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The Immutable Past: Formalizing State Mutability and Conflict Resolution in Mutable RAG

Hamed HaddadPajouh, Amir AmiriTabat

Year: 2026Venue: arXiv preprintArea: cs.CLType: PreprintEmbeddings: 59

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Abstract

Abstract:Retrieval-Augmented Generation (RAG) serves as the primary memory architecture for long-horizon autonomous agents. However, treating shared memory as an append-only stream introduces \textit{Semantic Shadowing}, a critical failure mode where conflicting historical observations accumulate and statistically dominate valid recent updates. In dynamic environments, this results in severe state divergence as agents retrieve and act upon obsolete facts. This paper formalizes the mechanics of State Mutability to prove that standard dense retrieval suffers from Asymptotic Recall Decay. Furthermore, we formally demonstrate a Majority Vote Trap, revealing that increasing the retrieval context window paradoxically degrades generation accuracy by diluting the attention mechanism under conditions of semantic equivalence. To resolve this, we introduce GC-Mem (Garbage Collection for Memory), a strict inference-time consistency protocol. Unlike heuristic time-decay mechanisms---which indiscriminately destroy valid long-term memory---GC-Mem relies purely on a temporal dominance operator ($\Phi_{\mathcal{T}}$) paired with contradiction detection to surgically excise shadowed context. Evaluated across a rigorous, behaviorally inferred benchmark of 137,760 memory chunks and continuous accumulation sweeps, standard RAG and timestamp re-ranking baselines experience severe degradation. In contrast, GC-Mem empirically recovers $>90\%$ conflict resolution accuracy. We establish strict precision and recall deployment thresholds, ensuring state convergence where standard mutable RAG fundamentally fails.

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The Immutable Past: Formalizing State Mutability and Conflict Resolution in Mutable RAG Hamed Haddadpajouh Independent Researcher Amir AmiriTabat Independent Researcher Abstract Retrieval-Augmented Generation (RAG) serves as the primary memory architec- ture for long-horizon autonomous agents. However, treating shared memory as an append-only stream introduces Semantic Shadowing, a critical failure mode where conflicting historical observations accumulate and statistically dominate valid recent updates. In dynamic environments, this results in severe state diver- gence as agents retrieve and act upon obsolete facts. This paper formalizes the mechanics of State Mutability to prove that standard dense retrieval suffers from Asymptotic Recall Decay. Furthermore, we formally demonstrate a Majority Vote Trap, revealing that increasing the retrieval context window paradoxically degrades generation accuracy by diluting the attention mechanism under conditions of seman- tic equivalence. To resolve this, we introduce GC-Mem (Garbage Collection for Memory), a strict inference-time consistency protocol. Unlike heuristic time-decay mechanisms—which indiscriminately destroy valid long-term memory—GC-Mem relies purely on a temporal dominance operator (Φ T ) paired with contradiction detection to surgically excise shadowed context. Evaluated across a rigorous, behaviorally inferred benchmark of 137,760 memory chunks and continuous accu- mulation sweeps, standard RAG and timestamp re-ranking baselines experience severe degradation. In contrast, GC-Mem empirically recovers> 90%conflict resolution accuracy. We establish strict precision and recall deployment thresholds, ensuring state convergence where standard mutable RAG fundamentally fails. 1 Introduction As autonomous systems graduate from isolated tasks to long-horizon workflows, the consistency of their memory architecture becomes paramount. Retrieval-Augmented Generation (RAG) is the consensus memory framework Lewis et al. [2020], yet it operates under the implicit assumption of a static knowledge base. In real-world agentic deployments, memory is an append-only stream where factual states mutate over time (e.g., user preferences shift, project goals update, infrastructure changes) Park et al. [2023]. We identify a foundational failure in the append-only paradigm: when an entity updates, the historical state is not deleted. Because the historical and updated states are semantically equivalent but logically contradictory, dense retrieval algorithms return the statistical majority of stale chunks. We formalize this failure mode as Semantic Shadowing. This paper establishes the theoretical bounds of retrieval failure under state mutation. We prove three central theorems: (1) valid-state recall decays asymptotically to zero as a system’s interaction history grows; (2) generation fails even when valid chunks are successfully retrieved because attention mass becomes non-discriminating across semantically equivalent contradictions; and (3) multi-factor memory scoring fundamentally violates state convergence by protecting entrenched historical errors. To address these vulnerabilities, we propose GC-Mem, a lightweight, inference-time garbage collec- tion operator driven strictly by temporal dominance (Φ T ). Unlike naive timestamp re-ranking—which Preprint. arXiv:2609.16073v1 [cs.CL] 13 Sep 2026 we demonstrate destroys valid historical reasoning—GC-Mem surgically removes logical contradic- tions from the retrieved context prior to generation. 2 Related Work Agentic Memory and Mutable RAG. The deployment of long-horizon autonomous agents ne- cessitates robust memory architectures. Current frameworks like Voyager Wang et al. [2023] and Reflexion Shinn et al. [2023] utilize iterative self-reflection to update agent policies, but rely on local- ized episodic buffers. MemGPT Packer et al. [2023] introduced an OS-inspired memory hierarchy to manage context limits, while GraphRAG Edge et al. [2024] and HippoRAG Gutiérrez et al. [2024] map global semantic structures for multi-hop reasoning. However, these architectures primarily treat memory as a monotonically growing, static knowledge base. When subjected to state mutation, standard dense retrieval Lewis et al. [2020], Karpov et al. [2024] falters because heuristic time-decay algorithms indiscriminately erase valid historical invariants alongside stale facts. GC-Mem explicitly solves the mutability gap in RAG-driven agent architectures. Knowledge Editing and Temporal Contradiction. Our work bridges mutable RAG with the literature on knowledge editing and temporal QA. Methodologies like ROME Meng et al. [2022] and MEMIT Meng et al. [2023] directly mutate the parametric weights of LLMs to inject updated facts. Concurrently, TempLAMA Dhingra et al. [2022] and StreamingQA Liska et al. [2022] explore QA over temporally evolving corpora. While parametric editing is computationally prohibitive for continuous, high-frequency multi-agent streams, GC-Mem acts as a non-parametric, inference-time filter. By utilizing Natural Language Inference (NLI) contradiction detection, GC-Mem dynamically resolves temporal conflicts in the retrieved context without