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Relevance Is Not Sufficiency: What Actually Closes the Evidence Gap in Long-Term Memory QA

Yufeng Li, Shuxin Li, Zhenhua Xu, Junxian Li, Peng Zeng, Sheng Yao, Changting Lin, Gaolei Li, Ran Bi, Meng Han

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

Intelligence

Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 94%

Last extracted: 10/8/2026, 7:34:54 AM

Summary

The paper introduces Budgeted Flat Reconstruction (BFR), a two-stage framework for long-term memory QA in LLM agents. It addresses the 'evidence gap' where relevance-based retrieval fails to provide sufficient information by combining Formal Concept Analysis for Memory Selection (FCA-MS) to compose complementary evidence and a budgeted multi-view search to complete missing support.

Entities (11)

Budgeted Flat Reconstruction · method · 98%LoCoMo · dataset · 97%LongMemEval-S · dataset · 97%East China Normal University · organization · 95%Formal Concept Analysis for Memory Selection · algorithm · 95%Yufeng Li · person · 95%Gold Hit · metric · 92%LLM-Suff@Set · metric · 92%Turn Hit · metric · 92%A-MEM · system · 90%Mem0 · system · 90%

Relation Signals (6)

Budgeted Flat Reconstruction → evaluatedon → LongMemEval-S

confidence 97% · Experiments on LoCoMo and LongMemEval-S show that BFR outperforms same-store adaptations of recent agent-memory systems in both answer quality and evidence coverage.

Budgeted Flat Reconstruction → evaluatedon → LoCoMo

confidence 97% · Experiments on LoCoMo and LongMemEval-S show that BFR outperforms same-store adaptations of recent agent-memory systems in both answer quality and evidence coverage.

Yufeng Li → affiliatedwith → East China Normal University

confidence 95% · Affiliation: East China Normal University, Shanghai, China

Budgeted Flat Reconstruction → uses → Formal Concept Analysis for Memory Selection

confidence 95% · Specifically, we first apply Formal Concept Analysis for Memory Selection (FCA-MS) to decompose the question into information requirements and select a compact candidate subset that jointly covers them.

Budgeted Flat Reconstruction → outperforms → Mem0

confidence 90% · Experiments on LoCoMo and LongMemEval-S show that BFR outperforms same-store adaptations of recent agent-memory systems

Budgeted Flat Reconstruction → outperforms → A-MEM

confidence 90% · Experiments on LoCoMo and LongMemEval-S show that BFR outperforms same-store adaptations of recent agent-memory systems

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Abstract

Abstract:LLM agents that interact with a user across many sessions accumulate histories that exceed their context window, so they store past interactions in an external memory and answer each question from a small set of retrieved records. Existing memory systems rank records by lexical or embedding relevance, yet the top-ranked memories can each be relevant while jointly omitting a complementary fact that the answer requires, especially for multi-session and temporal questions. Drawing on the distinction between relevance and sufficiency in legal evidence scholarship, we recast memory retrieval as constructing a sufficient memory set. To operationalize this view, we introduce a blinded LLM judgment over the retrieved set, together with Gold Hit and Turn Hit as evidence-coverage proxies. We then propose Budgeted Flat Reconstruction (BFR), which builds sufficient sets over a fixed flat memory store in two stages. Specifically, we first apply Formal Concept Analysis for Memory Selection (FCA-MS) to decompose the question into information requirements and select a compact candidate subset that jointly covers them. Then, we repeatedly acquire unseen records through deeper text search or complementary entity and session views, stopping when the budget is exhausted. Experiments on LoCoMo and LongMemEval-S show that BFR outperforms same-store adaptations of recent agent-memory systems in both answer quality and evidence coverage. Specifically, on LongMemEval-S it raises judged accuracy from 72.4% to 82.2% and Turn Hit to 91.4%.

