StressLab Flagship Research Report

Across 5,000 systems and 5 topology families, StressLab found that collapse risk accelerates sharply once baseline utilization enters a shared transition band around 0.10-0.19, with shared variance and recovery-lag warning signals appearing before failure across domains.

Systems
5,000

Topology families
5

Shared threshold band
0.097–0.186

Healthcare case root
runs\flagship_healthcare_case_workspace\2026-03-17_194529_994433_flagship_healthcare_case_study_batch

Key Findings

Across 5,000 synthetic systems spanning 5 topology families, collapse risk rises sharply in a shared utilization band centered near 0.152, with the middle 50% of per-topology thresholds lying between 0.097 and 0.186.
The transition is not identical across domains, but the threshold spread remains compact at 0.140 utilization points, which is consistent with a common collapse-onset regime rather than unrelated topology-specific behavior.
Utilization is the dominant driver, while secondary structural variables such as capacity_slack, baseline_utilization, routing_entropy, average_degree materially shift how fast collapse accelerates near the threshold.
Early-warning signals are shared across domains: collapse cases show about 1.09x higher variance growth and 1.16x longer recovery lag than stable cases.
Cascade tails are broadly heavy-tailed, but in this run a lognormal tail model consistently fits better than a strict power law, suggesting multiplicative cascade growth rather than a single universal power-law exponent.
The strongest interpretable law candidate from this run is: collapse_probability = -0.1795 + 3.9192 * utilization + 0.2942 * centralization_index.

Threshold Table

topology_type	topology_label	critical_utilization	transition_low	transition_high	peak_slope	mean_collapse_probability
scale_free	Scale-Free	0.061827	0.078714	0.180735	8.504414	0.247000
random_queue	Random Queue	0.096818	0.104050	0.140489	12.674950	0.137000
hierarchical_supply	Hierarchical Supply	0.152108	0.106869	0.249759	9.125011	0.558333
small_world	Small-World	0.186424	0.103293	0.205428	7.542121	0.378000
market_microstructure	Market Microstructure	0.202117	0.139265	0.208130	7.207031	0.768000

Top Predictors

feature	correlation	score
capacity_slack	-0.795639	0.795639
baseline_utilization	0.795639	0.795639
routing_entropy	0.470095	0.470095
average_degree	-0.263592	0.263592
edge_count	-0.241198	0.241198
clustering_coefficient	-0.219609	0.219609
buffer_ratio	0.164216	0.164216
max_eigenvector	0.150227	0.150227
coupling_strength	-0.140501	0.140501
node_count	-0.121322	0.121322

Best Candidate Laws

target	feature	model_type	coefficient	intercept	exponent	r2	observations	formula	complexity	source
collapse_probability	utilization+centralization_index	multivariate_linear	3.919246	-0.179536	0.294189	0.647397	5000	collapse_probability = -0.1795 + 3.9192 * utilization + 0.2942 * centralization_index	85	fragility
collapse_probability	capacity_slack+centralization_index	multivariate_linear	-3.919246	3.739711	0.294189	0.647397	5000	collapse_probability = 3.7397 + -3.9192 * capacity_slack + 0.2942 * centralization_index	88	fragility
collapse_probability	utilization+redundancy_index	multivariate_linear	3.952377	-0.151676	0.543641	0.637317	5000	collapse_probability = -0.1517 + 3.9524 * utilization + 0.5436 * redundancy_index	81	fragility
collapse_probability	capacity_slack+redundancy_index	multivariate_linear	-3.952377	3.800700	0.543641	0.637317	5000	collapse_probability = 3.8007 + -3.9524 * capacity_slack + 0.5436 * redundancy_index	84	fragility
collapse_probability	utilization+coupling_strength	multivariate_linear	3.871861	0.028998	-0.346175	0.636136	5000	collapse_probability = 0.0290 + 3.8719 * utilization + -0.3462 * coupling_strength	82	fragility
collapse_probability	capacity_slack+coupling_strength	multivariate_linear	-3.871861	3.900859	-0.346175	0.636136	5000	collapse_probability = 3.9009 + -3.8719 * capacity_slack + -0.3462 * coupling_strength	86	fragility
collapse_probability	utilization	log	4.459317	-0.124757	NaN	0.633373	5000	collapse_probability = -0.1248 + 4.4593 * log1p(utilization)	60	fragility
collapse_probability	utilization+routing_entropy	multivariate_linear	3.879833	-0.106966	0.016518	0.633078	5000	collapse_probability = -0.1070 + 3.8798 * utilization + 0.0165 * routing_entropy	80	fragility
collapse_probability	capacity_slack+routing_entropy	multivariate_linear	-3.879833	3.772866	0.016518	0.633078	5000	collapse_probability = 3.7729 + -3.8798 * capacity_slack + 0.0165 * routing_entropy	83	fragility
collapse_probability	utilization+capacity_slack	multivariate_linear	2.568646	1.236055	-1.332591	0.633041	5000	collapse_probability = 1.2361 + 2.5686 * utilization + -1.3326 * capacity_slack	79	fragility

Heavy-Tail Summary

topology_type	topology_label	best_model	sample_size	alpha	log_likelihood_gap
market_microstructure	Market Microstructure	lognormal	1000	1.472681	467.405786
hierarchical_supply	Hierarchical Supply	lognormal	1000	1.510951	434.811327
random_queue	Random Queue	lognormal	1000	1.784196	294.729240
small_world	Small-World	lognormal	1000	1.609559	214.329668
scale_free	Scale-Free	lognormal	998	1.840400	129.070765

Early-Warning Summary

metric	collapse_mean	stable_mean	fragile_mean	robust_mean	separation
variance_increase	4.535714e+06	4.147499e+06	4.573395e+06	4.101277e+06	388215.362454
recovery_lag	3.387935e+00	2.911350e+00	3.224520e+00	3.064280e+00	0.476584
autocorrelation_increase	-2.552599e-02	-1.815677e-02	-2.247434e-02	-2.104629e-02	-0.007369

Figures

Collapse probability vs utilization with all topology families overlaid.

Collapse risk heatmap across utilization and coupling bands.

Cascade size survival curves on log-log axes by topology family.

Per-topology collapse transition curves with estimated threshold markers.

Shared early-warning signal trends across low- to high-fragility systems.

Top collapse predictors alongside ranked symbolic/interpretable law candidates.

Healthcare case study: baseline, collapse, and optimized response traces.

Multi-panel summary figure suitable for README or paper intro.