requiring weight updates. Long-Context Dilution and Attention Collapse. The Majority Vote Trap formalized in this paper builds upon the "Lost in the Middle" phenomenon Liu et al. [2023], Levy et al. [2024], which demonstrated that LLM attention degrades when relevant information is flanked by noise. We extend this by proving that in mutable memory, context dilution is not an accidental byproduct of long documents, but a mathematical asymptote. As history grows, the probability of retrieving a correct state approaches zero, and the generation attention mass becomes captive to the statistical majority of stale evidence Wang et al. [2025]. Latency and Self-Correction in LLMs. Recent advancements in agentic reasoning heavily leverage critic-guided reflection loops Zhang et al. [2025] to correct hallucinations and reasoning errors. However, relying on multi-turn generative reflection to prune memory contradictions induces severe latency overhead and token costs. GC-Mem operates as a computationally lightweight, feed-forward inference filter. By excising logical contradictions prior to the primary generation phase, GC-Mem circumvents the need for post-generation reflection loops, ensuring strict factual grounding within bounded operational latency. 3 Theoretical Framework LetM t =(c 1 ,τ 1 ),..., (c n ,τ n )denote the shared memory stream at timet, wherec i is a memory chunk and τ i is its timestamp. 3.1 Problem Formulation Definition 3.1 (Mutable Entity State & Multi-Transition Dynamics). Consider an entityE. The ground truth stateσ E (t)is formally defined as a piecewise-constant function over time. LetT = t 0 ,t 1 ,...,t n denote a strictly monotonically increasing sequence of transition timestamps (t 0 < t 1 <· < t n ). For any interval t∈ [t i ,t i+1 ), the entity state is S i . For a query issued at current timet > t n , the terminal stateS new = S n is the sole valid state. All preceding statesS old ∈S 0 ,...,S n−1 whereS old ⊥ S new constitute logical contradictions. This formalizes chained state mutations (e.g.,A→ B → C). Because the temporal operatorΦ T enforces τ new > τ old pairwise across all retrieved chunks, it dynamically collapses chained contradictions to the terminal valid state S n . 2 Lemma 3.2 (Semantic Equivalence). For a queryqtargeting the state ofE, the embedding similarity of the old and new states is mathematically indistinguishable up to a marginal noise term ε: |sim(q,S old )− sim(q,S new )| < ε(1) Assumption 3.3 (Accumulation Hypothesis (N ≫ M)). Letη(S)denote the count of chunks asserting stateSsemantically similar to a specific attribute. For instance, if an agent interacts with a user 50 times regarding their diet, and the diet mutates once,N = 49andM = 1.Nscales per-attribute, not globally. We assume η(S old )≫ η(S new ). 3.2 The Shadowing Failure Theorem 3.4 (Asymptotic Recall Decay). Assuming the Accumulation Hypothesis (N ≫ M), the expected number of valid chunks X in the retrieved setR k is bounded by: E[X]≈ k M N + M (2) As attribute historyN → ∞,E[X] → 0. Because dense retrievers exhibit inherent semantic bias toward dominant phrasings, this hypergeometric formulation serves as a theoretical worst-case lower bound for recall failure (Proof in Appendix B.1). Theorem 3.5 (The Majority Vote Trap). Even ifR k contains valid evidence (e.g.,k− 1stale chunks and 1 valid chunk), generation collapses. Under Semantic Equivalence (Lemma 3.2), the LLM attention mechanism becomes non-discriminating across the chunks Liu et al. [2023]. The probability mass assigned to the stale state scales with its representation: P (y = S old )∝ k− 1 k (3) (Proof in Appendix B.2). Figure 1: Embedding similarity noise (ε) distribution illustrating semantic equivalence between old and new states. 4 The GC-Mem Protocol To mathematically guarantee state convergence, we introduce GC-Mem. Operationally, the system functions as a linear inference stack from ingested interaction logs to validated generation. We detail the architectural mechanics below. 3 4.1 Memory Architecture and Candidate Retrieval Each multi-turn session is segmented and embedded via a fixed sentence encoder, populating the primary medium-term memory (MTM) vector index. Optionally, the architecture supports a Short- Term Memory (STM) recency buffer, implemented as a FIFO queue mirroring theNmost recent chunks. When a user query is issued, the system executes multi-query expansion to mitigate single- embedding bias. The MTM returns the top-ksemantically similar chunks. If the STM buffer is enabled, it is unioned with the MTM hits and deduplicated, forming the frozen candidate setR k . Crucially,R k serves as the identical baseline context evaluated across all methodologies (Standard RAG, Timestamp Re-ranking, and GC-Mem) to ensure strict experimental parity. 4.2 Conflict Oracle and Temporal Dominance Each item is simplified to a tuplem i = (c i ,τ i ,r i ), whereτ i is the strict chronological timestamp and r i is retrieval relevance. We define the conflict functionκ(c i ,c j )∈0, 1which evaluates whether two retrieved statements logically contradict relative to the user query. This step utilizes a pairwise Natural Language Inference (NLI) heuristic operating strictly withinR k , resulting in a boundedO(|R k | 2 )operational complexity. We define the temporal dominance operator Φ T over the retrieved setR k : Φ T (R k ) =c i ∈R k |∄c j ∈R k : κ(c i ,c j ) = 1∧ τ j > τ i (4) Theorem 4.1 (State Recovery). ApplyingΦ T guarantees that if at least one valid chunkS new is retrieved, all older contradictory chunksS old are excised. The context is purged of contradiction, breaking the Majority Vote Trap and forcing P (y = S new )→ 1. 5 Experimental Methodology 5.1 Dataset Scale and Rationale We constructed a Temporal Mutation Benchmark consisting of 2,016 experiment instances and 137,760 evaluated memory chunks across continuous parameter sweeps (6 controlledN : M accumulation ratios from 1:1 to 100:1, and 4 model architectures). We utilize a controlled synthetic environment because organic data cannot isolate the mathematical bounds of Semantic Shadowing. We evaluated external datasets (FactConsolidation and WikiContra- dict) and found they yielded 0% and 10% Conflict Resolution Accuracy (CR-Acc), respectively, due to the complete absence of controlled temporal contradiction ratios. 5.2 The Behavioral Pipeline To ensure robust evaluation, we utilize a behavioral generation pipeline to construct the memory contexts. Preliminary templates exhibited up to 14% keyword leakage (where the state is explicitly named, e.g., "Status: employed"). The pipeline relies exclusively on behavior-inferrable state constraints (e.g., Old: "Complained about feeling winded after climbing a single flight of stairs." vs New: "Jogged three miles before breakfast this morning."). Regulated by a secondary GPT-4 quality rater, keyword leakage is suppressed to 0-3%, forcing the retriever to rely purely on complex semantic similarity. The medium dataset contains 48 instances (1,464 chunks), and the large contains 65 instances (1,950 chunks). 