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Relevance Is Not Sufficiency: What Actually Closes the Evidence Gap in Long-Term Memory QA Yufeng Li †thanks: Yufeng Li and Shuxin Li contributed equally. Emails: yufeng03@stu.ecnu.edu.cn and shuxin.li@ntu.edu.sg. Affiliation: East China Normal University, Shanghai, China Shuxin Li11footnotemark: 1 Affiliation: Nanyang Technological University, Singapore Zhenhua Xu Affiliation: Zhejiang University, Hangzhou, China Junxian Li Peng Zeng †thanks: Corresponding author. Email: pzeng@sei.ecnu.edu.cn. Affiliation: East China Normal University, Shanghai, China Affiliation: Shanghai Jiao Tong University, Shanghai, China Sheng Yao Affiliation: University of Southern California, Los Angeles, USA Changting Lin Affiliation: Zhejiang University, Hangzhou, China Gaolei Li Affiliation: Shanghai Jiao Tong University, Shanghai, China Ran Bi Affiliation: Northeastern University, Shenyang, China Meng Han Affiliation: Zhejiang University, Hangzhou, China Abstract LLM agents that interact with a user across many sessions accumulate histories that exceed their context window, so they store past interactions in an external memory and answer each question from a small set of retrieved records. Existing memory systems rank records by lexical or embedding relevance, yet the top-ranked memories can each be relevant while jointly omitting a complementary fact that the answer requires, especially for multi-session and temporal questions. Drawing on the distinction between relevance and sufficiency in legal evidence scholarship, we recast memory retrieval as constructing a sufficient memory set. To operationalize this view, we introduce a blinded LLM judgment over the retrieved set, together with Gold Hit and Turn Hit as evidence-coverage proxies. We then propose Budgeted Flat Reconstruction (BFR), which builds sufficient sets over a fixed flat memory store in two stages. Specifically, we first apply Formal Concept Analysis for Memory Selection (FCA-MS) to decompose the question into information requirements and select a compact candidate subset that jointly covers them. Then, we repeatedly acquire unseen records through deeper text search or complementary entity and session views, stopping when the budget is exhausted. Experiments on LoCoMo and LongMemEval-S show that BFR outperforms same-store adaptations of recent agent-memory systems in both answer quality and evidence coverage. Specifically, on LongMemEval-S it raises judged accuracy from 72.4% to 82.2% and Turn Hit to 91.4%. Code is available at: GitHub. 1 Introduction LLM agents interact with users across many sessions, accumulating preferences, events, and other information that may matter much later (Zhong et al., 2024; Maharana et al., 2024; Wu et al., 2025; Tan et al., 2025). Because the full interaction history is too long to remain in the context window (Packer et al., 2023), these agents commonly rely on external memory to retain and access past information. Agent memory has therefore become an important component for maintaining continuity across conversations and answering questions about earlier interactions. Recent agent-memory systems improve answer quality by designing how memories are represented and retrieved. For example, Mem0 distills conversations into salient facts, consolidates them over time, and retrieves them by embedding similarity (Chhikara et al., 2025). A-Mem instead maintains evolving, interlinked notes retrieved in the same way (Xu et al., 2025). CoM builds coherent memory chains from relevance-ranked candidates (Xu et al., 2026), while MRAgent reasons over a Cue–Tag–Content graph (Ji et al., 2026; Hu et al., 2025; Luo et al., 2026). Despite their different memory structures, these systems typically acquire candidates by relevance, whether through lexical matching, embedding similarity, or guided traversal (Zhang et al., 2025). Yet relevance is a property of each record, not of the set, i.e., a ranking can return several memories about the right topic while the one partner fact the answer requires falls below the cutoff. It means that retrieving relevant memories does not by itself ensure that the resulting set can support the answer. This raises a question: what determines whether the retrieved records made available to an agent support a correct answer? Legal evidence scholarship offers a useful distinction: relevance concerns whether an individual item bears on a claim, whereas sufficiency concerns whether the evidence considered together supports a finding (Lempert, 1986; Pardo, 2023). We apply this distinction to memory QA and ask whether the retrieved memories, taken together, contain enough information to determine the answer. Figure 1 illustrates this failure with a real LongMemEval-S case. The question asks how many days a remote shutter release took to arrive, which requires two records together: the February 5 order and the February 10 arrival. The top-k retrieved memories include the order alongside other photography-related records, but the arrival, a less similar record from another session, falls below the cutoff. The agent then responds about selling an old tripod instead of the five-day interval. This example shows that individually relevant records do not guarantee a sufficient set. Figure 1: A real error: relevant but insufficient records. The question asks how many days the remote shutter release took to arrive. Relevance ranking returns Key evidence 1 together with other photography memories, while Key evidence 2 falls below the top-k cutoff. We therefore recast memory retrieval as the construction of a sufficient memory set, one from which the answer can be determined. Constructing such a set raises two coupled challenges. First, a set must bring together complementary facts. A question may depend on several pieces of information, and a limited context budget can be spent on records that repeat one piece while leaving another uncovered. Second, the necessary facts must be reachable. Evidence missing from the initial candidate pool cannot be recovered by improving selection within that pool. Both challenges must be met without knowing which records are required. At inference time, no oracle declares a set sufficient, so a method must itself decide how far to search and when to stop. To address both challenges, we propose Budgeted Flat Reconstruction (BFR), a two-stage, requirement-aware framework that assembles answer-supporting evidence over a flat memory store under a fixed retrieval budget. Specifically, at Stage I, Formal Concept Analysis for Memory Selection (FCA-MS) first decomposes the question into answer requirements, and then applies an FCA-based prefilter followed by LLM selection of a compact, complementary subset. These selected candidates are grounded to source records to form the initial evidence set. At Stage I, we acquire further supporting evidence from the current evidence set, excluding records already obtained and accumulating new support within a fixed retrieval budget. We instantiate this stage with two schedules: Budgeted Flat Reconstruction with Text Access (BFR-Text) extends text retrieval, and Budgeted Flat Reconstruction with Multi-View Access (BFR-MV) combines text, entity, and session views. Stage I thus composes the evidence already present among the candidates, Stage I reaches evidence beyond them, and the fixed budget supplies a stopping rule that does not presume sufficiency can be recognized. Finally, we evaluate BFR on LoCoMo and LongMemEval-S under protocols that hold the memory store, answerer, and judge fixed within each benchmark. Extensive results show that BFR improves judged answer quality and annotated evidence coverage over same-store baselines. On LongMemEval-S, it raises judged accuracy from 72.4%72.4\% to 82.2%82.2\% and attains a 91.4%91.4\% Turn Hit. In summary, this paper makes three contributions: (i) We formulate memory retrieval as the construction of a sufficient memory set and make set-level sufficiency measurable: LLM-Suff@Set judges whether a retrieved set supports the answer, while Gold Hit and Turn Hit track coverage of annotated answer-bearing evidence. (i) We propose BFR, a two-stage method for building sufficient sets over a flat memory. Its two stages recover complementary evidence missing within and beyond the initial candidates. (i) We conduct extensive experiments on LoCoMo and LongMemEval-S. These results show that BFR improves answer quality and evidence coverage, and identify where additional evidence is recovered and clarify the distinct roles of evidence composition and acquisition. 