Recursive Knowledge Synthesis for Multi-LLM Systems: Stability Analysis and Tri-Agent Audit Framework

TL;DR

This work tackles the problem of logical drift and opaque coordination in multi-LLM systems by proposing Recursive Knowledge Synthesis (RKS), a tri-agent cross-validation framework that couples semantic generation, analytical checking, and transparency auditing under human supervision. The authors formalize a contraction-mapping–based stability theory around a cross-validation operator $V_{Op} = M_T \circ M_A \circ M_S$, and empirically validate the approach across 47 trials using public, freemium LLMs, reporting $\text{RRS} = 0.78 \pm 0.06$, $\text{TS} \ge 0.8$ in most trials, and $\approx 89\%$ convergence. Key contributions include (1) a structured tri-agent architecture with session-level decomposition, (2) a formal fixed-point stability framework for RKS, and (3) an empirical evaluation under realistic deployment constraints that demonstrates strong stability and auditability while maintaining safety via human-in-the-loop bridging. The findings suggest that safe, humansupervised multi-LLM workflows can achieve stable recursive knowledge synthesis in accessible environments, offering a path toward reproducible, interpretable multi-model reasoning without privileged API access. This framework provides a blueprint for democratized research into robust, explainable multi-LLM systems and sets the stage for future automation with preserved safety guarantees.

Abstract

This paper presents a tri-agent cross-validation framework for analyzing stability and explainability in multi-model large language systems. The architecture integrates three heterogeneous LLMs-used for semantic generation, analytical consistency checking, and transparency auditing-into a recursive interaction cycle. This design induces Recursive Knowledge Synthesis (RKS), where intermediate representations are continuously refined through mutually constraining transformations irreducible to single-model behavior. Across 47 controlled trials using public-access LLM deployments (October 2025), we evaluated system stability via four metrics: Reflex Reliability Score (RRS), Transparency Score (TS), Deviation Detection Rate (DDR), and Correction Success Rate (CSR). The system achieved mean RRS = 0.78+-0.06 and maintained TS >= 0.8 in about 68% of trials. Approximately 89% of trials converged, supporting the theoretical prediction that transparency auditing acts as a contraction operator within the composite validation mapping. The contributions are threefold: (1) a structured tri-agent framework for coordinated reasoning across heterogeneous LLMs, (2) a formal RKS model grounded in fixed-point theory, and (3) empirical evaluation of inter-model stability under realistic, non-API public-access conditions. These results provide initial empirical evidence that a safety-preserving, humansupervised multi-LLM architecture can achieve stable recursive knowledge synthesis in realistic, publicly deployed environments.

Figures (9)

• Figure 1: Tri-agent cross-validation architecture showing the External Supervisor coordinating the Semantic Module ($M_S$), Analytical Module ($M_A$), and Transparency Audit Module ($M_T$) through control and recursive feedback loops.
• Figure 2: Weight distribution of the Reflex Reliability Score (RRS), showing relative contributions of Transparency Score (TS, 30%), Deviation Detection Rate (DDR, 40%), and Correction Success Rate (CSR, 30%) to overall system stability.
• Figure 3: Sequential validation workflow illustrating the composition of the validation operator $V_{Op} = M_T \circ M_A \circ M_S$ through the three-stage processing pipeline.
• Figure 4: Extended roles in the multi-LLM tri-agent framework, illustrating the interaction between the External Supervisor and the three core modules with bidirectional control and feedback pathways.
• Figure 5: Session-Level Role Decomposition (SLRD) implementation within ChatGPT Plus, showing three isolated sessions for Semantic Refinement, Analytical Critique, and Audit Evaluation, with all inter-session transfers mediated by the Human Supervisor.