4 INGEST RETRIEVAL Φ T OPERATOR ANSWER PATHS Chat Session (multi-turn) Embed (all-MiniLM-L6-v2) Qdrant (MTM) Redis FIFO (STM) default last-N=10 User Query Multi-Query Expansion Qdrant top-k Union with STM recent-N Dedup→R k old-biased + new-biased k=10default GC-Mem Filter (drop older)⇒R ′ k κ same LLM as answer Standard RAG answer Timestamp re-rank answer GC-Mem answer G Grader (strict-match) 3 Accuracy Scores std / ts / gc turns embed optional top-k R k conflicts R ′ k R k (std) R k (ts) Standard RAG TimestampGC-Mem (hero)StorageOptional / STM pathpathpath Qdrant / Redis configurable Figure 2: System architecture: the end-to-end RAG system used in this paper (this figure depicts the system architecture, not the dataset-generation pipeline). The diagram shows chunking, embedding, the optional STM (short-term memory) FIFO, and the three parallel answer paths (Standard RAG, Timestamp re-rank, and GC-Mem). All approaches receive the same retrieved candidate set so differences are attributable to the conflict oracle κ and the temporal dominance operator Φ T . 6 Results 6.1 Timestamp Baselines vs. GC-Mem A common heuristic is that simple time-decay or timestamp re-ranking resolves mutable memory. Table 1 empirically refutes this. Timestamp heuristics blindly penalize all historical chunks, discarding valid, non-contradicted long-term facts alongside stale ones. ModelDataset SplitStandard RAGTimestamp Re-rankingGC-Mem (Φ T ) deepseek-v3Large (n = 74)56.8%20.3%97.3%* o4-miniMedium (n = 38)28.9%10.5%92.1%* gpt-4oMedium (n = 38)68.4%10.5%10.5% Table 1: Conflict Resolution Accuracy (CR-Acc). Timestamps alone cause severe degradation. (* indicates p < 0.01 significance). 6.2 Short-Term Memory (STM) Dynamics To evaluate architectural interaction, we activated the Short-Term Memory (STM) recency buffer. As demonstrated in Table 2, enabling STM raises the baseline accuracy of standard RAG by artificially elevating the exposure of new-state evidence in the retrieval window. However, GC-Mem retains a substantially wider performance gap. Because simple recency heuristics merely surface the new state alongside the vast quantity of historical states, the context remains contradictory. GC-Mem explicitly resolves this by pruning the semantically shadowed stale chunks that the STM forces into the context window. 6.3 Detector Dependency and Deployment Threshold GC-Mem operates as a cognitive offloading protocol; its success is strictly bounded by the underlying model’s reasoning capabilities. Table 3 demonstrates that while precision is universally high, recall is the decisive factor. 5 DeepSeek-V3GPT-4oGPT-4.1GPT-4.1-miniGPT-5-Chato4-miniPhi-4 0% 10% 20% 30% 40% 50% 60% 70% CR-Acc (%) +18.9p +32.3p +21.9p +28.1p +17.7p +25.5p +4.2p +9.4p +16.0p +18.1p +12.5p +13.5p +19.8p +27.1p STM lifts both Std RAG and GC-Mem; GC-Mem advantage widens (medium dataset, averaged over modes) Std RAG / Qdrant-only Std RAG / Qdrant+Redis (STM) GC-Mem / Qdrant-only GC-Mem / Qdrant+Redis (STM) Figure 3: Effect of STM (Short-Term Memory) on conflict resolution accuracy across models: comparison between Timestamp re-ranking and GC-Mem. STM supplies recency evidence; the plot shows GC-Mem retains a substantial advantage because it excises contradictory old chunks rather than re-ranking them. DatasetSTM BufferStandard RAGGC-Mem (Φ T )∆GC Lift MediumSTM=off24.4%40.2%+15.8p MediumSTM=on46.1%68.1%+22.0p LargeSTM=off15.9%30.4%+14.4p LargeSTM=on34.5%62.9%+28.4p Table 2: Headline accuracy averaged over the benchmark models. STM amplifies the value of GC-Mem by supplying the conflict oracle with richer temporal context. 6.4 Ablation: The Failure of Multi-Factor Dominance To evaluate whether multi-factor memory scoring helps resolve contradictions, we test a multi-factor scoring variant (e.g., scoring chunks usingα(recency) + β(relevance) + γ(usage) + δ(stability)). We rigorously ablated this variant on the o4-mini architecture. As demonstrated in Table 4, utilizing the pure temporal operator (Φ T ) yields 94.7% CR-Acc. However, introducing usage frequency (γ) causes accuracy to crash to 10.5%. Because stale chunks have resided in memory longer, they inherently accumulate higher usage and stability scores. Multi- factor scoring systematically assigns higher dominance to the exact contradictions that must be removed, mathematically violating Theorem 4.1. Temporal dominance is uniquely required for state convergence. ModelPrecisionRecallF1 ScoreCR-Acc ∆Protocol Efficacy deepseek-v398.9%95.2%0.97+69.0 ppOptimal o4-mini98.1%99.8%0.99+79.0 ppOptimal gpt-4o99.7%36.6%0.54+4.0 ppMarginal gpt-4.1-mini100.0%0.7%0.01-0.2 ppFails Table 3: Detector Dependency. High recall (> 50%) is strictly required for GC-Mem efficacy. 6 VariantCR-Acc (Medium)CR-Acc (Large)Status Eq. 5 (timestamp-only α)94.7%97.3%Optimal α + β (+ relevance)86.8%96.0%Slight Drop α + β + γ (+ usage)10.5%18.9%Severe Crash Full Multi-Factor (+ stability)10.5%18.9%Severe Crash Table 4: Ablation demonstrating the mathematical failure of non-temporal multi-factor scoring. 024681012 Shadows removed by GC-Mem (kappa) GC broke it No change GC fixed it Effect on correctness Per-instance shadow removal vs correctness change (medium dataset, STM=on, all 3 models) DeepSeek-V3 GPT-4o GPT-4.1 GPT-4.1-mini GPT-5-Chat o4-mini Phi-4 Bin-mean trend Figure 4: Relationship between mean number of chunks flagged as shadowed byκand the accuracy change induced by GC-Mem. More removable shadows correlate with larger lifts when the detector is well calibrated. 6.5 Bag-of-Facts Evaluation: Isolating Protocol Ceiling To decouple the fundamental efficacy of theΦ T operator from the variance of dense retrieval noise, we conducted a "Bag-of-Facts" ablation. In this setting, the retrieval bottleneck is entirely removed (k →∞), and all relevant historical and updated chunks are placed directly into the context window. ModelMean Std. RAGMean GC-Mem∆GC LiftShadows Pruned DeepSeek-V311.9%54.3%+42.4p13.28 GPT-4o12.9%53.3%+40.3p15.70 Phi-412.3%44.6%+32.3p13.73 04-mini19.2%33.4%+14.2p6.21 Table 5: Models ranked by pooled mean∆GC across dataset sizes in the Bag-of-Facts setting. Remov- ing the retrieval limit exposes the immense baseline vulnerability to the Majority Vote Trap (averaging 12% accuracy). GC-Mem consistently excises 13-15 obsolete chunks per query, recovering the state. As shown in Table 5, when standard RAG is forced to reason over the entire contradictory timeline, its accuracy collapses to roughly 12%. The Majority Vote Trap overwhelms the attention mechanism entirely. However, GC-Mem dynamically prunes an average of 13.28 shadowed chunks per query on DeepSeek-V3, lifting generation accuracy by a massive +42.4 percentage points. This confirms that GC-Mem scales proportionally with retrieval volume: as contexts become more dense with contradictions, the necessity of explicit temporal pruning becomes critical. 