2 Related Work Evidence relevance and sufficiency. Evidence scholarship treats relevance as a property of an item’s bearing on a claim and sufficiency as a judgment over the complete evidentiary record (Pardo, 2023). In RAG, sufficient-context evaluation uses this distinction diagnostically, separating failures caused by missing context from failures to use available context (Joren et al., 2025). We bring this distinction to long-term agent memory and make it constructive: rather than diagnosing whether a retrieved set was sufficient, retrieval should assemble and complete the evidence set that supports an answer. Appendix A spells out the mapping from Pardo’s record-level test to our method. Memory construction and relevance-based access. Memory systems increasingly transform interaction history before retrieval. Mem0 maintains salient facts through add, update, and delete operations and retrieves semantically similar memories (Chhikara et al., 2025). A-Mem creates evolving linked notes but still answers from a top-k similarity-ranked subset (Xu et al., 2025). Zep represents temporal validity in a bi-temporal graph (Rasmussen et al., 2025); MemoryOS uses hierarchical storage (Kang et al., 2025); and SeCom segments conversations into coherent units (Pan et al., 2025). CoM improves post-retrieval organization by growing chains from top-ranked anchors according to query relevance and contextual consistency (Xu et al., 2026). MRAgent applies active reconstruction on a Cue–Tag–Content memory graph, allowing an LLM to choose retrieval tools from accumulated evidence (Ji et al., 2026). These systems improve what can be retrieved or how relevant candidates are organized. BFR instead asks whether the resulting set covers all answer requirements, then acquires missing support without changing the underlying store. 3 WHAT COUNTS AS A SUFFICIENT CANDIDATE MEMORY SET Motivation. Similarity search can return several memories about the right topic while missing the fact that makes an answer possible. In figure 1, the retrieved records include the shutter-release order and other photography-related memories, but not the arrival date. The records are relevant to the question; together they cannot establish the delivery interval. Legal evidence scholarship makes the same item-versus-set distinction: an item can bear on a claim without the assembled record being sufficient to support a finding (Lempert, 1986; Pardo, 2023) (Appendix A). For memory QA, the practical difficulty is twofold. Relevant candidates may repeat one part of the answer instead of supplying complementary facts, and a necessary fact may fall outside the initial candidate pool even when it remains in the memory store. Figure 2 illustrates why a memory system must address both the composition of the retrieved set and access to evidence beyond the first retrieval boundary. Figure 2: Similarity top-k vs. set-level sufficiency. (a) Prior memory architectures rank records by query similarity and return the top-k slice. (b) BFR returns a sufficient set over the flat store: it first selects complementary records that jointly cover the question’s requirements, then completes missing support under a budget by adding unseen records through text, entity, and session views. Quantifying candidate-set sufficiency. Let q be a question, y⋆(q)y (q) its reference answer, ℳM a fixed memory store, and E⊆ℳE the retrieved candidate set. We write text⁡(E)text(E) for the evidence text rendered from E and src⁡(E)src(E) for the set of source-record or source-turn identifiers linked to E. As usual, [P]1[P] equals 11 when proposition P holds and 00 otherwise. The ideal set-level property is S⁡(q,E)=[y⋆(q) is determinable from q and text⁡(E)].S(q,E)=1\! [y (q) is determinable from q and text(E) ]. (1) Thus, S⁡(q,E)S(q,E) concerns what the evidence makes answerable, independently of whether a particular answerer generates the correct response. To assess this property offline, let a⁡(q,E)a(q,E) be the final decided label from a blinded, reference-conditioned LLM adjudication given q, y⋆(q)y (q), and text⁡(E)text(E) (Appendix M), with a⁡(q,E)∈sufficient,insufficienta(q,E)∈\sufficient,insufficient\. We define LLM-Suff@Set by S^LLM(q,E)=[a(q,E)=sufficient]. S_LLM(q,E)=1\! [a(q,E)=sufficient ]. (2) Here, S^LLM(q,E) S_LLM(q,E) is the operational, reference-conditioned assessment of joint answer support. It is undefined when adjudication is uncertain or missing; such cases are excluded from the reported rate rather than counted as insufficient. For questions with annotated supporting records, let ⁡(q)G(q) be their nonempty set of source identifiers and ℋ⁡(q)H(q) be their set of annotated source-turn identifiers, which may be empty. Gold Hit and Turn Hit are defined as follows: G⁡(q,E) G(q,E) =[src(E)∩(q)≠∅] =1\! [src(E) (q)≠ ] (3) TH⁡(q,E) (q,E) =[src(E)∩ℋ(q)≠∅] =1\! [src(E) (q)≠ ] (4) The value G⁡(q,E)G(q,E) is 11 if E reaches at least one annotated supporting record; it does not require retrieval of every supporting record. Gold Hit is undefined when ⁡(q)=∅G(q)= and is averaged over questions with nonempty supporting-record annotations. The value TH⁡(q,E)TH(q,E) is 11 if E reaches at least one annotated answer-bearing turn. Our main LongMemEval-S results average Turn Hit over all 500500 questions. These proxies measure whether annotated evidence was reached, not whether the set suffices. In Table 1, each singleton has Gold Hit 11, and the arrival alone has Turn Hit 11. Neither yields the five-day answer, but together they do. A hit is therefore necessary for sufficiency but does not establish it, which is why we report the proxies alongside, not in place of, the set-level judgment. Table 1: Illustrative delivery-time question. Both dates are required to derive the five-day answer. Retrieved evidence LLM-Suff@Set Gold Hit Turn Hit Order only (Feb. 5) 0 1 0 Arrival only (Feb. 10) 0 1 1 Order + arrival 1 1 1 4 BFR: Composing and Completing Sufficient Evidence 4.1 Problem: construct a sufficient set under a retrieval budget Let ℳ=m1,…,mNM=\m_1,…,m_N\ be a fixed memory store, q a question, and y⋆y its reference answer. An access policy constructs E⊆ℳE , after which the fixed answerer f emits y^=f⁡(q,E) y=f(q,E). The set-level sufficiency property S⁡(q,E)S(q,E) is defined in Section 3. Holding ℳM and f fixed, the construction problem is to maximize expected sufficiency under a retrieval-call budget B: maxπ⁡[S⁡(q,ET)]s.t.Cret(π,q)≤B. _π\ E\! [S(q,E_T) ] .t. C_ret(π,q)≤ B. (5) A one-shot reader returns E=TopK⁡(q,ℳ)E=TopK(q,M) and cannot recover once a required exhibit is missing. Budgeted reconstruction instead starts from an initial set E0E_0 and adds only unseen records, Et+1=Et∪Kt,Kt⊆ℳ∖Et.E_t+1=E_t∪ K_t, K_t E_t. (6) Equation 5 is the problem. The two gaps in Section 3 say what a solution must do. Composition chooses E0E_0 so that distinct answer requirements are covered rather than redundant relevant items. Completion chooses each KtK_t so that a missing exhibit can still enter the record after the first page. BFR assigns one stage to each gap. Let ℳ~ M be an agent-memory note representation and ϕφ a grounding map into ℳM. Stage I builds E0E_0 with FCA-MS and Stage I runs a completion schedule π: E0 E_0 =ϕ⁡(ρFCA(q,ℳ~)), =φ\! ( _FCA(q, M) ), (7) At A_t =π⁡(q,Et,t), =π(q,E_t,t), Et+1 E_t+1 =Et∪κπ(q,Et,Ct),t<T. =E_t∪ _π(q,E_t,C_t), t<T. AtA_t names the retrieval views and cues at round t, CtC_t is the unseen candidate pool those calls return, and κπ _π retains added records. The answerer reads ETE_T after the budget is spent. Figure 3 makes this data flow explicit. Stage I asks the agent memory system for an expanded candidate pool beyond its usual top-k, decomposes the query into requirements, filters the pool by requirement-aware FCA, and asks an LLM to select a compact supporting subset. A bounded grounding map then supplies the initial source-record evidence E0E_0. Stage I treats this set as a cumulative evidence state, retrieves through the views specified by π, removes records already in EtE_t, and retains novel support until an observable budget is exhausted. The figure instantiates this loop with BFR-MV; BFR-Text uses the same exclusion, retention, accumulation, and stopping operations with text access only. Appendix A records how S, R, ℛqR_q, and the two stages correspond to Pardo’s item/record distinction. Figure 3: The two-stage evidence-construction pipeline in BFR. Stage I (FCA-MS) retrieves a candidate pool larger than the usual top-k, decomposes the query into answer requirements, prefilters candidates with FCA, and has an LLM select a compact subset that jointly covers the requirements. The selected candidates are mapped to source records to form E0E_0. Stage I (shown for BFR-MV instantiation) completes the set under a fixed budget: text, entity, and session access retrieve unseen records. Only new records are accumulated into Et+1E_t+1 until the budget is exhausted. The comprehensive evidence set returns to Agent, and Agent answers the question based on the set. 4.2 Stage I: Compose complementary evidence with FCA-MS Expanded retrieval and requirement decomposition. An agent memory system returns an ordered pool q=TopN⁡(Retrieveagent⁡(q,ℳ~))C_q=TopN(Retrieve_agent(q, M)), with N>kN>k relative to its usual top-k retrieval cutoff. An LLM decomposes q into answer-oriented requirements ℛq=rjj=1JR_q=\r_j\_j=1^J, including distinct facts, bridges, list items, and temporal constraints. Requirement-aware prefilter. An FCA-based prefilter uses the requirements and retrieved candidates to retain a smaller pool q=FCAPrefilter⁡(ℛq,q)P_q=FCAPrefilter(R_q,C_q). This step exposes a broader range of potentially complementary notes to the selector while bounding its input. Minimum-subset selection and grounding. An LLM receives q and qP_q and is instructed to select the smallest memory subset that jointly supplies the required information. Its selected IDs are checked against the prefiltered pool and deduplicated; the implementation uses requirement-coverage output and a fixed fallback if the valid subset is empty (Appendix E). Only the resulting selected notes S are grounded to source turns by ϕφ to produce E0⊆ℳE_0 ; the retriever’s initial top-k is a reference cutoff, not a retained base set. This stage improves requirement coverage within the initial candidate pool but remains bounded by that pool. A required record can therefore be absent from E0E_0 even when E0E_0 already contains several records related to the question. Stage I treats this remaining gap as an acquisition problem instead of reselecting repeatedly from the same pool. Algorithm 1 in Appendix D summarizes the selection and grounding steps. 