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

TL;DR

This paper introduces a tri-agent framework for multi-LLM systems that enhances stability and explainability through recursive knowledge synthesis, supported by empirical trials demonstrating promising stability metrics.

Contribution

It proposes a novel tri-agent recursive framework, formalizes RKS with fixed-point theory, and empirically evaluates stability in real-world multi-LLM deployments.

Findings

Achieved mean Reflex Reliability Score of 0.78

Maintained transparency score >= 0.8 in 68% of trials

89% of trials converged, confirming theoretical stability predictions

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.