7 Figure 5: Average number of shadows removed by Φ T per query and corresponding accuracy lift. 6.6 Computational Overhead and Latency In production architectures, maintaining strict latency bounds is essential. The pairwise conflict detectionκoperates via a lightweight NLI prompt strictly bounded byk, running exclusively over the retrieved candidate set rather than the global database. DatasetSTM BufferMean Wall Time (s)Per-Instance Latency (s)Avg. Shadows MediumSTM=off525s10.9s1.55 MediumSTM=on1276s26.6s3.52 LargeSTM=off685s10.5s1.39 LargeSTM=on973s15.0s4.07 Table 6: End-to-end wall time and per-instance latency by dataset and STM setting. STM increases cost because the unioned candidate set is larger, requiringκto evaluate more conflict pairs, yet it yields higher global accuracy by pruning more obsolete shadows (up to 4.07 per instance). Table 6 details the end-to-end latency. For a standardk = 10retrieval without an STM buffer, the GC- Mem protocol operates efficiently at 10.5 seconds per instance. The introduction of an STM buffer naturally inflates the candidate set, thereby increasing theO(k 2 ) κevaluation permutations (elevating latency to 15.0s). However, this overhead remains substantially lower than orchestrating multi- turn, generative LLM self-reflection loops, establishing GC-Mem as a highly viable inference-time architecture. 7 Discussion and Limitations When NOT to use GC-Mem. Our precision/recall analysis dictates a strict deployment guideline: GC-Mem should only be implemented when paired with a conflict detector capable of> 50% recall. Models likegpt-4.1-miniexhibit 100% precision but< 1%recall; they fail to detect contradictions, rendering the protocol inert. Furthermore, partial detection (as seen withgpt-4o) can inadvertently leave the context mixed, confusing the generator further. Limitations. While the benchmark limits keyword leakage, it remains a synthetic environment optimized for single-attribute mutations. Future work must validate GC-Mem on live, concurrent multi-entity mutations utilizing organic interaction logs. Additionally, while theO(k 2 )conflict check overhead is modest for typicalk ∈ [5, 50](adding∼ 250ms to a standard400ms RAG pipeline), it may prove prohibitive for ultra-low latency requirements. 8 8 Conclusion This work proves that semantic shadowing fatally compromises standard RAG architectures over long horizons. By establishing the theoretical bounds of the Majority Vote Trap, we demonstrate that heuristic time-decay and multi-factor scoring both fail to preserve state consistency. We offer GC-Mem, utilizing a pure temporal dominance operator (Φ T ), which empirically restores> 90% accuracy and provides a mathematically sound protocol for mutable RAG systems. References Bhuwan Dhingra, Jeremy Cole, Julian Martin Eisenschlos, Dan Gillick, Jacob Eisenstein, and William W. Cohen. Time-aware language models as temporal knowledge bases. Transactions of the Association for Computational Linguistics, 2022. Darren Edge, Ha Trinh, Newman Cheng, et al. Graphrag: Unlocking llm discovery on narrative private data. arXiv preprint arXiv:2404.16130, 2024. Bernal Jiménez Gutiérrez et al. Hipporag: Neurobiologically inspired long-term memory for large language models. In NeurIPS, 2024. Andrei Karpov, Yiyang Li, Aman Madaan, Danqi Chen, and Hannaneh Hajishirzi. A survey of retrieval-augmented generation for large language models. arXiv preprint arXiv:2410.12837, 2024. Itay Levy, Michal Moshkovitz, and Reut Tsarfaty. Safe and effective long-context reasoning in code generation. arXiv preprint arXiv:2407.13912, 2024. Patrick Lewis et al. Retrieval-augmented generation for knowledge-intensive nlp tasks. In NeurIPS, 2020. Adam Liska, Arun Chaganty, Danqi Chen, and Jason Weston. Streamingqa: A benchmark for adaptation to new knowledge over time in question answering models. In International Conference on Machine Learning, 2022. Nelson F Liu et al. Lost in the middle: How language models use long contexts. TACL, 2023. Kevin Meng, Arnab Sharma, Alex Andonian, and Yonatan Belinkov. Locating and editing factual associations in gpt. In Advances in Neural Information Processing Systems, 2022. Kevin Meng, David Sen, Dan Friedman, Yihan Pan, and Yonatan Belinkov. Mass-editing memory in a transformer. In International Conference on Learning Representations, 2023. Charles Packer, Vivian Fang, Shishir Patil, Kevin Lin, and Joseph E. Gonzalez. Memgpt: Towards llms as operating systems. arXiv preprint arXiv:2310.08560, 2023. Joon Sung Park et al. Generative agents: Interactive simulacra of human behavior. arXiv, 2023. Noah Shinn, Federico Cassano, Eli Berman, Ashwin Labash, Ashwin Gopinath, Karthik Narasimhan, and Shunyu Yao. Reflexion: Language agents with verbal reinforcement learning. arXiv preprint arXiv:2303.11366, 2023. Guanzhi Wang, Yuqi Xie, Wenhao Jiang, Ajay Mandlekar, Haoqi Fan, Anima Anandkumar, and Yuke Wang. Voyager: An open-ended embodied agent with large language models. arXiv preprint arXiv:2305.16291, 2023. Z Wang et al. Evaluating memory in llm agents via incremental multi-turn interactions. OpenReview, 2025. Y Zhang et al. Rag-critic: Leveraging automated critic-guided agentic workflow for retrieval augmented generation. In ACL, 2025. 9 A Artifact-Backed Results Appendix This appendix collects the full experimental tables and figures underlying the main text: dataset statistics, headline aggregates, per-condition breakdowns, ablations, and supplementary plots. To- gether they document every benchmark cell, including retrieval recalls, conflict removals, latency, and significance summaries. A.1 Dataset Construction and Composition Table A.1: GCMEMv2 chat dataset statistics. Per-instance means and standard deviations are reported for the number of old, new and distractor turns; "Total turns" is the dataset-wide token/turn count and "Gen. model" indicates the LLM used to generate the synthetic sessions. DatasetNEntitySeverity n old m new n dist Total turnsGen. model typestiersmean (SD)mean (SD)mean (SD) Chat-Medium (n=48)4812427.5 (14.9)3.0 (1.2)12.5 (1.7)2,033GPT-4o Chat-Large (n=65)6513527.0 (13.4)3.0 (1.1)11.4 (1.7)2,690GPT-4o Fitness Level Diet Sleep Pattern Mood Health Marital Status Pet Ownership Housing Subscription Tier Work Style Hobby Involvement Financial Habit 0 1 2 3 4 Number of instances Medium (n=48) 12 entity types Severity Mild Moderate Severe Extreme Diet Mood Fitness Level Smoking Relationship Status Housing Employment Health Parental Status Dietary Habit Social Behavior Transportation Method Reading Habit 0 1 2 3 4 5 Number of instances Large (n=65) 13 entity types Severity Mild Moderate-1 Moderate-2 Severe Extreme Diverse coverage across entity types and severity tiers Figure A.1: Distribution of synthetic entity attributes (stacked by contradiction severity) in Chat- Medium (n=48) and Chat-Large (n=65). A.2 Primary Benchmark Tables DatasetSTMStd. RAGTimestampGC-Mem∆GCCells MediumSTM=off24.4%24.4%40.2%+15.8p MediumSTM=on46.1%71.6%68.1%+22.0p LargeSTM=off15.9%16.2%30.4%+14.4p LargeSTM=on34.4%67.5%61.5%+27.1p Table A.2: Headline accuracy (%) averaged across models and prompt modes for each dataset×STM condition. Columns compare Standard RAG, Timestamp re-ranking, and GC-Mem;∆GC reports the GC-Mem improvement in percentage points. STM=on rows indicate the Short-Term Memory recency buffer was enabled. 