4.3 Stage I: Complete missing support under a budget Multi-view access to one fixed store. Text, entity, and session indices provide different access paths to the same source-grounded records in ℳM. At round t, each action a=(v,c)∈Ata=(v,c)∈ A_t specifies a view v and a cue c. The retrievers exclude all records already contained in EtE_t: Ct=Unique⁡(⋃(v,c)∈AtRv(c,ℳ∖Et)).C_t=Unique\! ( _(v,c)∈ A_tR_v(c,M E_t) ). (8) The exclusion constraint makes acquisition cumulative and duplicate-free. The retention rule κπ _π ranks the returned records by relevance and by novelty with respect to the current set, keeps at most kkeepk_keep of them, and adds them to EtE_t by set union. Consequently, each round either extends the reachable evidence or leaves the set unchanged. Budgeted stopping. The budget B=(Bstep,Bcall,Bnew)B=(B_step,B_call,B_new) limits the number of rounds, retrieval calls, and newly retained records. The main configuration allows three rounds, six calls, and 3030 new records. We use budget exhaustion as the stopping condition because the offline sufficiency measures in Section 3 require either a reference answer or gold annotations and are therefore unavailable at inference time. Algorithm 2 in Appendix D gives the shared completion loop; the fixed schedules differ only in how they instantiate AtA_t. 4.4 Access schedules for completion The shared completion loop admits two fixed schedules for the two ways required support can remain outside E0E_0. They share FCA-MS, ℳM, the exclusion rule, the budget, and the answerer; only the allocation of retrieval calls changes. We also evaluate state-conditioned completion as a controlled variant of Stage I; its settings and results are reported in Section 5.2 and Appendix I. BFR-Text: deepen the text ranking. Each round queries the text index with the original question q, removes ids already in EtE_t, and keeps the first kkeep=8k_keep=8 unseen hits. Repeating the same query advances beyond the initial page without query rewriting. This schedule targets cases in which the missing evidence is relevant to q but appears below the first cutoff. BFR-MV: diversify the access path. The multi-view schedule issues text, entity, and session actions in a fixed order. The text action uses q; the entity action uses the first person named in q when available; the session action uses the latest retained record as an anchor. Entity and session access can recover records that do not rank highly under the full question string. 5 Experiments In this section, we conduct controlled experiments to evaluate BFR and answer four research questions: (RQ1) How does BFR compare with same-store memory baselines in answer quality? (RQ2) Do retrieved sets contain sufficient evidence to answer the question, and how does direct sufficiency compare with annotated-support hits? (RQ3) How do the two stages and access schedules contribute to performance? (RQ4) How do answer quality and evidence coverage change with additional retrieval cost? The appendix reports full operating-point, question-type, and cross-system results. 5.1 Experimental setup Datasets. We evaluate on two benchmarks for long-term conversational memory. LoCoMo (Maharana et al., 2024) tests understanding of long, multi-session conversations, including questions that require linking information across turns. LongMemEval-S (Wu et al., 2025) tests whether a memory system can answer questions about information distributed across extended interaction histories and sessions. Both provide evidence annotations, allowing us to assess retrieval as well as final answers. To keep multi-arm evaluation costs manageable, we use a fixed stratified 200200-question LoCoMo development subset; we evaluate all 500500 questions of LongMemEval-S. Dataset provenance and the construction of every derived evaluation subset are documented in Appendix G. Baselines. We evaluate BFR against four representative memory-augmented baselines: Mem0 (Chhikara et al., 2025), A-Mem (Xu et al., 2025), CoM∗ (Xu et al., 2026), and MRAgent-Flat∗ (Ji et al., 2026). Within each benchmark, all arms share the same flat turn store, extractive answerer, and answer judge. The starred methods are controlled same-store adaptations of the published systems. Baseline retrieval and BFR initialization are detailed in Appendix E. Metrics. Answer quality is measured by Porter stem F1 and LLM-Judge (J) on LoCoMo, and by Judge on LongMemEval-S. The answer judge is gpt-5.5 at temperature zero with prompt mem0_accuracy_v1. On LoCoMo, ⁡(q)G(q) is the released set of supporting-record identifiers. We report the sufficiency indicators in Section 3 and two finer measures of annotated-evidence recovery: ER(q,E)=|src⁡(E)∩⁡(q)||⁡(q)|,CER(q,E)=[(q)⊆src(E)].ER(q,E)= |src(E) (q)||G(q)|, (q,E)=1[G(q) (E)]. (9) Evidence Recall (ER) is the fraction of annotated supporting records in ⁡(q)G(q) that E recovers, while Complete Evidence Recall (CER) requires every annotated supporting record. On LongMemEval-S, ℋ⁡(q)H(q) comprises turns marked has_answer; Turn Hit measures whether the retrieved set reaches one. These retrieval and set-level measures complement rather than replace end-to-end answer scores. Prompts are listed in Appendix O. 5.2 Experimental Result RQ1: Does BFR improve answer quality under the same memory store? Table 2: Performance across different question types on LoCoMo (n=200n=200). Same flat store and extractive answerer; BFR is BFR-MV C6. F1 and LLM-Judge (J) are percentages. Bold denotes the best value in each column. Method Multi-Hop Temporal Open Domain Single-Hop Overall F1 J F1 J F1 J F1 J F1 J Mem0 (Chhikara et al., 2025) 29.3 42.4 74.1 78.0 2.2 0.0 58.5 59.6 55.3 59.0 A-Mem (Xu et al., 2025) 32.3 42.4 70.2 72.0 3.8 0.0 47.1 51.4 48.7 53.0 CoM∗ (Xu et al., 2026) 29.3 36.4 66.2 70.0 3.2 0.0 52.3 56.0 50.0 54.0 MRAgent-Flat∗ (Ji et al., 2026) 32.8 45.5 72.1 78.0 2.9 0.0 63.2 68.8 58.0 64.5 BFR (ours) 44.6 48.5 78.1 80.0 2.7 12.5 75.7 77.1 68.3 70.5 Table 3: Performance across different question types on LongMemEval-S (n=500n=500). The four question-type columns report Judge accuracy; All values are percentages. All rows share the same turn store, extractive answerer, and judge. Bold and underline denote the best and second-best values in each column. The full six-type Turn Hit breakdown is in Appendix K. Judge by question type Overall Method Multi-S Single-S Temporal Preference Judge Turn Hit Mem0 (Chhikara et al., 2025) 60.9 87.1 65.4 26.7 72.4 64.8 A-Mem (Xu et al., 2025) 54.1 87.1 57.1 33.3 68.6 82.2 CoM ∗(Xu et al., 2026) 54.1 87.1 57.1 33.3 68.6 80.6 MRAgent-Flat∗ (Ji et al., 2026) 58.6 90.0 63.2 30.0 71.4 78.8 BFR (ours) 69.2 92.9 84.2 30.0 82.2 91.4 BFR achieves the best overall answer quality among same-store methods on both benchmarks (Table 2, Table 3). On LoCoMo, it leads in Stem F1 and Judge across Multi-Hop, Temporal, and Single-Hop questions. On LongMemEval-S, it also leads in overall Judge and Turn Hit, with a particularly strong gain on Temporal questions. The small LoCoMo Open Domain slice is reported without a separate type-level conclusion. These results are consistent with the two-stage design: FCA-MS assembles complementary initial evidence, and budgeted completion retrieves unseen support beyond the initial set. The following analyses test whether this support closes evidence gaps and how stage, access schedule, and budget contribute. Paired same-store comparisons and the separate comparison with CoM and Full-MRAgent are in Appendix H and Appendix C, respectively. Table 4: Set sufficiency and annotated-evidence reach across same-store systems. On LoCoMo (n=200n=200), LLM-Suff@Set is the blinded set-level judgment and Gold Hit measures annotated-evidence access. On LongMemEval-S, LLM-Suff@Set is the set-level judgment and Turn Hit measures annotated-evidence access over all 500500 questions, with unannotated items counted as misses. All values are percentages. BFR-Text uses C3 and BFR-MV uses C6. System LoCoMo (n=200n=200) LongMemEval-S (n=500n=500) LLM-Suff@Set Gold Hit LLM-Suff@Set Turn Hit Mem0 (Chhikara et al., 2025) 45.5% 57.0% 48.0% 64.8% A-Mem (Xu et al., 2025) 36.5% 50.0% 38.0% 82.2% CoM∗ (Xu et al., 2026) 44.0% 49.0% 49.0% 80.6% MRAgent-Flat∗ (Ji et al., 2026) 54.5% 62.5% 56.0% 78.8% FCA-MS (Stage I Only) 42.5% 51.0% 48.0% 85.0% BFR-Text 62.0% 72.5% 63.0% 88.6% BFR-MV 63.5% 73.5% 65.0% 91.4% Table 5: Where budgeted completion closes the evidence gap on LoCoMo (n=200n=200). CER is Complete Evidence Recall; LLM-Suff@Set is the blinded set-level judgment. Text and MV denote BFR-Text at C3 and BFR-MV at C6, with mean realized calls of 3.003.00 and 5.995.99; FCA-MS uses no completion calls. Open Domain contains only eight