? Three lines of experimental evidence. (1) FRAMES has internalized L2, yet EM is still only 2.56%; a per-hop replanning pilot hits 0 of 15 questions—the intermediate entities of broken chains are simply not in the lattice (12 of 13 dissected cases), so replanning has nothing to choose from. (2) HotpotQA hop-2 oracle injection gives L3’s capability upper bound: placing the gold answer directly into the correct hop-2 dimension still fails to converge on 11 of 13 questions—the residual is an upstream coverage / landing-point problem that no L3-level improvement can address. (3) L3 requires one LLM call per hop, degrading the system to IRCoT-style iterative retrieval, which is incompatible with this paper’s “zero LLM on the answer path” positioning. HotpotQA re-extraction, measured (details in Appendix E): re- playing all formerly hop-1-broken questions (푛=1,509) under the frozen repaired configuration lifts first-hop connectivity to 78.9%, but only 21.9% of connected questions are ultimately answered correctly (bucket EM 0→17.3%); extrapolated to all first-hop gaps, full-pool EM gains only about +0.6p. A per-question residual de- composition rewrites the bottleneck from “choosing wrong among candidates” to “gold not in the returned set” (77% of resolved-but- wrong questions; returned sets average just 3.6 candidates). Funda- mental improvement requires changing the extraction mechanism itself; the IIRC value-cleaning repair (Section 8.2) has not been ap- plied here (future work). Table 7 summarizes the operating envelope with frozen final values. 8 Abstention as a First-Class Capability 8.1 IIRC: Abstention in Practice Traditional EM/F1 mixes questions on which the system should abstain with the answerable ones, hiding the cost of bluffing. We separate a recall measure (EM on answerable questions) from a preci- sion measure (abstain accuracy×(1−leak rate)), making “knowing when not to answer” reportable, ablatable, and regression-testable for the first time. IIRC questions are written by humans who cannot see the linked documents, so a substantial fraction is unanswerable in context (the none class). From the official dev split (1,301 ques- tions) we stratify by answer_type (seed 88) into a frozen held-out Table 8: IIRC main results (held-out푛=130; dev_tune as drift check). MetricHeld-out 130dev_tune 1,171 EM full (Phase-1-hit denominator)0.0417 (1/24)0.0264 (6/227) Recall measure (answerable EM)0.01050.0070 Resolved (Phase-1 hit rate)25.3% (24/95)26.4% Leak rate (none answered)0.029 (1/35)0.016 (5/312) Abstain accuracy0.971 (34/35)0.984 Precision measure (abstain× non-leak) 0.94370.9682 set (푛=130: span 59 / value 23 / binary 13 / none 35) and a tune pool (remaining 1,171; no model weights trained). The held-out set is tested once under the Phase-1 strict exact-only lattice-direct protocol—38 LLM calls, all query-side—and that run is the final score. Held-out and tune pool agree item by item (Table 8): zero drift. The single leak is a Phase-1 value-match false positive, not gener- ative hallucination. The 35 unanswerable questions split into 21 no_hit, 13 sentinel abstains, and 1 leak; the 93 answerable abstains split into 71 no_hit (39 in-grid / 32 not-in-grid) and 22 sentinel refusals (two-axis attribution: phase×gold-in-grid, Appendix Ta- ble 13). 8.2 Value Cleaning (Ablation) A dev-side ablation (IIRC dev푛=1,301, Phase-1 only, same pipeline; details in Appendix F) rewrites sentence-level dimension values into clean entities on the ingestion side: EM full rises 0.0156→ 0.0279 (+79%) and the leak rate falls 0.052→0.017 (−67%)—the leak reduction far exceeds the recall gain, a payoff only the two-measure separation can characterize. 8.3 Two Honest Boundaries (a) value boundary (IIRC dev 233 questions; held-out 23 all abstained or wrong): answers are 100% derived quantities whose anchors exist in the lattice only∼1.5% of the time—abstaining is correct (echoing Section 3.2). 