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

The KA Shared Precursor Geometry Conjecture predicts that systems satisfying axioms A1-A5 exhibit a common precursor structure before critical transitions: monotone rise of F_KA, 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 F_KA, A(t), R(t), and compare against CSD variance and lag-1 autocorrelation baselines. Main findings: (1) F_KA 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) F_KA 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.