questions and is interpreted descriptively. Question type n FCA-MS BFR-Text BFR-MV CER LLM-Suff@Set CER LLM-Suff@Set CER LLM-Suff@Set Multi-Hop 33 6.1 15.2 18.2 27.3 12.1 30.3 Temporal 50 66.0 60.0 82.0 74.0 82.0 74.0 Open Domain 8 12.5 0.0 12.5 0.0 25.0 0.0 Single-Hop 109 41.3 45.9 71.6 71.6 70.6 73.4 Overall 200 40.5 42.5 63.0 62.0 62.0 63.5 RQ2: Do the retrieved sets contain the evidence needed for an answer? Table 6: Stage and access-schedule ablation. Configuration LoCoMo LongMemEval-S F1 J J TH FCA-MS 48.6 53.5 70.4 85.0 FCA-MS w/ BFR-Text 67.8 70.0 81.6 88.6 FCA-MS w/ BFR-MV 68.3 70.5 82.2 91.4 BFR achieves the highest observed LLM-Suff@Set on both benchmarks among the compared same-store systems (Table 4). Under the main budget configuration, both completion schedules exceed FCA-MS alone and all baselines on set-level sufficiency and annotated-evidence coverage, with BFR-MV highest on every measure. Since FCA-MS alone trails both schedules, the gain comes from completing the initial set beyond its candidate pool rather than from selection within it. Table 5 further shows that completion improves complete recovery of annotated evidence on LoCoMo. However, the two measures rank the schedules differently: BFR-Text has higher overall CER, whereas BFR-MV has higher LLM-Suff@Set. On LongMemEval-S, A-Mem likewise has higher Turn Hit than Mem0 but lower set-level sufficiency. Thus, annotated-evidence access alone does not establish whether the retrieved set jointly supports the answer. Detailed LoCoMo ER, CER, and LLM-Suff@Set results are in Appendix I, and the six-type LongMemEval-S Turn Hit breakdown is in Appendix K. RQ3: Which stage and access schedule produce the gains? Figure 4: Coverage relative to one-shot ranking. FCA-MS improves annotated-evidence reach over one-shot ranking on both benchmarks; budgeted completion from this initializer yields further gains in evidence access and answer quality. In Figure 4, FCA-MS raises LoCoMo Gold Hit from 50.0%50.0\% to 51.0%51.0\% and LongMemEval-S Turn Hit from 82.2%82.2\% to 85.0%85.0\%. Adding either BFR schedule retrieves more annotated support at the reported operating points. Table 6 shows that, relative to FCA-MS alone, both schedules also raise Stem F1 and Judge on LoCoMo and Judge on LongMemEval-S. The schedules favor different reported operating points. At the matched C3 point in figure 4, BFR-Text has higher LoCoMo Gold Hit than BFR-MV. The full BFR-MV C6 configuration has the highest LongMemEval-S Judge and Turn Hit in Table 6, at a higher call budget than BFR-Text C3. Type-level results are in Table 13 and Appendix K. RQ4: What does additional retrieval cost buy? Figure 5: Answer quality and annotated-evidence recovery versus retrieval cost on LoCoMo (n=200n=200). Figure 5 shows the cost–quality tradeoff. The panels show BFR-Text and BFR-MV starting from the same FCA-MS C0 set. The horizontal axis is the mean realized number of retrieval calls; ER and CER measure partial and complete recovery of annotated evidence, respectively. Lines connect observed operating points only. BFR-Text C4 and C6 coincide at four realized calls. Most of the answer-quality gain over FCA-MS appears after the first completion call. At the matched three-call point, BFR-Text exceeds BFR-MV on all four plotted metrics. BFR-MV reaches its highest scores at C9, but requires nearly nine calls, and its curves are not monotonic between budgets. The C6 configuration in the main tables remains the fixed default operating point rather than a sweep-selected maximum. The complete numerical grid, including evidence-set size and LLM-Suff@Set, is in Appendix I; the matched-call RSC comparison is in Appendix L. 6 Conclusion and Discussion In this paper, we proposed BFR, a two-stage method for building sufficient evidence sets that can support answers in long-term memory QA. On LoCoMo and LongMemEval-S, budgeted completion alone raises annotated-evidence reach over one-shot ranking, and the full two-stage framework further improves evidence coverage and judged answer quality over same-store baselines. Ablations attribute most of the gain to broader evidence access rather than adaptive state control, and human checks show that gold-free sufficiency estimates remain too unreliable to serve as stopping criteria. More broadly, these results motivate a different objective for long-term memory retrieval: not to rank individually relevant memories, but to construct a set whose members collectively satisfy the information requirements of the question. From this view, retrieval involves both composition, assembling complementary support within reach, and completion, continuing beyond the initial retrieval boundary when necessary. This makes set-level sufficiency a natural bridge between memory access and downstream reasoning: retrieval should deliver an answer-supporting evidentiary record, not simply a list of similar items. As agent histories become longer and required evidence is increasingly distributed across sessions, we expect this distinction between relevance and sufficiency to become central to how long-term memory systems are designed and evaluated. AI use statement Generative AI systems were used in two roles. As part of the reported method and evaluation, language models perform requirement decomposition, candidate–requirement coverage judgments, answer synthesis, answer judging, and blinded LLM-Suff@Set labeling and adjudication; the corresponding roles, prompts, and evaluation rules are documented in the paper and appendix. Cursor and OpenAI Codex also assisted with experimental planning, code generation and debugging, result organization, literature discovery, and manuscript drafting and language editing. The authors inspected AI-produced code and outputs, reran the reported computations, verified citations and numerical claims against stored experiment artifacts, and made all final methodological and editorial decisions. Public benchmark conversations, questions, and reference answers were not generated or altered by these tools. The authors take responsibility for the complete contents of the submission. References Chhikara et al. (2025) P. Chhikara, D. Khant, S. Aryan, T. 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Contents 1 Introduction 2 Related Work 3 WHAT COUNTS AS A SUFFICIENT CANDIDATE MEMORY SET 4 BFR: Composing and Completing Sufficient Evidence 4.1 Problem: construct a sufficient set under a retrieval budget 4.2 Stage I: Compose complementary evidence with FCA-MS 4.3 Stage I: Complete missing support under a budget 4.4 Access schedules for completion 5 Experiments 5.1 Experimental setup 5.2 Experimental Result 6 Conclusion and Discussion References A Evidence-law mapping B Case trace for figure C Structured memory boundary D Algorithmic specification E Implementation details F Data usage and sealing G Dataset provenance and derived evaluation sets H Same-store LoCoMo controls I Budget sweep J Development robustness K Full LongMemEval-S type breakdown L Comparison with learned residual set completion M Annotation protocol N Metric definitions O Prompts P Matched three-call comparison of BFR-MV and BFR-Text Appendix A Evidence-law mapping Pardo asks what makes evidence sufficient, and answers by separating two judgments that legal fact-finding already treats as distinct (Pardo, 2023). Relevance is a property of an item: an exhibit is relevant when it has a bearing on a fact of consequence. Sufficiency is a property of a record: the body of evidence is sufficient when a reasonable finder of fact could make the finding from that record as assembled. The finder does not score items independently and then threshold the sum. The question is whether the assembled exhibits, taken together, could support one explanation of the disputed fact over its competitors. Pardo therefore emphasizes explanatory facts: relations between exhibits and the elements of a finding, rather than a per-item probability that an exhibit is “about” the claim. Memory QA uses the same two objects. A memory m∈ℳm is an exhibit, and R⁡(q,m)R(q,m) denotes its item-wise relevance to question q: does this memory have any tendency to matter for q? The retrieved set E is the evidentiary record. The ideal property S⁡(q,E)S(q,E) in equation 1 adapts Pardo’s reasonable-finder test to conversational memory; the blinded LLM label S^LLM(q,E) S_LLM(q,E) in equation 2 is its reference-conditioned operational measurement. The shutter-release case in figure 1 is exactly this split: the February 5 order is a relevant exhibit, and the photography memories around it are also relevant, but the record cannot support the finding “five days” until the February 10 arrival enters E. The method in Section 4 implements the two operations that this split requires. Information requirements ℛq=rjR_q=\r_j\ are the explanatory elements of the finding: order date and arrival date in the running case; a fact and a bridge in multi-hop questions; the items of a list. The requirement-conditioned candidate assessment in Stage I concerns relations between an exhibit and a needed element, rather than a single query–memory score. Stage I composition is the assembly of a record whose exhibits jointly cover those elements. Stage I completion is what a finder does when the current record is insufficient: further exhibits are