A canonical scoring framework for systemic fragility.
Ω-Fragility (ΩF) is a 0–10 score for any node in a critical system, built from five canonical pillars under configurable weights.
How impossible to substitute, technically or commercially.
Captures the true cost of substitution: technical compatibility, certification windows, contractual lock-in, and supplier concentration. A node with I=10 cannot be replaced on any meaningful timeline.
Time to restore equivalent capacity after catastrophic failure.
Models the recovery clock: lead times, capital requirements, regulatory approvals, and skill availability. A node with R=10 has effectively no near-term recovery path — failure is permanent on operational horizons.
Sanctions, conflict, export controls, and regulatory exposure.
Encodes geopolitical and regulatory exposure: sanctions risk, conflict zones, export controls, dual-use restrictions. A node with J=10 sits at the intersection of multiple hostile regimes or under a single decisive lever.
Downstream impact depth: GDP, sectors, nonlinear propagation.
Quantifies the systemic blast radius: how many downstream nodes lose function, how deep the cascade runs, what nonlinear amplifiers (panic, hoarding, deleveraging) kick in. A node with C=10 is load-bearing for the system itself.
Distributional depth beyond VaR — fat-tail severity.
Goes past Value-at-Risk to characterize the depth of the tail: how bad is the bad case, conditional on being bad. Heavy-tailed processes routinely produce realizations multiple sigmas beyond historical VaR.
A reinsurer evaluating sovereign credit cares about J and T. A supply-chain operator cares about I and R. The same five pillars, reweighted to your risk model.
Throughput-weighted system fragility. Each node contributes proportional to its share of system flow.
Exposure-weighted system fragility. Weighted by sanctions, geographic concentration, capital risk.
Number of downstream nodes whose loss exceeds threshold τ when node i fails.
Time between a node's failure and the onset of systemic failure. The operational window for response.
Watch ΩF scoring on a live graph.
Trial accounts include the full pillar breakdown, configurable weights, and system-level aggregation.
