Follow-up Controlled Threshold Study

In the controlled follow-up sweep over 2,700 fixed-size synthetic systems plus 144 healthcare variants, StressLab found that the collapse threshold stays primarily utilization-led, while higher coupling shifts it only modestly on average (0.008 utilization points) but reduces the shock margin to failure by about 39.2%.

Counts

Synthetic controlled systems: 2,700
Healthcare variants: 144

Threshold shift table

topology_type topology_label low_threshold medium_threshold high_threshold threshold_shift
scale_free Scale-Free 0.223129 0.225859 0.222352 -0.000778
hierarchical_supply Hierarchical Supply 0.298518 0.299785 0.300335 0.001816
market_microstructure Market Microstructure 0.218241 0.224300 0.224785 0.006544
small_world Small-World 0.245826 0.251937 0.254477 0.008650
random_queue Random Queue 0.289177 0.283908 0.312077 0.022900

Failure shock margin shift

topology_type topology_label mean_pct_change_high_vs_low median_low_budget median_high_budget
hierarchical_supply Hierarchical Supply -0.921638 0.000000 0.000000
market_microstructure Market Microstructure -0.510785 0.000000 0.000000
scale_free Scale-Free -0.279359 0.055910 0.040342
random_queue Random Queue -0.260210 0.636697 0.445645
small_world Small-World 0.011982 0.237774 0.212637

Healthcare threshold table

topology_type topology_label coupling_regime critical_utilization peak_slope mean_collapse_probability feature
healthcare_referral Healthcare ED Family high 0.975 3.333333 0.694444 util_target
healthcare_referral Healthcare ED Family low 0.975 3.333333 0.694444 util_target
healthcare_referral Healthcare ED Family medium 0.975 3.888889 0.701389 util_target

Figures

Controlled synthetic collapse curves by topology and coupling regime.
Estimated threshold shifts between low and high coupling regimes.
How higher coupling changes the minimum shock required to trigger failure.
Healthcare ED family collapse curves under utilization and dependency coupling sweeps.
Multi-panel summary of the controlled follow-up study.