Asymmetric Coherence Index (ACI)
A dual-dimension metrological framework for characterizing resilience dynamics in complex systems
Domains: Simulation · Institutional systems · Neurophysiology · Limnology Abstract
We present the Asymmetric Coherence Index (ACI), a dual-dimension metrological framework for characterizing coherence dynamics in complex systems. Each element is described by two independent dimensions — a conformity degree t_i and a deviation degree f_i — from which local coherence C_i = 1 − |t_i + f_i − 1| and global coherence C_glob (Łukasiewicz aggregation) are derived. Four standardized dynamic tests characterize each domain: attractor existence (Test A), resilience asymmetry (Test B), structural ratio R₁ = θ/C_glob (Test C), and fluctuation distribution (Test D). Applied to simulation (N = 120 agents, 3 topologies, 25 seeds), institutional data (Polity5, 184 countries, 1800–2018), neurophysiology (EEG at rest, PhysioNet eegmmidb, 13 subjects), and limnology (NTL-LTER, 5 Wisconsin lakes, 1984–2016), we identify a robust transversal result: coherence-increasing transitions are significantly more resilient than decreasing ones across all empirical domains (Polity5: 95.2% vs. 21.3%, Δ = 73.8 pts; NTL-LTER: 96.3% vs. 60.7%, Δ = 35.6 pts; EEG: 80.3% vs. 53.4%, Δ = 26.9 pts; N = 886 total transitions). For lacustrine systems, this asymmetry corresponds to the known phenomenon of ecological hysteresis (Scheffer et al. 2001) — here evidenced by a new standardized instrument rather than discovered as a new phenomenon.
Two prospective baseline analyses qualify the scope of results: (1) the structural ratio R₁ is not specific to the bilattice formalism on simulation data (maximum deviation vs. simple average <0.005); (2) comparative simulations (HA_RESILIENCE v3, 75 replicates) show that bilattice and 1D models recover identically after equivalent perturbations, indicating that the observed asymmetry is a property of the empirical systems studied, not a specific prediction of the dual formalism. ACI thus functions as an instrument capable of revealing this property across heterogeneous domains, rather than as a theory explaining it.