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A FRAMES: Controlled Single-Variable Ablation—Locating the Failing Stage FRAMES (Krishna et al., 2025; factuality×multi-hop, 824 questions, each with gold evidence pages) is used here not as an additional, harder stress test but as a controlled single-variable ablation that separates two stages—whether the seed anchor lands in the lattice, and whether the chain semantics line up—to locate which stage the chain break actually occurs in. We apply a uniform 90/10 devel- opment/frozen split (seed 88): dev 742 questions for development, held-out 82 frozen and used for final testing only; construction is question-blind open extraction, with the LLM used only for query- side planning. Main results: dev EM=19/742 (2.56%), oracle diagnostic ceiling (gold falls in the candidate set; not the main EM measure) 36/742 (4.9%). The held-out 82 are reported under two settings: evidence- page-excluded construction gives EM=1/82 (F1=0.0521), evidence- page-included construction gives EM=1/82 (F1=0.1826)—the two EMs are identical (statistically inseparable), yet including the evi- dence pages lifts seed-entity resolution from 20.7% to 100% and the share of chain-walkable questions from 15% to 87%. This is the con- trolled single-variable conclusion of this appendix: adding the pages rescues the first stage (“does the anchor land”), while the bottleneck at the second stage (“does the chain line up”) is unchanged—so the failing stage is precisely located in chain semantics, not in extraction coverage. Three-line falsification chain: (1) after executor-layer fixes EM is flat, a net effect of zero; (2) a replanning pilot scores 0 hits on 15 questions — when the break is a coverage gap there is no alternative chain to take; (3) dissecting 13 questions from the targeted re- extraction candidate list, 12 have an intermediate entity that is simply not in the lattice (never landed as a lattice point), while in 4 control cases (where the entity has 64–129 dimensions in the lattice) the break-point relation still does not exist in its instance set— the break comes from the planner inventing a relation the entity does not have, a chain-design error against which re-extraction is ineffective in principle. The three lines jointly support Section 7.3. Capability strata: FACT_MEET / BOOL / EXTREME / COMPUTE, with the decision table in Appendix B. Transferable conclusion: filling coverage does not equal getting chains right—construction coverage is only a necessary condition, whereas chain-semantic alignment and chain landing-point precision (whether gold enters the returned set) are the bottleneck on the sufficient-condition side (in the same direction as the HotpotQA H2 oracle injection experiment). B Evaluation Protocol Details Measures: EM/F1 follow each benchmark’s official evaluation script, and F1* is this paper’s variant (defined in Section 5.4). Seed 88 throughout; the 90/10 split manifests are frozen as files (each bench- mark’s held-out manifest is on disk). LLM configuration: temp 0.0, context_size 32K (configurable), max_tokens 1280 (with automatic escalation to 2048 on truncation). The FRAMES capability-class decision table (FACT_MEET / BOOL / EXTREME / COMPUTE) is included in the supplementary material. C Prompt Templates The extraction prompt (hybrid extraction, A/B modes), the plan- ner prompt (including the KNOWN RELATIONS injection and the entity-menu variant), and the RAG baseline reader prompt are provided in full in the supplementary material. D Construction Statistics Per-domain scale (frozen final values): the 2Wiki dataset has 1.2M instances (125,760 passages); MetaQA has 19 dimensions / 269,482 instances (134,741 triples / 43,234 entities); the full MuSiQue lattice has 40,566 instances / 1,741 dimensions, and the held-out-only sublattice has 3,996 instances / 535 passages / 502 dimensions / 5,202 nodes; HotpotQA has 852 dimensions / 120,981 instances / 26,258 subject nodes; IIRC has 350 normalized dimensions / 6,768 instances. E HotpotQA Re-extraction Repair, Measured Can re-extracting the same corpus at the build layer (same open extractor) repair the coverage gap? Two small-scale experiments answer no. Hop-1 (푛=150): only 16 questions (10.7%) gain a gen- uine first-hop bridge in the lattice (an edge connecting the seed to the gold intermediate entity); and connectivity is not correctness— replaying all formerly hop-1-broken questions (푛=1,509) under the frozen configuration (re-extraction, relation mapping, and planner fixes included), the first-hop connectivity rate is 78.9%, 21.9% of con- nected questions are ultimately answered correctly (51.3% resolved), and the bucket’s EM rises from 0 to 17.3% — the repair works but has a