acquired, from the same store, rather than re-ranking exhibits already known to be relevant. The exclusion Kt⊆ℳ∖EtK_t E_t in equation 6 is the legal analogue of not re-admitting the same exhibit. Gold Hit G and Turn Hit ask whether an annotated answer-bearing exhibit has entered the record; they correspond to coverage of at least one marked element, which is why Section 3 treats them as proxies associated with S rather than as the sufficiency test itself. This mapping is conceptual, not a claim that agent memory should mimic courtroom procedure. It specifies the object we optimize: a record that could support a reasonable finding, constructed by composing complementary exhibits and completing the record when it cannot. Appendix B Case trace for figure 1 Figure 1 uses question b3c15d39 from LongMemEval-S. The answer requires two user turns: the remote shutter release was ordered on February 5 and arrived on February 10. Both lexical top-k and FCA-MS reach the order turn but miss the arrival turn, leaving evidence recall at 50%50\% and producing an incorrect answer. BFR-MV reaches both turns and answers “5 days” under the same extractive answerer and judge. Table 7: Trace behind the relevance–sufficiency case. Case evidence recall counts the two required turns; the first two sets contain relevant photography memories but miss one required date. Access Order date Arrival date Gold recall Judge Lexical top-k ✓ — 50% Wrong FCA-MS (Stage I) ✓ — 50% Wrong BFR-MV ✓ ✓ 100% Correct Appendix C Structured memory boundary This appendix reports the cross-system comparison that was removed from the main LoCoMo table. The slice is the conv-30 overlap (n=81n=81) under a unified extractive answerer and judge. BFR-Text and MRAgent-Flat still read flat turns; CoM uses an organized candidate pool; Full-MRAgent uses a Cue–Tag–Content graph. Open Domain is absent from this slice. The comparison is a boundary, not a fair same-store baseline: the store, derived facts, and tools move together. Table 8: Cross-system boundary on the LoCoMo conv-30 overlap (n=81n=81), unified extractive answerer and judge; † marks rows re-scored under this protocol. Bold / underline: best / second-best. Open Domain is absent from the slice. Multi-Hop Temporal Single-Hop Overall Method F1 J F1 J F1 J F1 J BFR-Text† 41.4 54.5 100.0 100.0 75.5 77.3 78.7 81.5 CoM† (Xu et al., 2026) 41.2 63.6 96.2 96.2 71.8 84.1 75.5 85.2 MRAgent-Flat† (Ji et al., 2026) 12.9 45.5 92.3 92.3 62.3 68.2 65.2 72.8 Full-MRAgent† (Ji et al., 2026) 26.5 90.9 92.3 96.2 78.8 95.5 76.1 95.1 Table 9 reports the same slice by store type. Full-MRAgent reaches 88.9%88.9\% Gold Hit and 95.1%95.1\% judged accuracy, while MRAgent-Flat reaches 67.9%67.9\% / 72.8%72.8\% and BFR-Text reaches 77.8%77.8\% / 81.5%81.5\%. CoM reaches 80.2%80.2\% / 85.2%85.2\% under the same unified answerer. Table 9: Flat acquisition vs. structured memory on the 8181-question overlap slice under a shared extractive answerer and judge. Full MRAgent and CoM change the store and are reported as a boundary, not as fair same-substrate baselines. Configuration Store Gold Hit (%) Judge Acc (%) MRAgent-Flat flat turns 67.9 72.8 BFR-Text flat turns 77.8 81.5 CoM organized pool 80.2 85.2 Full MRAgent Cue–Tag–Content graph 88.9 95.1 Paired against BFR-Text, Full-MRAgent reaches gold on 1212 questions that BFR-Text misses; the reverse occurs on 33 questions. Comparing Full-MRAgent with MRAgent-Flat, the full pipeline is judged correct alone on 2020 questions, while the flat variant is correct alone on 22. Mean evidence-set sizes are 2.42.4 (Full), 14.214.2 (Flat), and 34.034.0 (BFR-Text), so the graph pipeline reaches gold more often while retaining far less text. This pattern is consistent with associative precision rather than search volume alone, but the store, tools, and derived facts still move together. A causal graph-edge claim would require toggling the graph under identical tools. Appendix D Algorithmic specification Algorithm 1 specifies how Stage I constructs the initial evidence set, and algorithm 2 gives the Stage I completion loop shared by the fixed access schedules. Algorithm 1 Stage I: Formal Concept Analysis for Memory Selection (FCA-MS) 1: Question q, agent-memory notes ℳ~ M, source store ℳM, usual retrieval cutoff k, expanded-pool size N>kN>k, prefilter cap P, grounding limit b, fallback size f 2: Source-grounded initial evidence set E0E_0 3: q←TopN⁡(Retrieveagent⁡(q,ℳ~),N)C_q (Retrieve_agent(q, M),N) ⊳ Search beyond the usual top-k 4: ℛq←Decompose⁡(q)R_q (q) ⊳ Identify facts, bridges, list items, and temporal constraints 5: q←FCAPrefilter⁡(ℛq,q,P)P_q (R_q,C_q,P) ⊳ Reduce the expanded pool to at most P notes 6: (S^,Γ)←LLMMinSubset⁡(q,q)( S, ) (q,P_q) ⊳ Request selected IDs and requirement coverage 7: S←Sanitize⁡(S^,Γ,q)S ( S, ,P_q) ⊳ Keep valid IDs once; use coverage order if needed 8: if S=∅S= then 9: S←Firstf⁡(q)S _f(P_q) ⊳ Fall back to the prefilter head 10: end if 11: E0←PositiveOverlapTopb⁡(S,ℳ)E_0 _b(S,M) ⊳ Score turns; keep positive scores in stable order 12: return E0E_0 ⊳ Pass the composed evidence set to Stage I Algorithm 2 Stage I: Budgeted Flat Reconstruction (BFR) Completion 1: Question q, initial evidence E0E_0, flat store ℳM, schedule π∈BFR-Text,BFR-MVπ∈\BFR-Text,BFR-MV\, budget B=(Bstep,Bcall,Bnew)B=(B_step,B_call,B_new), keep limit k 2: Completed evidence set ETE_T 3: E←E0E← E_0; t←0t← 0; bcall←0b_call← 0; bnew←0b_new← 0 ⊳ Initialize the cumulative evidence state and counters 4: while t<Bstept<B_step and bcall<Bcallb_call<B_call and bnew<Bnewb_new<B_new do 5: if π=BFR-Textπ=BFR-Text then 6: At←(text,q)A_t←\(text,q)\ ⊳ Advance beyond the current text-ranking cutoff 7: else 8: At←(text,q),(entity,FirstPerson⁡(q)),(session,Latest⁡(E))A_t←\(text,q),(entity,FirstPerson(q)),(session,Latest(E))\ ⊳ Diversify access through text, entity, and session cues 9: end if 10: Ct←∅C_t← ⊳ Hold the current evidence fixed throughout this round 11: for all (v,c)∈At(v,c)∈ A_t in schedule order do 12: if c=∅c= or bcall=Bcallb_call=B_call then 13: continue ⊳ Skip unavailable cues or exhausted call budgets 14: end if 15: Ct←Ct∪Rv(c,ℳ∖E)C_t← C_t∪ R_v(c,M E) 16: bcall←bcall+1b_call← b_call+1 ⊳ Collect candidates relative to the same round-start evidence 17: end for 18: Ct←Unique⁡(Ct)C_t (C_t) 19: Kt←κπ(Ct,q,E,k)K_t← _π(C_t,q,E,k) ⊳ Apply the retention rule once to the merged candidates 20: Kt←ClipToBudget⁡(Kt,Bnew−bnew)K_t (K_t,B_new-b_new) 21: E←E∪KtE← E∪ K_t; bnew←bnew+|Kt|b_new← b_new+|K_t| ⊳ Update evidence after the round’s candidate union and retention 22: t←t+1t← t+1 ⊳ Proceed until an observable budget is exhausted 23: end while 24: return ET←E_T← E ⊳ Supply the completed set to the fixed answerer Appendix E Implementation details Same-store baselines. Within each benchmark, the flat conversational turn pool, extractive answerer, and Mem0-style judge are fixed across arms. Mem0 uses BM25-lite over the turn pool; A-Mem uses dense top-k over the same pool without note evolution. CoM∗ uses MiniLM candidates with anchor, chain, and blocking. MRAgent-Flat∗ restricts its tools to flat turns, omitting the Cue–Tag–Content graph and derived facts. The starred methods are controlled same-store adaptations, not the official full systems. FCA-MS initialization. In the LoCoMo pilot, dense A-Mem note retrieval yields N=50N=50 candidates. fca_prefilter_candidates uses the decomposed requirements to retain at most P=20P=20 notes. The setr_pool v1 prompt asks an LLM for the smallest subset that jointly answers the question, with no fixed note-count cap. Invalid or duplicate IDs are removed; an empty selection uses requirement-coverage output and then the prefilter head as fallback. The resulting sets contain 11–55 notes (mean 1.861.86). Only these notes enter map_amem_ids_to_turns(..., top_n=10), which ranks source turns by positive token overlap with the selected note content and context. All 200200 pilot questions yielded 1010 mapped turns; these turn IDs form E0E_0 for Stage I. A deployment with direct source pointers can replace this approximate alignment with an exact grounding map ϕφ. Budgeted completion. BFR-Text is recorded as IterRAG-Text in experiment logs. It resubmits the original question to the text index, excludes current evidence ids, and retains the first eight unseen results. BFR-MV is recorded as Q-Fixed; it runs the fixed text→ → schedule in Section 4.4. The default BmidB_mid point allows 33 rounds, 66 retrieval calls, and 3030 newly retained records. This repeated, exclusion-aware schedule generalizes one-pass acquisition by continuing to collect unseen support until the observable budget is exhausted. Appendix F Data usage and sealing All 1010 LoCoMo conversations were visible during development, so every LoCoMo number measures stability across conversations rather than generalization to unseen data. LongMemEval-S was not read, scored, or inspected until the LoCoMo protocol, arm definitions, budget grid, and metrics were frozen. After the initial BFR evaluation on LongMemEval-S, CoM∗ and MRAgent-Flat∗ were evaluated under the same flat-store protocol and included in the main comparison. Appendix G Dataset provenance and derived evaluation sets Public source benchmarks. LoCoMo was introduced by Maharana et al. (2024) as a benchmark for very long-term conversational memory. Its released QA