What question did this study set out to answer?

The research aims to validate the KA Shared Precursor Geometry Conjecture across multiple domains to identify common precursors leading to critical transitions.

May 16, 2026Open Access

A Calibrated Cross-Domain Benchmark for Coupling-Degradation Observables: Sepsis Onset, Seismicity, LLM Instability, and Ecological Collapse

Key Points

The research aims to validate the KA Shared Precursor Geometry Conjecture across multiple domains to identify common precursors leading to critical transitions.
Utilized calibrated simulations for sepsis onset, seismicity, LLM inference stability, and ecological collapse.
Constructed synthetic time series using stochastic differential equations based on domain-specific calibrated parameters.
Computed F_KA and R(t) to evaluate transitions while comparing with CSD variance and lag-1 autocorrelation baselines.
F_KA shows a rise before critical transitions across all domains, with specific lead times identified for each: sepsis (34.2), seismicity (58.7), LLM (41.5), ecological (62.1).
Achieved area under the curve (AUC) >= 0.82 for F_KA compared to binary indicators, outperforming CSD variance (0.69-0.77) and lag-1 autocorrelation (0.64-0.74).
R(t) ratio increases steadily before transitions, spiking sharply (>3 sigma) during external shocks, confirming the conjecture's predictions.

Abstract

The KA Shared Precursor Geometry Conjecture predicts that systems satisfying axioms A1-A5 exhibit a common precursor structure before critical transitions: monotone rise of FKA, irreversibility dominance R (t) to infinity, and measurable lead time over classical indicators. We test this prediction across four domains using real-parameter calibrated simulations: (1) sepsis onset (MIMIC-III-calibrated parameters: inflammatory cytokine-organ coupling degradation) ; (2) seismicity (Parkfield fault-calibrated parameters: stress-slip rate coupling near Omori-law criticality) ; (3) LLM inference instability (calibrated from prior KA empirical studies: attention-entropy coupling degradation) ; and (4) ecological collapse (Sahel dryland-calibrated parameters: vegetation-rainfall coupling near fold bifurcation). For each domain, we generate synthetic time series from domain-calibrated stochastic differential equations, compute FKA, A (t), R (t), and compare against CSD variance and lag-1 autocorrelation baselines. Main findings: (1) FKA rises before the critical transition in all four domains, with domain-specific lead times (sepsis: 34. 2 +/- 4. 1 time units; seismicity: 58. 7 +/- 6. 3; LLM: 41. 5 +/- 5. 2; ecological: 62. 1 +/- 7. 8). (2) FKA achieves AUC >= 0. 82 against a binary transition indicator in all domains, outperforming CSD variance (AUC 0. 69-0. 77) and lag-1 autocorrelation (AUC 0. 64-0. 74). (3) The R (t) ratio rises gradually before endogenous transitions and spikes sharply (>3 sigma) at injected exogenous shocks, supporting OP3. (4) Optimal temperature T* approximately 0. 8-1. 2 across domains, with domain-specific calibration improving AUC by 0. 04-0. 07, supporting OP4.

A Calibrated Cross-Domain Benchmark for Coupling-Degradation Observables: Sepsis Onset, Seismicity, LLM Instability, and Ecological Collapse

Key Points

Abstract

Cite This Study

Also Consider

Also Consider