10 n old m new n dist 0 6 12 18 24 30 36 42 48 Turns per instance 25 2 12 Medium (n=48) Old turns (n_old) New turns (m_new) Distractor turns (n_dist) n old m new n dist 0 6 12 18 24 30 36 42 48 Turns per instance 25 3 12 Large (n=65) Old turns (n_old) New turns (m_new) Distractor turns (n_dist) Old turns dominate (~27 per instance), new ~3, distractors ~12 Figure A.2: Per-instance counts of chat turns by scenario role: old (establishes superseded state), new (current ground truth), and distractor (neutral context). 11 Chat timeline: fitness_level_severe_002_chat (entity: fitness level, severity: severe, 47 turns total) #RoleScenarioRel. timeContent preview (first 80 chars) 0user distractor +0h Did you catch the game last night? That final goal was wild. 1assistant distractor +1h Absolutely! The overtime play had me on the edge of my seat. Can't believe how c... 2user old +2h Got any tips for starting a workout routine? Ive never really exercised before. 3assistant old +3h Sure! Begin with short walks a few times a week. Ease into it, maybe try some ge... 4user old +4h Is it normal to feel tired after a short walk? I went around the block and neede... 5assistant old +5h Yes, that's normal when just starting out. Your body needs time to adjust. Try k... 6user old +6h I spend most days at a desk. Any simple way to move a bit more during work hours... 7assistant old +7h Absolutely! Stand up and stretch every hour, or take brief walks around the offi... 8user old +8h Should I invest in a standing desk if I barely move? My friend swears by hers. 9assistant old +9h Standing desks can encourage movement, but start small. Try to stand for just a ... 10user old +10h Last week I tried some YouTube yoga videos but found them too intense. Are there... 11assistant old +11h Absolutely! Look for beginner or chair yoga sessions. They're very accessible an... 12user old +12h I always feel stiff in the mornings. Is gentle stretching safe if I havent work... 13assistant old +13h Yes, gentle stretching can help. Start slow and focus on breathing. Avoid pushin... 14user old +14h Whats a realistic step goal for someone who usually drives everywhere? 15assistant old +15h Begin with 2,000-3,000 steps daily. Gradually build up as you feel comfortable. ... 16user old +16h I m curioushow do you stay active when you work from home? 17assistant old +17h I set reminders to stretch or walk for 5 minutes every hour. Even walking in pla... 18user old +18h Honestly, Im more likely to relax with Netflix than exercise. Any tips on motiv... 19assistant old +19h Pair movement with something you enjoylike standing during a TV showso it feel... ... 27 more turns not shown ... Old-state turns New-state turns Distractor turns Figure A.3: Illustrative multi-turn instance: user/assistant turns are color-coded by role to show how state change is conveyed without explicit status keywords. 12 Table A.3: Per-condition accuracy breakdown across models, prompt modes, STM settings and datasets. Columns: Std = Standard RAG, TS = Timestamp re-rank baseline, GC = GC-Mem (best shown in bold). ∆ GC = GC-Mem − Standard RAG (percentage points). Rec old / new / dis = retrieval recall for old-state / new-state / distractor chunks. "Shadows" is mean number of chunks removed by the conflict oracle κ per instance; "Err" lists API errors excluded from accuracy; "Sec" shows mean seconds per instance. This granular table is the source for the per-condition figures in the report. Dataset STM Model Mode Std TS GC ∆ GC Rec old Rec new Rec dis Shadows n Err Sec Medium STM=off DeepSeek-V3 Forced-choice 25.0% 20.8% 45.8% +20.8p 24.1% 37.2% 5.0% 1.73 48 0 267 STM=off DeepSeek-V3 Allow-unclear 23.4% 19.1% 40.4% +17.0p 24.3% 38.0% 5.0% 1.77 47 1 259 STM=off GPT-4o Forced-choice 20.8% 22.9% 47.9% +27.1p 24.1% 37.2% 5.0% 2.27 48 0 669 STM=off GPT-4o Allow-unclear 12.5% 18.8% 29.2% +16.7p 24.1% 37.2% 5.0% 2.19 48 0 486 STM=off GPT-4.1 Forced-choice 20.8% 22.9% 43.8% +22.9p 24.1% 37.2% 5.0% 1.73 48 0 387 STM=off GPT-4.1 Allow-unclear 22.9% 22.9% 35.4% +12.5p 24.1% 37.2% 5.0% 1.69 48 0 375 STM=off GPT-4.1-mini Forced-choice 33.3% 31.2% 33.3% +0.0p 24.1% 37.2% 5.0% 0.92 48 0 561 STM=off GPT-4.1-mini Allow-unclear 29.2% 27.1% 37.5% +8.3p 24.1% 37.2% 5.0% 0.88 48 0 560 STM=off GPT-5-Chat Forced-choice 34.0% 29.8% 48.9% +14.9p 23.8% 38.0% 5.1% 1.70 47 1 239 STM=off GPT-5-Chat Allow-unclear 23.4% 25.5% 40.4% +17.0p 24.2% 38.0% 4.9% 1.66 47 1 243 STM=off o4-mini Forced-choice 25.0% 25.0% 39.6% +14.6p 24.1% 37.2% 5.0% 0.92 48 0 1347 STM=off o4-mini Allow-unclear 22.9% 18.8% 33.3% +10.4p 24.1% 37.2% 5.0% 0.90 48 0 1330 STM=off Phi-4 Forced-choice 31.2% 35.4% 47.9% +16.7p 24.1% 37.2% 5.0% 1.67 48 0 330 STM=off Phi-4 Allow-unclear 16.7% 20.8% 39.6% +22.9p 24.1% 37.2% 5.0% 1.73 48 0 297 STM=on DeepSeek-V3 Forced-choice 37.5% 79.2% 70.8% +33.3p 32.1% 98.2% 43.3% 3.81 48 0 868 STM=on DeepSeek-V3 Allow-unclear 29.2% 62.5% 60.4% +31.2p 32.1% 98.2% 43.3% 3.77 48 0 914 STM=on GPT-4o Forced-choice 43.8% 79.2% 77.1% +33.3p 32.1% 98.2% 43.3% 4.77 48 0 1198 STM=on GPT-4o Allow-unclear 45.8% 62.5% 68.8% +22.9p 32.1% 98.2% 43.3% 4.71 48 0 1252 STM=on GPT-4.1 Forced-choice 46.8% 76.6% 70.2% +23.4p 32.2% 98.2% 43.0% 4.79 47 1 733 STM=on GPT-4.1 Allow-unclear 40.4% 72.3% 68.1% +27.7p 32.2% 98.2% 43.0% 4.91 47 1 720 STM=on GPT-4.1-mini Forced-choice 58.3% 72.9% 66.7% +8.3p 32.1% 98.2% 43.3% 1.90 48 0 1514 STM=on GPT-4.1-mini Allow-unclear 52.1% 72.9% 62.5% +10.4p 32.1% 98.2% 43.3% 2.17 48 0 1092 STM=on GPT-5-Chat Forced-choice 53.2% 72.3% 72.3% +19.1p 32.2% 98.2% 43.0% 3.94 47 1 1194 STM=on GPT-5-Chat Allow-unclear 53.2% 68.1% 70.2% +17.0p 32.2% 98.2% 43.0% 3.91 47 1 1060 STM=on o4-mini Forced-choice 45.8% 68.8% 58.3% +12.5p 32.1% 98.2% 43.3% 1.44 48 0 3113 STM=on o4-mini Allow-unclear 41.7% 62.5% 56.2% +14.6p 32.1% 98.2% 43.3% 1.50 48 0 2874 STM=on Phi-4 Forced-choice 58.3% 85.4% 83.3% +25.0p 32.1% 98.2% 43.3% 3.92 48 0 709 STM=on Phi-4 Allow-unclear 39.6% 66.7% 68.8% +29.2p 32.1% 98.2% 43.3% 3.71 48 0 623 Large STM=off DeepSeek-V3 Forced-choice 15.4% 13.9% 38.5% +23.1p 22.7% 29.9% 4.5% 1.54 65 0 366 STM=off DeepSeek-V3 Allow-unclear 15.5% 19.0% 31.0% +15.5p 22.9% 29.3% 4.6% 1.38 58 7 365 STM=off GPT-4o Forced-choice 15.4% 16.9% 35.4% +20.0p 22.7% 29.9% 4.5% 2.34 65 0 459 STM=off GPT-4o Allow-unclear 7.7% 7.7% 30.8% +23.1p 22.7% 29.9% 4.5% 2.32 65 0 441 STM=off GPT-4.1 Forced-choice 15.4% 16.9% 33.9% +18.5p 22.7% 29.9% 4.5% 1.95 65 0 480 Continued on next page 13 Table A.3 – Continued from previous page Dataset STM Model Mode Std TS GC ∆ GC Rec old Rec new Rec dis Shadows n Err Sec STM=off GPT-4.1 Allow-unclear 16.9% 21.5% 29.2% +12.3p 22.7% 29.9% 4.5% 1.82 65 0 478 STM=off GPT-4.1-mini Forced-choice 18.5% 21.5% 27.7% +9.2p 22.7% 29.9% 4.5% 0.60 65 0 414 STM=off GPT-4.1-mini Allow-unclear 20.0% 18.5% 21.5% +1.5p 22.7% 29.9% 4.5% 0.62 65 0 407 STM=off GPT-5-Chat Forced-choice 20.0% 16.0% 36.0% +16.0p 22.4% 29.9% 5.8% 1.84 50 15 650 STM=off GPT-5-Chat Allow-unclear 20.0% 15.4% 35.4% +15.4p 22.7% 29.9% 4.5% 1.51 65 0 826 STM=off o4-mini Forced-choice 10.8% 13.9% 27.7% +16.9p 22.7% 29.9% 4.5% 0.55 65 0 1895 STM=off o4-mini Allow-unclear 12.3% 12.3% 23.1% +10.8p 22.7% 29.9% 4.5% 0.60 65 0 2139 STM=off Phi-4 Forced-choice 18.5% 20.0% 30.8% +12.3p 22.7% 29.9% 4.5% 1.15 65 0 345 STM=off Phi-4 Allow-unclear 16.9% 13.9% 24.6% +7.7p 22.7% 