corpus contains ten long, multi-session conversations produced by the authors’ persona- and event-conditioned conversation-generation framework. The release pairs questions and reference answers with category labels and, when available, the dialogue-turn identifiers that support the answer. We use the released conversations and QA annotations; we do not generate new dialogue content or alter the reference answers. LongMemEval was introduced by Wu et al. (2025) using an attribute-controlled pipeline that places evidence sessions inside coherent, timestamped conversation histories. We use the official cleaned LongMemEval-S file, which contains 500500 questions covering single-session user and assistant facts, preferences, multi-session reasoning, temporal reasoning, and knowledge updates. The complete 500500-question split is evaluated. Turn Hit and turn recall use the official answer-bearing-turn fields; 479479 questions contain at least one such turn. The main Turn Hit results use all 500500 questions and count the 2121 questions without an annotated answer turn as misses. The matched-C3 analysis in Appendix P instead reports Turn Hit over the 479479 questions with nonempty answer-turn annotations. Derived LoCoMo evaluation sets. The 200200-question pilot is a fixed, stratified subset drawn from the official ten conversations and shared by every same-store arm. The pilot was sampled with seed 2026090820260908 and contains 33 Multi-Hop, 50 Temporal, 8 Open Domain, and 109 Single-Hop questions, using the released manifest labels without reclassification. It is a development subset for controlled method, ablation, annotation, and budget comparisons, not an official held-out split. The 1,5361,536-question gold subset contains all questions in our LoCoMo release with usable supporting dialogue-turn identifiers; it is used only for development robustness across conversations. The conv-30 slice contains the 8181 question ids with aligned outputs for the cross-system comparison in Appendix C. It is an overlap set rather than an independently sampled benchmark, and Open Domain is absent from this slice. Evidence-state and budget artifacts. For method-aligned sufficiency analysis, seven arms (Mem0, A-Mem, CoM∗, MRAgent-Flat∗, FCA-MS, BFR-Text C3, and BFR-MV C6) are evaluated on each of the fixed 200200 questions by the same blinded LLM-Suff@Set protocol in Appendix M. These 1,4001,400 method–question evaluations concern retrieval outputs rather than additional conversations. The budget grid applies the fixed BFR access policies and call caps to the same pilot; identical evidence states are deduplicated by question and evidence hash. These artifacts evaluate retrieval behavior over the public benchmark; they are not presented as new datasets. Table 10: Provenance of the public benchmarks and derived evaluation sets. Only LoCoMo and LongMemEval-S are independently released benchmarks; all other rows are fixed subsets or evidence states constructed from them. Evaluation set Parent Size Construction and role LoCoMo release Public benchmark 10 conversations Official multi-session conversations, QA pairs, categories, and supporting turn ids. LoCoMo pilot LoCoMo 200 questions Fixed stratified development subset shared by all same-store arms. LoCoMo gold subset LoCoMo 1,536 questions All questions with usable gold turn ids; used for development robustness. conv-30 overlap LoCoMo 81 questions Qid intersection for cross-system scoring; not a held-out split. LLM-Suff@Set evaluations LoCoMo pilot 1,400 arm–question pairs 200200 questions paired with Mem0, A-Mem, CoM∗, MRAgent-Flat∗, FCA-MS, BFR-Text C3, and BFR-MV C6 under blinded method identities. Budget grid LoCoMo pilot Fixed policy–budget runs BFR-Text and BFR-MV call budgets evaluated before evidence-hash deduplication. LongMemEval-S Public benchmark 500 questions Official cleaned small split, evaluated in full after protocol freezing. Appendix H Same-store LoCoMo controls Table 11: Retrieval cost of the adapted same-store controls on the fixed 200200-question pilot. Calls and evidence-set size are realized means. Method Gold Hit Calls Evidence-set size CoM∗ 49.0 1.00 10.0 MRAgent-Flat∗ 62.5 2.54 11.8 Table 12: Paired LoCoMo comparisons against the adapted controls. Δ is the first method minus the second. Judge uses two-sided exact McNemar; Stem F1 uses a 10,000-sample question-level paired bootstrap (seed 2026090820260908). Comparison ΔJ J p Δ F1 95% CI BFR-Text −- CoM∗ +16.0+16.0 1.4×10−51.4× 10^-5 +17.8+17.8 [11.3,24.2][11.3,24.2] BFR-MV −- CoM∗ +16.5+16.5 8.7×10−68.7× 10^-6 +18.2+18.2 [11.8,24.8][11.8,24.8] BFR-Text −- MRAgent-Flat∗ +5.5+5.5 0.0710.071 +9.8+9.8 [5.0,14.8][5.0,14.8] BFR-MV −- MRAgent-Flat∗ +6.0+6.0 0.0430.043 +10.2+10.2 [5.5,15.2][5.5,15.2] CoM∗ completes all 200200 questions. MRAgent-Flat∗ completes 199199; q_00208 has empty evidence and remains in the denominator as an empty prediction. These rows are distinct from the 8181-question full-system comparison in Appendix C. Appendix I Budget sweep Table 13: BFR access schedules by question type on LoCoMo (n=200n=200). F1 and J are percentages; Text and MV use the C3 and C6 operating points, respectively. Multi-Hop Temporal Open Domain Single-Hop Overall Schedule F1 J F1 J F1 J F1 J F1 J BFR-Text 44.7 54.5 78.1 80.0 1.9 0.0 74.9 75.2 67.8 70.0 BFR-MV 44.6 48.5 78.1 80.0 2.7 12.5 75.7 77.1 68.3 70.5 Table 14: Evidence Recall and Complete Evidence Recall by question type on the LoCoMo pilot. Text and MV use the C3 and C6 operating points, respectively. FCA-MS BFR-Text BFR-MV Question type n ER CER ER CER ER CER Multi-Hop 33 24.8 6.1 42.6 18.2 41.8 12.1 Temporal 50 68.0 66.0 82.0 82.0 82.0 82.0 Open Domain 8 18.8 12.5 27.1 12.5 31.2 25.0 Single-Hop 109 42.7 41.3 72.0 71.6 70.6 70.6 Overall 200 45.1 40.5 67.9 63.0 67.2 62.0 Table 15: Blinded LLM-Suff@Set by question type on the LoCoMo pilot. Differences use BFR minus FCA-MS. Open Domain contains only eight questions. Type n FCA Text MV Δ Δ Multi-Hop 33 15.2 27.3 30.3 +12.1+12.1 +15.2+15.2 Temporal 50 60.0 74.0 74.0 +14.0+14.0 +14.0+14.0 Open Domain 8 0.0 0.0 0.0 0.00.0 0.00.0 Single-Hop 109 45.9 71.6 73.4 +25.7+25.7 +27.5+27.5 Overall 200 42.5 62.0 63.5 +19.5+19.5 +21.0+21.0 Overall, BFR-Text −- FCA-MS is +4.0+4.0 points (p=0.332p=0.332), while BFR-MV −- FCA-MS is 0.00.0 points (p=1.000p=1.000). No type-specific LLM-Suff@Set difference is significant after Holm correction. Table 16: Matched-budget quality on the LoCoMo pilot (n=200n=200). Calls and set size are realized means; size counts grounded source turns. FCA-MS selects 11–55 notes (mean 1.861.86) before mapping to 1010 turns. J: judged accuracy; CER: Complete Evidence Recall. Method Budget Calls Size F1 J LLM- Suff@Set CER FCA-MS C0 0.00 10.00 48.6 53.5 42.5 40.5 BFR-MV C1 1.00 21.91 65.4 67.5 57.5 59.0 C2 2.00 29.05 66.8 68.5 58.0 59.5 C3 3.00 29.84 66.8 69.5 58.0 59.5 C4 4.00 39.72 68.3 71.5 61.0 62.5 C6 5.99 39.88 68.3 70.5 63.5 62.0 C9 8.98 59.23 69.9 72.0 62.5 64.0 BFR-Text C1 1.00 18.00 64.4 67.5 56.0 57.0 C2 2.00 26.00 66.3 69.0 59.5 60.5 C3 3.00 34.00 67.8 70.0 62.0 63.0 C4/C6 4.00 40.00 69.3 70.0 62.5 63.5 Table 16 gives the full operating-point grid discussed in Section 5.2. Calls are realized means rather than caps. Across the full grid, BFR-Text occupies the three-call frontier for Judge, F1, LLM-Suff@Set, and Complete Evidence Recall, while BFR-MV reaches the highest Judge score at C9 and contributes non-dominated Judge points at C4 and C9. These operating points make the acquisition-cost frontier explicit. The source-level Pareto classification uses realized calls and evidence-set size and treats higher quality and lower cost as preferred. Table 17 contrasts the Stage-I evidence set with the completed text and multi-view schedules on both benchmarks. Table 18 reports the state-conditioned controllers from Section 4.4; their results motivate the simpler fixed completion schedules used in the main framework. Table 17: Annotated-evidence reach before and after completion. LoCoMo reports Gold Hit and LongMemEval-S reports Turn Hit. The one-shot LongMemEval-S cell lists FCA-MS / Mem0; parenthesized gains use FCA-MS. Step LoCoMo Gold Hit LME-S Turn Hit One-shot (FCA-MS / Mem0) 51.0 85.0 / 64.8 BFR-MV 73.5 (+22.5) 91.4 (+6.4) BFR-Text (vs. one-shot) 72.5 (+21.5) 88.6 (+3.6) Table 18: Evidence-state ablations on the LoCoMo pilot at BmidB_mid. Brackets: clustered 95%95\% CI. Budgeted access drives the gain; state control does not. CI for Text vs. Initial [19.1,26.7][19.1,26.7]; State vs. MV [−0.8,4.5][-0.8,4.5]. Factor Variant G (%) Δ Access Initial 51.0 ref. BFR-Text 72.5 +21.5+21.5 State BFR-MV 73.5 ref. BFR-State 73.0 −0.5-0.5 BFR-Adaptive 73.0 −0.5-0.5 BFR-State adds a missing-requirement cue and coverage/bridge retention; BFR-Adaptive also selects views and stops early from the evidence state. At BmidB_mid on LoCoMo, both reach 73.0%73.0\% Gold Hit versus 73.5%73.5\% for fixed BFR-MV. The clustered 95%95\% CI for BFR-State minus BFR-MV is [−0.8,4.5][-0.8,4.5] points, so this ablation does not establish a gain over fixed access. Appendix J Development robustness On the broader development-contact LoCoMo set (n=1536n=1536), conversation-level five-fold analysis raises Gold Hit from 54.8%54.8\% for initial retrieval to 78.0%78.0\% and 78.1%78.1\% for text and multi-view completion. Table 