# Delayed Verification Destabilizes Multi-Agent LLM Belief: Instability Thresholds and Optimal Corrector Placement

arXiv: https://arxiv.org/abs/2606.27409 · HTML: https://mlsanity.com/paper/2606.27409/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 35 of its 56 references that are in the map.
- First posted on arXiv 25 Jun 2026.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 30 of 35)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [How Language Model Hallucinations Can Snowball](https://mlsanity.com/paper/2305.13534/) (2023)
- [ReConcile: Round-Table Conference Improves Reasoning via Consensus among Diverse LLMs](https://mlsanity.com/paper/2309.13007/) (2023)
- [Which Agent Causes Task Failures and When? On Automated Failure Attribution of LLM Multi-Agent Systems](https://mlsanity.com/paper/2505.00212/) (2025)
- [Improving Multi-Agent Debate with Sparse Communication Topology](https://mlsanity.com/paper/2406.11776/) (2024)
- [TRAIL: Trace Reasoning and Agentic Issue Localization](https://mlsanity.com/paper/2505.08638/) (2025)
- [Talk Isn't Always Cheap: Understanding Failure Modes in Multi-Agent Debate](https://mlsanity.com/paper/2509.05396/) (2025)
- [Multi-Agent Consensus Seeking via Large Language Models](https://mlsanity.com/paper/2310.20151/) (2023)
- [GUARDIAN: Safeguarding LLM Multi-Agent Collaborations with Temporal Graph Modeling](https://mlsanity.com/paper/2505.19234/) (2025)
- [AgentHallu: Benchmarking Automated Hallucination Attribution of LLM-based Agents](https://mlsanity.com/paper/2601.06818/) (2026)
- [When Models Lie, We Learn: Multilingual Span-Level Hallucination Detection with PsiloQA](https://mlsanity.com/paper/2510.04849/) (2025)
- [From Spark to Fire: Modeling and Mitigating Error Cascades in LLM-Based Multi-Agent Collaboration](https://mlsanity.com/paper/2603.04474/) (2026)
- [Hallucination Cascade: Analyzing Error Propagation in Multi-Agent LLM Systems](https://mlsanity.com/paper/2606.07937/) (2026)
- [Sherlock: Reliable and Efficient Agentic Workflow Execution](https://mlsanity.com/paper/2511.00330/) (2025)
- [AgentForesight: Online Auditing for Early Failure Prediction in Multi-Agent Systems](https://mlsanity.com/paper/2605.08715/) (2026)
- [Opinion Consensus Formation Among Networked Large Language Models](https://mlsanity.com/paper/2601.21540/) (2026)
- [MARCH: Multi-Agent Reinforced Self-Check for LLM Hallucination](https://mlsanity.com/paper/2603.24579/) (2026)
- [Collective Hallucination in Multi-Agent LLMs:Modeling and Defense](https://mlsanity.com/paper/2606.07941/) (2026)
- [Unveiling the Entropy Dynamics of Chain-of-Thought Reasoning](https://mlsanity.com/paper/2606.02020/) (2026)
- [Self-Correction as Feedback Control: Error Dynamics, Stability Thresholds, and Prompt Interventions in LLMs](https://mlsanity.com/paper/2604.22273/) (2026)
- [PropGuard: Safeguarding LLM-MAS via Propagation-Aware Exploration and Remediation](https://mlsanity.com/paper/2605.16346/) (2026)
- [CASPIAN: Online Detection and Attribution of Cascade Attacks in LLM Multi-Agent Systems via Cross-Channel Causal Monitoring](https://mlsanity.com/paper/2605.19240/) (2026)
- [Submodular Optimization for Consensus Networks with Noise-Corrupted Leaders](https://mlsanity.com/paper/1712.08212/) (2017)
- [Interacting Large Language Model Agents. Interpretable Models and Social Learning](https://mlsanity.com/paper/2411.01271/) (2024)
- [Hidden Anchors in Multi-Agent LLM Deliberation](https://mlsanity.com/paper/2606.19494/) (2026)
- [Contagion Networks: Evaluator Preference Propagation in Multi-Agent LLM Systems](https://mlsanity.com/paper/2606.20493/) (2026)

## Built on by (most cited first, 4 of 4)

- [Onnes: A Physics-Grounded Multi-Agent LLM Simulator for Cryogenic Fault Diagnosis in Quantum Computing Infrastructure](https://mlsanity.com/paper/2607.05805/) (2026)
- [How Much Does Correctness Cost? Budgeted Placement of Strong Correctors in a Weak Multi-Agent Swarm](https://mlsanity.com/paper/2607.09765/) (2026)
- [Uncertainty Quantification for LLM Agents: A Taxonomy, an Evaluation Protocol, and an Empirical Study](https://mlsanity.com/paper/2609.07395/) (2026)
- [Maat: Independent Deterministic Contract-Based Governance for Multi-Agent LLM Workflows](https://mlsanity.com/paper/2609.34017/) (2026)

## Abstract (arXiv)

Multi-agent large language model (LLM) systems often rely on verifier and critic agents to suppress hallucinations, but verification is delayed. During this delay, false claims can propagate through the agent network. We model this process as delayed consensus on a graph with grounded corrector nodes. Spectral decomposition by the grounded Laplacian yields a closed-form stability threshold for the verification dose: correction that is too strong or too delayed can turn consensus into oscillation. The most unstable regime occurs when the communication and verification delays coincide; for delay two, the threshold is the inverse golden ratio. The same framework gives a supermodular placement objective and a greedy (1-1/e)-approximation rule for assigning a limited corrector budget to influential nodes. Experiments across five open models confirm the predicted dose-delay oscillations. By contrast, grounded factual answering makes truth an absorbing boundary and eliminates the effect, suggesting that the instability is specific to signed-belief tasks while grounded verification remains stabilizing