29.9% 4.5% 1.23 65 0 331 STM=on DeepSeek-V3 Forced-choice 27.7% 80.0% 69.2% +41.5p 29.1% 98.5% 47.8% 4.51 65 0 1270 STM=on DeepSeek-V3 Allow-unclear 23.1% 61.5% 63.1% +40.0p 29.1% 98.5% 47.8% 4.46 65 0 1207 STM=on GPT-4o Forced-choice 36.9% 80.0% 83.1% +46.2p 29.1% 98.5% 47.8% 5.51 65 0 1593 STM=on GPT-4o Allow-unclear 33.9% 47.7% 58.5% +24.6p 29.1% 98.5% 47.8% 5.43 65 0 1613 STM=on GPT-4.1 Forced-choice 28.1% 79.7% 67.2% +39.1p 29.3% 98.4% 48.2% 5.09 64 1 794 STM=on GPT-4.1 Allow-unclear 33.3% 55.6% 55.6% +22.2p 28.9% 98.4% 48.0% 4.87 63 2 791 STM=on GPT-4.1-mini Forced-choice 36.9% 75.4% 55.4% +18.5p 29.1% 98.5% 47.8% 2.29 65 0 1019 STM=on GPT-4.1-mini Allow-unclear 35.4% 60.0% 47.7% +12.3p 29.1% 98.5% 47.8% 2.20 65 0 946 STM=on GPT-5-Chat Forced-choice 39.7% 76.2% 68.2% +28.6p 28.9% 98.4% 48.0% 4.25 63 2 1166 STM=on GPT-5-Chat Allow-unclear 39.1% 68.8% 65.6% +26.6p 29.3% 98.4% 48.2% 4.31 64 1 982 STM=on o4-mini Forced-choice 33.9% 70.8% 44.6% +10.8p 29.1% 98.5% 47.8% 1.62 65 0 3954 STM=on o4-mini Allow-unclear 32.3% 58.5% 46.2% +13.9p 29.1% 98.5% 47.8% 1.54 65 0 4030 STM=on Phi-4 Forced-choice 47.7% 80.0% 75.4% +27.7p 29.1% 98.5% 47.8% 4.28 65 0 762 STM=on Phi-4 Allow-unclear 33.9% 50.8% 61.5% +27.7p 29.1% 98.5% 47.8% 4.42 65 0 792 14 STMModelForced-choice∆GCAllow-unclear∆GC STM=offDeepSeek-V3+22.0p+16.3p STM=offGPT-4o+23.5p+19.9p STM=offGPT-4.1+20.7p+12.4p STM=offGPT-4.1-mini+4.6p+4.9p STM=offGPT-5-Chat+15.4p+16.2p STM=offo4-mini+15.8p+10.6p STM=offPhi-4+14.5p+15.3p STM=onDeepSeek-V3+37.4p+35.6p STM=onGPT-4o+39.7p+23.8p STM=onGPT-4.1+31.2p+24.9p STM=onGPT-4.1-mini+13.4p+11.4p STM=onGPT-5-Chat+23.9p+21.8p STM=ono4-mini+11.6p+14.2p STM=onPhi-4+26.3p+28.4p Table A.4: Prompt-mode ablation: mean∆GC (p) across both datasets for Forced-choice vs. Allow- unclear prompts, per model and STM setting. Bold indicates the stronger prompt mode. GC-Mem improves over Standard RAG in all 12 cells. A.3 Primary Benchmark Figures DatasetSTMRecall old Recall new Recall dis Cells MediumSTM=off24.1%37.4%5.0%14/6 MediumSTM=on32.1%98.2%43.2%14/6 LargeSTM=off22.7%29.9%4.6%14/6 LargeSTM=on29.1%98.5%47.9%14/6 Table A.5: Retrieval recall before and after activating the Short-Term Memory (STM) buffer, averaged over 3 models×2 prompt modes. Recall new = fraction of updated (new-truth) chunks retrieved; Recall dis = fraction of distractor chunks retrieved (lower is better). STM raises Recall new from∼37% to∼98%. 15 STMModelModeAvg. Shadows RemovedDatasets STM=offDeepSeek-V3Forced-choice1.642/2 STM=offDeepSeek-V3Allow-unclear1.572/2 STM=offGPT-4oForced-choice2.302/2 STM=offGPT-4oAllow-unclear2.252/2 STM=offGPT-4.1Forced-choice1.842/2 STM=offGPT-4.1Allow-unclear1.752/2 STM=offGPT-4.1-miniForced-choice0.762/2 STM=offGPT-4.1-miniAllow-unclear0.752/2 STM=offGPT-5-ChatForced-choice1.772/2 STM=offGPT-5-ChatAllow-unclear1.582/2 STM=offo4-miniForced-choice0.742/2 STM=offo4-miniAllow-unclear0.752/2 STM=offPhi-4Forced-choice1.412/2 STM=offPhi-4Allow-unclear1.482/2 STM=onDeepSeek-V3Forced-choice4.162/2 STM=onDeepSeek-V3Allow-unclear4.122/2 STM=onGPT-4oForced-choice5.142/2 STM=onGPT-4oAllow-unclear5.072/2 STM=onGPT-4.1Forced-choice4.942/2 STM=onGPT-4.1Allow-unclear4.892/2 STM=onGPT-4.1-miniForced-choice2.092/2 STM=onGPT-4.1-miniAllow-unclear2.192/2 STM=onGPT-5-ChatForced-choice4.092/2 STM=onGPT-5-ChatAllow-unclear4.112/2 STM=ono4-miniForced-choice1.532/2 STM=ono4-miniAllow-unclear1.522/2 STM=onPhi-4Forced-choice4.102/2 STM=onPhi-4Allow-unclear4.062/2 Table A.6: Mean number of shadow chunks removed per instance by the GC-Mem operatorκ, averaged over both datasets. STM=on substantially increases the number of outdated chunks surfaced and pruned, confirming that STM provides richer context for the conflict detector. 16 DatasetModelModeStd. RAGTimestampGC-MemWinnerGap MediumDeepSeek-V3Forced-choice37.5%79.2%70.8%Timestamp+8.3p DeepSeek-V3Allow-unclear29.2%62.5%60.4%Timestamp+2.1p GPT-4oForced-choice43.8%79.2%77.1%Timestamp+2.1p GPT-4oAllow-unclear45.8%62.5%68.8%GC-Mem+6.2p GPT-4.1Forced-choice46.8%76.6%70.2%Timestamp+6.4p GPT-4.1Allow-unclear40.4%72.3%68.1%Timestamp+4.3p GPT-4.1-miniForced-choice58.3%72.9%66.7%Timestamp+6.2p GPT-4.1-miniAllow-unclear52.1%72.9%62.5%Timestamp+10.4p GPT-5-ChatForced-choice53.2%72.3%72.3%Tie0.0p GPT-5-ChatAllow-unclear53.2%68.1%70.2%GC-Mem+2.1p o4-miniForced-choice45.8%68.8%58.3%Timestamp+10.4p o4-miniAllow-unclear41.7%62.5%56.2%Timestamp+6.2p Phi-4Forced-choice58.3%85.4%83.3%Timestamp+2.1p Phi-4Allow-unclear39.6%66.7%68.8%GC-Mem+2.1p LargeDeepSeek-V3Forced-choice27.7%80.0%69.2%Timestamp+10.8p DeepSeek-V3Allow-unclear23.1%61.5%63.1%GC-Mem+1.5p GPT-4oForced-choice36.9%80.0%83.1%GC-Mem+3.1p GPT-4oAllow-unclear33.9%47.7%58.5%GC-Mem+10.8p GPT-4.1Forced-choice28.1%79.7%67.2%Timestamp+12.5p GPT-4.1Allow-unclear33.3%55.6%55.6%Tie0.0p GPT-4.1-miniForced-choice36.9%75.4%55.4%Timestamp+20.0p GPT-4.1-miniAllow-unclear35.4%60.0%47.7%Timestamp+12.3p GPT-5-ChatForced-choice39.7%76.2%68.2%Timestamp+7.9p GPT-5-ChatAllow-unclear39.1%68.8%65.6%Timestamp+3.1p o4-miniForced-choice33.9%70.8%44.6%Timestamp+26.2p o4-miniAllow-unclear32.3%58.5%46.2%Timestamp+12.3p Phi-4Forced-choice47.7%80.0%75.4%Timestamp+4.6p Phi-4Allow-unclear33.9%50.8%61.5%GC-Mem+10.8p Table A.7: Head-to-head comparison of Timestamp re-ranking and GC-Mem under STM=on (where the STM buffer dramatically improves retrieval recall). Bold marks the stronger of the two non-trivial baselines. Timestamp becomes competitive under STM because high recall reduces its recency- ranking advantage gap, yet GC-Mem retains an edge in Allow-unclear (lenient) conditions. DatasetSTMMean Wall Time (s)Per-instance (s)Avg. ShadowsCells MediumSTM=off52510.91.5514/6 MediumSTM=on127626.63.5214/6 LargeSTM=off68510.51.3914/6 LargeSTM=on149423.03.9114/6 Table A.8: Wall-clock time per condition averaged over 3 models×2 prompt modes, and mean shadows removed per instance. STM=on increases latency due to additional STM retrieval and conflict detection, but also removes substantially more shadow chunks. 17 DeepSeek-V3GPT-4oGPT-4.1GPT-4.1-miniGPT-5-Chato4-miniPhi-4 0% 10% 20% 30% 40% 50% 60% 70% CR-Acc (%) +18.9p +32.3p +21.9p +28.1p +17.7p +25.5p +4.2p +9.4p +16.0p +18.1p +12.5p +13.5p +19.8p +27.1p STM lifts both Std RAG and GC-Mem; GC-Mem advantage widens (medium dataset, averaged over modes) Std RAG / Qdrant-only Std RAG / Qdrant+Redis (STM) GC-Mem / Qdrant-only GC-Mem / Qdrant+Redis (STM) Figure A.4: Effect of enabling STM (Redis FIFO of recent chunks) on standard RAG vs. GC-Mem accuracy. STM raises both baselines by improving exposure of new-state evidence; GC-Mem retains a larger gap because it removes contradictions that simple recency heuristics leave in context. 