19: Development robustness on all LoCoMo questions with gold ids (n=1536n=1536). Conversation-level 55-fold; all conversations had development contact. Method Gold Hit (%) ↑ Initial retrieval 54.8 BFR-Text 78.0 BFR-MV 78.1 Appendix K Full LongMemEval-S type breakdown The six released types show the multi-session and temporal retrieval-coverage pattern behind the answer-quality results in Table 3. Table 20: Full type breakdown under the unified flat-store protocol on LongMemEval-S (all 500500 questions; unannotated answer-turn items count as misses). Upd.: knowledge-update; Mul.: multi-session; Tmp.: temporal; Pref.: preference; Asst./User: single-session. The six type columns and G report Turn Hit; J is judged accuracy over all questions. Method Upd. Mul. Tmp. Pref. Asst. User G J Mem0 78.2 53.4 61.7 16.7 87.5 80.0 64.8 72.4 A-Mem 88.5 82.0 75.2 70.0 98.2 81.4 82.2 68.6 CoM 88.5 81.2 72.9 63.3 98.2 78.6 80.6 68.6 MRAgent-Flat 79.5 75.9 78.9 60.0 91.1 81.4 78.8 71.4 FCA-MS 89.7 84.2 80.5 70.0 100.0 84.3 85.0 70.4 BFR-Text 91.0 85.7 88.7 70.0 100.0 90.0 88.6 81.6 BFR-MV 92.3 91.0 91.0 76.7 100.0 91.4 91.4 82.2 Appendix L Comparison with learned residual set completion Table 21: Learned residual set completion (RSC) comparison on the LoCoMo pilot (n=200n=200). The three completion policies use a matched budget of three retrieval calls; initial retrieval is shown as a zero-call reference. Method Gold Hit (%) ↑ Calls Initial retrieval 51.0 0.00 BFR-Text C3 72.5 3.00 BFR-MV C3 70.5 3.00 RSC (dense residual) 58.0 3.00 Under the same three-call budget, the fixed text and multi-view schedules recover more annotated gold evidence than RSC: Gold Hit is 72.5%72.5\% for BFR-Text C3, 70.5%70.5\% for BFR-MV C3, and 58.0%58.0\% for RSC. Under the current training signal and flat-store protocol, learning a residual query therefore does not improve over the fixed completion schedules. Appendix M Annotation protocol Suff@Set is labelled on a question–evidence snapshot rather than on the system answer. The blinded input contains the question, reference answer, and anonymized evidence text; it withholds the method, budget, system answer, and gold evidence identifiers. Two independent judges (gpt-5.5 and claude-sonnet-4-6) assign sufficient, insufficient, or uncertain; gpt-6-sol adjudicates disagreements. All calls use temperature zero. Because the protocol includes the reference answer and uses model judges, Suff@Set is an LLM-only, reference-conditioned offline evaluation measure rather than a human annotation or an inference-time stopping signal. An uncertain or missing final label is excluded from the binary-rate denominator; the originally reported FCA-MS, BFR-Text C3, and BFR-MV C6 pilot produced no uncertain labels. No human Suff@Set labels are reported. Appendix N Metric definitions The sufficiency-oriented measurements used in the main text are defined here because they answer different questions about the retrieved set. Set sufficiency S. S⁡(q,E)=1S(q,E)=1 when a careful reader can determine y⋆(q)y (q) from the question and the retrieved evidence text alone (equation 1). The blinded LLM protocol estimates this property through S^LLM(q,E) S_LLM(q,E) (equation 2; Appendix M). S is a reference-conditioned record-level test; it is not computed from similarity ranks or gold evidence identifiers. Gold Hit G. Gold Hit is 11 when the source identifiers in E intersect the annotated supporting-record identifiers (equation 3). G answers a narrower question than S: did at least one marked support record enter the context? A hit can still leave a compositional question underspecified, so we do not treat G as sufficiency. Evidence Recall and Complete Evidence Recall. For questions with a nonempty annotated gold set, Evidence Recall is the fraction of gold identifiers in src⁡(E)src(E); Complete Evidence Recall requires all gold identifiers to be present (equation 9). The former measures partial recovery; the latter requires all annotated support records. Complete Evidence Recall concerns completeness relative to benchmark annotations and is not identical to semantic Suff@Set. Turn Hit. Turn Hit is 11 when the source identifiers in E include any annotated answer-bearing turn (equation 4). Main LongMemEval-S results average over all 500500 questions, counting unannotated items as misses; Appendix P separately uses the 479479 questions with answer-turn annotations. Like Gold Hit, it measures access to marked evidence rather than support of the complete answer. Answer scores. Stem F1 follows the LoCoMo / MRAgent normalization with Porter stemming. Judge accuracy is the Mem0-style CORRECT/WRONG decision under gpt-5.5 at temperature 00 (Appendix O). Native free-form scores from other systems are never mixed into same-store rankings without the unified-answerer note. Appendix O Prompts We list the prompts used in our evaluation pipeline. Formatting follows the prompt-box style common in recent memory-agent papers. Your task is to label an answer to a question as ’CORRECT’ or ’WRONG’. You will be given the following data: • a question (posed by one user to another user), • a ’gold’ (ground truth) answer, • a generated answer which you will score as CORRECT/WRONG. The point of the question is to ask about something one user should know about the other user based on their prior conversations. The gold answer will usually be a concise and short answer that includes the referenced topic. The generated answer might be much longer, but you should be generous with your grading—as long as it touches on the same topic as the gold answer, it should be counted as CORRECT. For time related questions, the gold answer will be a specific date, month, year, etc. The generated answer might be much longer or use relative time references, but you should be generous with your grading—as long as it refers to the same date or time period as the gold answer, it should be counted as CORRECT. Even if the format differs (e.g., “May 7th” vs “7 May”), consider it CORRECT if it is the same date. Now it’s time for the real question:Question: question Gold answer: gold_answer Generated answer: generated_answer First, provide a short (one sentence) explanation of your reasoning, then finish with CORRECT or WRONG. Do NOT include both CORRECT and WRONG in your response. Just return the label CORRECT or WRONG in a json format with the key as “label”: ⬇ "label": "CORRECT" You will see a question, its reference answer, and an anonymized retained evidence set from a conversational memory store. The method, budget, system answer, and gold memory identifiers are not shown. Task: Decide whether the evidence text supports the complete reference answer. • Label sufficient if the complete answer is supported by the provided evidence. • Label insufficient if a required fact, bridge, or temporal detail is missing. • Label uncertain only when the evidence does not permit a reliable decision. • Do not use outside knowledge beyond what is written in the evidence. Two judges apply this rule independently; a third model adjudicates disagreements. Given the question and the ordered evidence snippets, produce a short answer string that is supported by the evidence. Prefer spans that appear in the evidence. If multiple candidates exist, choose the most specific span that answers the question. Do not invent entities that are absent from the evidence set. At each round t, issue up to three retrieval actions in fixed order: 1. text: cue == the original question q. 2. entity: cue == first person name extracted from q (skip if none). 3. session: cue == most recently retained evidence record (skip if none). Exclude ids already in EtE_t. Retain policy-selected unseen candidates and union into Et+1E_t+1. Stop when the call / round / retention budget is exhausted. Appendix P Matched three-call comparison of BFR-MV and BFR-Text Both policies start from the same FCA-MS initialization and make 3.00 retrieval calls. Differences are BFR-MV minus BFR-Text. Table 22 reports selected question-type results at the matched three-call budget. BFR-Text has higher Temporal LLM-Suff@Set; the Open Domain rows report the observed answer scores on eight questions. Table 22: Selected question-type results at a matched three-call budget. LoCoMo, C3, n=200n=200. Values are percentages; differences are BFR-MV minus BFR-Text in percentage points, computed before rounding. Open Domain has eight questions. Question type Metric n BFR-Text BFR-MV Δ Open Domain Judge 8 0.0 12.5 +12.5+12.5 Temporal LLM-Suff@Set 50 74.0 70.0 −4.0-4.0 Open Domain F1 8 1.9 3.4 +1.6+1.6 On LongMemEval-S the same budget favors BFR-MV on Turn Hit (figure 6). Overall is 95.295.2 against 92.592.5 (+2.7+2.7 p) on the 479479 items with an answer-turn label, whereas the main tables average Turn Hit over all 500500 questions. Preference is +6.7+6.7 (n=30n=30) and multi-session is +5.6+5.6 (n=125n=125); assistant questions are tied at 100%100\%. Paired outcomes are 13 to 0 (p=2.4×10−4p=2.4× 10^-4). Multi-session is 7 to 0 (raw p=0.016p=0.016; Bonferroni over six types p=0.094p=0.094). Judge does not separate the two policies. Figure 6: LongMemEval-S Turn Hit under matched C3 access. BFR-MV minus BFR-Text, on 479479 items with an answer-turn label; differences are percentage points.

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