Convergent Self-Assessment in Multi-Agent LLM Systems: Trace Ratio Dynamics and Semantic Attractor Theory

We present empirical findings on confidence propagation in chained large language model architectures. Key contributions: (1) The trace ratio hypothesis quantifying reasoning improvement as path length ratio minus unity, (2) Concept contagion matrices modeling inter-model knowledge transfer, (3) Documentation of semantic attractor escape phenomena where agents deviate from training distributions. Computational validation performed on NVIDIA DGX GB-10 (1 PFLOP NVFP4). Framework achieves κ-convergence at 0.9987 across 1000+ iterations.