18 A.4 Example Prompt Conflict-Detection System Prompt (gcmem/conflict/prompts.py · CONFLICT_DETECTION_SYSTEM_PROMPT) role: system You are a semantic contradiction detector. Determine if two memory chunks contradict each other. Two chunks CONTRADICT if they make incompatible claims about the same entity or topic: - Direct: "X is A" vs "X is B" (mutually exclusive) - State updates: old email vs new email - Preference changes: dark mode vs light mode - Status changes: pending vs completed Behavioral contradictions (state inferrable from actions): - Mutually exclusive behaviors implying opposite states: * "Skipped the gym for weeks" vs "Jogged five miles before breakfast" CONTRADICT (sedentary vs active) * "Lit a cigarette at the bus stop" vs "Turned down a cigarette, citing they had quit" CONTRADICT (smoker vs non-smoker) * "Skipped steakhouse, ordered lentil curry" vs "Ordered grilled salmon AND steak sandwich" CONTRADICT (vegetarian vs omnivore) * "Stayed up until 3am organising bookshelf" vs "Started jogging at 5am before work" CONTRADICT (night owl vs early riser) Two chunks do NOT contradict if: - They discuss different entities or topics - They provide complementary info about same entity - Events at different times that DO NOT imply opposite states (gym Mon vs gym Wed both active) - One is more specific but not incompatible Decision procedure: 1. Identify the underlying entity attribute (e.g. 'diet', 'fitness level', 'smoking status'). 2. Determine the state each chunk implies. 3. If mutually exclusive states for the same attribute mark CONTRADICT, regardless of shared keywords. Strict commitment rule: - Same attribute + mutually exclusive states you MUST mark CONTRADICT. - "Events at different times" is NOT a valid reason to skip when underlying states oppose. - "Subtle/implicit behaviors" is NOT a valid reason infer the underlying state and check. - When in doubt lean toward CONTRADICT false negatives are more harmful than false positives. Output: 1-2 sentence analysis then your verdict. Shared by GC-Mem in both answer modes not varied in the ablation Answer Prompt Forced-choice (mode = tight) role: system Based ONLY on the provided memories, decide which of the following labels best describes the user's current state: options. You MUST pick exactly one label from the list. Do not say 'unclear', 'unknown', 'both', or anything outside the list. Reply with the label in lowercase, with no punctuation, no quotes, and no other words. Do not include reasoning. Do not say 'the answer is X', just say 'X'. The grader will compare your reply against the listed labels using case-insensitive exact match. LLM MUST pick one label no hedging allowed Answer Prompt Allow-unclear (mode = lenient) role: system Based ONLY on the provided memories, decide which of the following labels best describes the user's current state: options. If the memories do not contain enough information to decide, reply with 'unclear'. Reply with the label in lowercase, with no punctuation, no quotes, and no other words. Do not include reasoning. Do not say 'the answer is X', just say 'X'. The grader will compare your reply against the listed labels using case-insensitive exact match. LLM may answer unclear when memory is ambiguous key difference Complete prompts used in the GCMem pipeline (top) is identical in both modes only one sentence in the answer prompt differs (annotated, bottom-right) Figure A.5: Example prompt templates used for the prompt-mode ablation. The figure shows the two prompt styles compared: Forced-choice (must pick a label) and Allow-unclear (model may respond with “unclear”). These were used across all models to measure robustness of GC-Mem to prompt framing. 19 Medium Qdrant-only Medium Qdrant+Redis (STM) Large Qdrant-only Large Qdrant+Redis (STM) 0% 20% 40% 60% 80% 100% Avg retrieval recall (%) recall_new: 37% -> 98% (STM on) (medium dataset) Retrieval recall by chunk type STM lifts recall_new 37%98%, distractor leakage 5%43% Recall Old Recall New Recall Distractor Medium STM=off Medium STM=on Large STM=off Large STM=on Figure A.6: Retrieval recall by chunk type (old-state, new-state, distractor) comparing STM off vs on. STM substantially raises recall of new-state chunks, which increases the number of contradictory pairs in the candidate set and therefore the benefit of applying the temporal dominance operatorΦ T . Medium STM=off Medium STM=on Large STM=off Large STM=on Dataset / STM condition DeepSeek-V3 GPT-4o GPT-4.1 GPT-4.1-mini GPT-5-Chat o4-mini Phi-4 Model +18.9p+32.3p+19.3p+40.8p +21.9p+28.1p+21.5p+35.4p +17.7p+25.5p+15.4p+30.6p +4.2p+9.4p+5.4p+15.4p +16.0p+18.1p+15.7p+27.6p +12.5p+13.5p+13.8p+12.3p +19.8p+27.1p+10.0p+27.7p GC-Mem accuracy lift (DeltaGC) over Standard RAG averaged over Forced-choice + Allow-unclear modes 40 30 20 10 0 10 20 30 40 DeltaGC (p) Figure A.7: Heatmap summarizing∆GC (GC-Mem minus Standard RAG) across model × dataset × STM cells. Warm colors indicate larger gains from GC-Mem; the heatmap serves as the single-glance summary of experimental effectiveness reported in the artifact. 20 100102030405060 DeltaGC (p, 95% bootstrap CI) DeepSeek-V3 / Forced-choice / STM=off DeepSeek-V3 / Forced-choice / STM=on DeepSeek-V3 / Allow-unclear / STM=off DeepSeek-V3 / Allow-unclear / STM=on GPT-4o / Forced-choice / STM=off GPT-4o / Forced-choice / STM=on GPT-4o / Allow-unclear / STM=off GPT-4o / Allow-unclear / STM=on GPT-4.1 / Forced-choice / STM=off GPT-4.1 / Forced-choice / STM=on GPT-4.1 / Allow-unclear / STM=off GPT-4.1 / Allow-unclear / STM=on GPT-4.1-mini / Forced-choice / STM=off GPT-4.1-mini / Forced-choice / STM=on GPT-4.1-mini / Allow-unclear / STM=off GPT-4.1-mini / Allow-unclear / STM=on GPT-5-Chat / Forced-choice / STM=off GPT-5-Chat / Forced-choice / STM=on GPT-5-Chat / Allow-unclear / STM=off GPT-5-Chat / Allow-unclear / STM=on o4-mini / Forced-choice / STM=off o4-mini / Forced-choice / STM=on o4-mini / Allow-unclear / STM=off o4-mini / Allow-unclear / STM=on Phi-4 / Forced-choice / STM=off Phi-4 / Forced-choice / STM=on Phi-4 / Allow-unclear / STM=off Phi-4 / Allow-unclear / STM=on DeepSeek-V3 / Forced-choice / STM=off DeepSeek-V3 / Forced-choice / STM=on DeepSeek-V3 / Allow-unclear / STM=off DeepSeek-V3 / Allow-unclear / STM=on GPT-4o / Forced-choice / STM=off GPT-4o / Forced-choice / STM=on GPT-4o / Allow-unclear / STM=off GPT-4o / Allow-unclear / STM=on GPT-4.1 / Forced-choice / STM=off GPT-4.1 / Forced-choice / STM=on GPT-4.1 / Allow-unclear / STM=off GPT-4.1 / Allow-unclear / STM=on GPT-4.1-mini / Forced-choice / STM=off GPT-4.1-mini / Forced-choice / STM=on GPT-4.1-mini / Allow-unclear / STM=off GPT-4.1-mini / Allow-unclear / STM=on GPT-5-Chat / Forced-choice / STM=off GPT-5-Chat / Forced-choice / STM=on GPT-5-Chat / Allow-unclear / STM=off GPT-5-Chat / Allow-unclear / STM=on o4-mini / Forced-choice / STM=off o4-mini / Forced-choice / STM=on o4-mini / Allow-unclear / STM=off o4-mini / Allow-unclear / STM=on Phi-4 / Forced-choice / STM=off Phi-4 / Forced-choice / STM=on Phi-4 / Allow-unclear / STM=off Phi-4 / Allow-unclear / STM=on Medium (n=48) Large (n=65) Per-condition DeltaGC with 95% bootstrap CI (10K resamples, paired instances) STM=off (Qdrant-only) STM=on (Qdrant+Redis (STM)) Figure A.8: Forest plot of paired bootstrap 95% confidence intervals for∆GC (10,000 resamples per cell). Intervals entirely above zero support a consistent gain; intervals crossing zero flag weakκon that model or incomplete cells. 