fleet divergence parameter

Ψ Dashboard

Interactive companion to Nicholls (2026), ANTS Conference. Explore the order parameter for cognitive stigmergy in LLM agent systems.

What is Ψ?

The Fleet Divergence Parameter Ψ = Syn / (Syn + Red) measures productive divergence in role-differentiated agent fleets. Unlike Vicsek's φ, which captures consensus, Ψ captures the information-theoretic balance between synergy and redundancy.

The Inverted-U

Output quality peaks near Ψ* = 0.588 — the stigmergy sweet spot. Below 0.4 (redundant zone), agents over-coordinate. Above 0.7 (fragmented zone), agents under-coordinate. Both extremes reduce quality. F = 35.95, p < 0.0001.

Validated on claude-bus

N=92 instances, 12 rounds, 56K+ heartbeats. Ψ explains 42.3% of variance in output quality (R² = 0.423). It subsumes Balch's K* by 60.6× — ΔR² = 0.551 adding Ψ to K* vs. ΔR² = 0.005 adding K* to Ψ.