clear ceiling; the rest either break at later hops or the answer never enters the returned set (landing points and value granularity). Extrapolating with the measured 10.7% bridge-recovery rate and 21.9% conversion, even re-extracting all 1,613 first-hop gaps would add only about +0.6p to full-pool (dev 6,664) EM, optimistically. Hop-2 (푛=36): conversion from re-extraction to a fully correct answer is only 5.6% (2/36; small푛, 95% confidence interval roughly 0.7%–18.9%). A per-question residual decomposition (diagnostic Meet, Compare, or Abstain: LatWeave for Deterministic Multi-Hop Question Answering on Knowledge Lattices statistics on the dev tune pool푛=6,664, held-out untouched) rewrites the bottleneck from “choosing wrong among candidates” to “gold not in the returned set”: among resolved-but-wrong ques- tions (푛=1,437), 77% have their gold answer outside the system’s returned candidate set at all—landing-point drift, coverage gaps, or extraction granularity; only about 11% have the gold’s content words fully inside the returned set (mostly as noisy long strings). This 77% is the residual after three repair paths—executor fixes (net-zero effect), per-hop replanning (0 of 15 hits), and re-extraction — have all been rejected; its magnitude corresponds to the true scale of the coverage gap on boundary datasets (Appendix Table 12), not an artifact of the evaluation protocol. Questions whose returned set contains two or more candidates account for only 9.3% (averaging just 3.6 candidates), and since the primary metric is any-hit (gold in the returned set counts as correct, Section 5.4), “choosing the wrong value among candidates” affects only a small share. F Value Cleaning Ablation (IIRC dev) An early version of open extraction poured whole sentences into di- mension values (value=sentence), causing two kinds of contamina- tion: on answerable questions value matching failed and depressed the recall measure, and on unanswerable questions sentence-level values were partially matched and triggered leaks. Value cleaning rewrites sentence values of entity-typed dimensions into clean en- tities on the ingestion side only, with no change to query or lattice logic: EM full rises from 0.0156 to 0.0279 (+79%), the leak rate falls from 0.052 to 0.017 (−67%), abstain accuracy rises from 0.948 to 0.983, and the precision measure rises from 0.899 to 0.966. The leak reduction far exceeds the recall gain—a payoff pattern that only the separation of the two measures can characterize, and direct evidence of the framework’s diagnostic value. G Additional Results Tables Tables 9–13 collect the supporting detail tables referenced from the main text: the approach-family positioning table, the 2Wiki- MultihopQA ablation, the MetaQA answer-set-size bucketing, the cross-dataset failure attribution matrix, and the per-question IIRC abstention attribution. natural-language question zero LLM calls LLM planner (replaceable front end) temp 0.0 · cacheable plans (oracle-plan ceiling, §7.3) typed plan (operator chain) deterministic execution on the lattice one of three states meet hit answer set (complete) compare verdict Boolean / extremum / full set abstain conflict or no support + reason deterministic functions of the lattice (§3.2) · answers carry evidence refusal comes from on-lattice execution — no external fallback Figure 4: Query-time flow. The LLM planner compiles the question into a typed plan; deterministic execution on the lattice returns a meet hit, a compare verdict, or abstain; the answer ships with its evidence text. Table 9: Positioning: only LatWeave ticks all four columns. Zero-training is graded because several families mix trained and training-free members (see footnotes). Detection (au- ditability) is graded because chunk-ID provenance yields engineering-level auditability only: the step from retrieved passage to answer remains unverifiable. Approach familyZero-trainDeterm.Audit.Abstain Neural multi-hop retriev- ers partial 1 × RAG / GraphRAGpartial 2 ×eng.-level × KBQA / semantic parsing × 3 ✓× Selective prediction× 4 —×prob. thresh. LatWeave (this work)✓ 1 MDR and Beam Retrieval train in-task retrievers; IRCoT and HopRAG are training-free (LLMs in the loop). 