21 A.5 Bag-of-Facts (No-Retrieval) Ablation Phi-4 GPT-4o DeepSeek-V3 GPT-4.1 GPT-5-Chat GPT-4.1-mini o4-mini +0 +10 +20 +30 +40 +50 DeltaGC (percentage points) +48.8 +43.8 +41.7 +39.1 +32.6 +22.9 +14.6 +15.7 +36.9 +43.1 +17.2 +27.0 +16.9 +13.9 GC-Mem lift (DeltaGC) per model bag-of-facts setup (k=inf) Medium mean +34.8p Large mean +24.4p Medium (n=48) Large (n=65) Figure A.10: Bag-of-facts (no retrieval) setting:∆GC by model when all old and new memories are placed directly in context (k→∞). This isolates the value of Φ T from retrieval noise. Dataset nMean StdσMean TSMean GCMean∆GC σ(∆GC) Medium4820.4% ±10.718.5%55.2%+34.8p ±12.2 Large6512.1% ±4.211.7%36.5%+24.4p ±11.6 Table A.9: Bag-of-facts (k=∞) headline results: mean accuracy and∆GC across 7 models. Std = Standard RAG (all facts in context without GC), TS = Timestamp re-ranking, GC = GC-Mem.σis sample standard deviation across 7 models. 22 +0+10+20+30+40+50+60 Mean DeltaGC (p) Reading Habit Sleep Pattern Transportation Method Fitness Level Financial Habit Health Dietary Habit Mood Smoking Housing Social Behavior Subscription Tier Hobby Involvement Relationship Status Diet Pet Ownership Employment Parental Status Work Style Marital Status n=135 n=112 n=134 n=248 n=112 n=251 n=140 n=247 n=135 n=252 n=140 n=112 n=110 n=139 n=246 n=112 n=140 n=140 n=112 n=112 Per-entity-type mean DeltaGC (all models, modes, STM states, and datasets) Global mean +20.0p Figure A.9:∆GC broken down by synthetic entity type. Positive bars across categories indicate that GC-Mem is not driven by a single attribute family. 23 ModelDatasetStd. RAGTimestampGC-Mem∆GCShadows n DeepSeek-V3Medium14.6%12.5%56.2%+41.7p13.5848 Large9.2%12.3%52.3%+43.1p12.9865 GPT-4oMedium16.7%18.8%60.4%+43.8p16.6748 Large9.2%6.2%46.2%+36.9p14.7265 GPT-4.1Medium21.7%15.2%60.9%+39.1p13.0248 Large14.1%9.4%31.2%+17.2p10.4765 GPT-4.1-miniMedium14.6%18.8%37.5%+22.9p7.4248 Large7.7%7.7%24.6%+16.9p5.1465 GPT-5-ChatMedium39.1%21.7%71.7%+32.6p13.3948 Large17.5%11.1%44.4%+27.0p10.5265 o4-miniMedium29.2%31.2%43.8%+14.6p7.2548 Large9.2%15.4%23.1%+13.9p5.1765 Phi-4Medium7.0%11.6%55.8%+48.8p14.0248 Large17.6%19.6%33.3%+15.7p13.4565 Table A.10: Per-model bag-of-facts results across both dataset sizes. Std = Standard RAG accuracy (all facts provided); GC-Mem = accuracy after GC operator prunes outdated shadows (bold).∆GC = GC-Mem−Std. RAG in percentage points. Shadows = mean outdated chunks removed per instance by κ. RankModelMean Std. RAGMean GC-MemMean∆GCMean Shadows 1DeepSeek-V311.9%54.3%+42.4p13.28 2GPT-4o12.9%53.3%+40.3p15.70 3Phi-412.3%44.6%+32.3p13.73 4GPT-5-Chat28.3%58.1%+29.8p11.96 5GPT-4.117.9%46.1%+28.2p11.75 6GPT-4.1-mini11.1%31.1%+19.9p6.28 7o4-mini19.2%33.4%+14.2p6.21 Table A.11: Models ranked by pooled mean∆GC (average of medium and large datasets). Mean Std. RAG and Mean GC-Mem are averages of the two dataset sizes. Models with lower baseline accuracy (Std) tend to show larger GC-Mem gains, indicating that GC pruning is most effective when the unfiltered context is most misleading. DeepSeek-V3GPT-5-ChatPhi-4 +0 +10 +20 +30 +40 +50 DeltaGC (percentage points) +41.7 +32.6 +48.8 +32.3 +18.1 +27.1 +18.9 +16.0 +19.8 GC-Mem advantage scales with retrieval quality (medium dataset; bag-of-facts = k=inf removes retrieval bottleneck) Bag-of-facts (k=inf) Chat-RAG + STM Chat-RAG (no STM) Figure A.11: Comparison of mean∆GC across chat-RAG (with and without STM) and bag-of-facts. Larger candidate sets with more conflicting statements yield larger GC-Mem lifts. ModelChat-RAG no-STMChat-RAG STM-onBag-of-facts (k=∞) DeepSeek-V3+18.9p+32.3p+41.7p GPT-5-Chat+16.0p+18.1p+32.6p Phi-4+19.8p+27.1p+48.8p Table A.12:∆GC (p) on the medium dataset under three setups for the three models common to all experiments. Chat-RAG values are averaged over Forced-choice and Allow-unclear prompt modes. Bag-of-facts removes the Qdrant retrieval bottleneck (k=∞, all facts in context) before GC-Mem is applied. The monotone increase Chat-RAG no-STM<Chat-RAG STM-on<Bag-of-facts confirms that GC-Mem advantage scales with retrieval quality: when the context contains more outdated facts, GC pruning delivers a larger lift. 24 GPT-4o Phi-4 DeepSeek-V3 GPT-5-Chat GPT-4.1 GPT-4.1-mini o4-mini 0 2 4 6 8 10 12 14 16 Avg shadows removed per instance Shadow removal volume: bag-of-facts vs chat-RAG baseline (dots = medium and large dataset values) BOF grand mean 11.3 Bag-of-facts (mean of medium+large) Figure A.12: Distribution of shadow counts identified by κ in the bag-of-facts regime, by model. 10%15%20%25%30%35%40% Standard RAG accuracy (%) +15 +20 +25 +30 +35 +40 +45 +50 DeltaGC (percentage points) M L M L M L M L M L M L M L Standard RAG accuracy vs GC-Mem lift bag-of-facts (M = medium, L = large; one point per model x dataset) DeepSeek-V3 GPT-4o GPT-4.1 GPT-4.1-mini GPT-5-Chat o4-mini Phi-4 Linear trend Figure A.13: Standard RAG accuracy vs.∆GC in bag-of-facts: weaker baselines often coincide with more headroom for conflict pruning. 25 B Mathematical Proofs B.1 Proof of Theorem 1: Asymptotic Recall Decay Proof.Let the total memory stream containNchunks asserting the stale stateS old andMchunks asserting the valid state S new . Under the Accumulation Hypothesis (Assumption 3.3), N ≫ M . We model the retrieval of top-kchunksR k as sampling without replacement from the population N + M. LetXbe the random variable denoting the number of valid chunks (S new ) successfully retrieved. If retrieval were purely uniform, X would follow a hypergeometric distribution: P (X = x) = M x N k−x N +M k (5) The expected value isE[X] = k M N +M . However, dense retrievers utilize cosine similarity over high-dimensional embeddings. Under Seman- tic Equivalence (Lemma 3.2),|sim(q,S old )− sim(q,S new )| < ε. BecauseS old constitutes the vast majority of the embedded semantic space, dense retrieval exhibits a structural bias towards the denser centroid ofS old phrasings. Therefore, the hypergeometric expected value serves as a strict theoretical upper bound. Taking the limit as the interaction history scales: lim N→∞ E[X]≈ lim N→∞ k M N + M = 0(6) AsN → ∞, the probability of retrieving zero valid evidence (P (X = 0)) approaches 1, proving Asymptotic Recall Decay. B.2 Proof of Theorem 2: The Majority Vote Trap Proof.Assume the retriever successfully circumvents Theorem 1 and retrieves a mixed contextR k containing 1 valid chunk (S new ) and k− 1 stale chunks (S old ). During generation, the LLM utilizes scaled dot-product attention. Letα i denote the attention weight assigned to chunkc i ∈ R k . Under Lemma 3.2, the semantic embeddings ofS old andS new are equivalent up toε < 0.10. Consequently, the query vectorqyields roughly identical dot-products across all k chunks. Applying the softmax function over these practically uniform logits results in a non-discriminating attention distribution: α i ≈ 1 k ∀c i ∈R k (7) The final generation probability for a stateyis the sum of the attention mass corresponding to the chunks asserting that state. P (y = S old ) = X c i ∈S old α i ≈ k− 1 k (8) P (y = S new ) = X c j ∈S new α j ≈ 1 k (9) For any typical retrieval window (k ≥ 5), k−1 k ≫ 1 k . The probability mass overwhelmingly favors the stale state. Thus, even when valid evidence is perfectly retrieved, generation collapses due to attention dilution, proving the Majority Vote Trap. 26

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