Koopman Spectral Analysis Gives Multi-Agent Debates a Convergence Deadline You Can Compute Before Running Them

arXiv 2608.05956·medium signalXBlueskyLinkedInCopy link

arXiv 2608.05956 (Aug 6) treats an LLM agent collective as one nonlinear dynamical system and estimates its Koopman transfer operator from interaction traces, yielding three machine-checkable certificates. The sub-dominant eigenvalue produces a convergence deadline computable before the debate runs — it tracked observed convergence with log-log correlation 0.93 and bounded it in 96% of 24 configurations; its eigenvector names the coherent factions driving the decision; and eight of 32 spectral coordinates preserved the decision at 99.7% fidelity. A certificate learned from 15 debates held on 60 of 60 held-out debates, and the whole analysis runs in minutes on CPU — cheap enough to bolt onto a production multi-agent voting setup as a round-budget oracle.