2 Self-RAG and RoG fine-tune; FLARE, GraphRAG, HippoRAG 2 and KAG [25] are training-free. KAG further compiles questions into logical forms for hybrid reasoning, yet the final answer is still LLM-synthesized. Causality-aware recalibration of KG-RAG confidence [32] is likewise training-free, yet it calibrates a probabilistic answer generator rather than removing one. Self-RAG and FLARE gate whether to retrieve, not whether to answer: the model still generates an answer, so they provide no abstention mechanism (cf. Section 2.4, where selective prediction does, but via confidence thresholds). 3 Exception: LLM-planned BFS over a given KG [34] needs no task training (Section 2.3). Schema-free KG construction from text [3] relaxes the predefined schema, but its query side is probabilistic retrieval over the induced graph, not deterministic execution. 4 Requires a trained selector or held-out calibration; conformal risk control calibrates the abstention threshold distribution-free (removing calibration drift) [1], yet abstention remains a thresholding operation and the underlying answer generator remains probabilistic. Trained refusal rules can also be tuned to abstain, but such a refusal is a learned probabilistic decision, not a structural guarantee that can be audited independently of the model. hop 1hop 2hop 3 0.0 0.1 0.2 0.3 0.4 0.5 P(correct | reached hop k) 0.37 0.20 0.43 0.22 0.02 (n=64) 0.44 0.09 0.00 (n=15) MuSiQue tune (n=2,175), first-error-stop n=1127n=419n=684n=293n=364n=159 2-hop (n=1,127) 3-hop (n=684) 4-hop (n=364) Figure 5: Per-hop conditional meet accuracy푃(correct | chain reaches hop 푘)on the MuSiQue tune pool (푛=2,175), grouped by the question’s true depth. Table 10: 2WikiMultihopQA ablation (dev tune pool, histori- cal protocol 푛= 11,318). ConfigurationEMResolved Full system0.87392.0% − train gold transfer (dev-only)0.73185.3% − alias normalization0.85390.8% − rule-based re-extraction (E15)0.84390.4% The full system, replayed after domain rebuild (grid-point hash dedup, 1.2M instances), gives tune-pool EM 0.886 / held-out 0.865; the remaining rows are historical-protocol ablation values. Yuze Ren, Shaoheng Fan, Tao Wang, Yabo Yan, and Han Han Table 11: MetaQA test bucketed by gold answer-set size (com- pleteness structural analysis). |퐴 ∗ | 푛any-hitrecall (complete)EM (strict) 114,8340.99740.99740.8332 25,7290.99770.99770.7413 3–57,2770.99740.99680.6442 6–104,0410.99680.99680.5494 ≥117,2120.99780.99760.3788 All39,0930.99750.99730.6714 Table 12: Failure attribution matrix. DatasetAttributionCount (share) HotpotQAExtraction coverage gap667/736 (90.6%) (residual broken chains) H1 missing / H2 missing / seed no-out-edge 527 / 81 / 59 Query-layer planner69/736 (9.4%) MuSiQueBreak at hop 1117/242 (48.3%) (chain-break locus) Break at hop 281/242 (33.5%) Break at hop 3 / hop 416 / 4 (6.6% / 1.7%) Chain survives (resolved-no- break: 6 correct / 18 wrong) 24/242 (9.9%) FRAMES (dev푛= 742) Coverage gap compounded by chain-design error 12/13 dissected: in- termediateentity off-lattice Table 13: IIRC held-out abstention attribution on two axes (phase×gold-in-grid), per-question reproducible (푛=130). The in-grid probe applies only to answerable questions— unanswerable ones have no gold answer by construction. The 22 answerable sentinel abstains split evenly (11 in-grid / 11 not-in-grid). The broken-chain bucket is empty by design on IIRC: this arm is Phase-1 exact-only single-value mapping with no multi-hop chain to break (chain-break attribution belongs to Section 7.1). A dev-scale isomorphic analysis (954 answerable questions, older grid convention) gives the same proportional structure. Question class PhaseDispositionNone (푛=35) Answerable (푛=95) Phase-1 hit answered correct—1 answered wrong—1 sentinel abstain1322 no_hit gold in grid (“not met”)n/a39 gold not in grid (“never extracted”)n/a32 subtotal2171 Leak (vacuous pass)1— Total3595 H Auditability and Material Availability To ensure reproducibility and auditability, we provide, with the supplementary material, all prompt templates (Appendix C), the held-out split manifests, per-question evaluation details, and the failure-attribution probe results, so that the numbers on all six benchmarks can be independently recomputed under this paper’s evaluation protocol; because the system implementation involves industrial deployment, the source code is not part of the supple- mentary material.

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