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 one fixed weighting.
The pillars aren’t hand-entered. Manifold’s four reasoning engines turn raw graph data into the five scores the composite consumes — each engine feeds specific pillars.
Full engine breakdown on the product page →
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.
The five pillar weights are fixed and identical across every domain. Manifold applies the same composite everywhere, so a ΩF of 7.0 on a semiconductor supply chain is directly comparable to a 7.0 on pancreatic biology.
What changes per domain is the vocabulary, not the math: on a biomedical graph “Irreplaceability” reads as mechanism rarity and “Jurisdictional Hazard” as regulatory exposure. The numbers stay on one scale.
Per-node ΩF is the input, not the output. Manifold aggregates the node scores into system-level readouts — the live signals on the Ω monitor that tell you how close the whole system is to failure.
Live 0–100 system fragility index. Rises with aggregate shock severity and depleted buffer, and drives the regime band (STABLE → CRASH) in the Ω monitor.
Count of downstream nodes whose loss exceeds threshold τ when node i fails — measured across Monte Carlo cascade runs.
Days from the current buffer to systemic failure: 365 nominal, compressing toward 3 at breach. The operational window for response.
Watch ΩF scoring on a live graph.
Trial accounts include the full pillar breakdown, the canonical weighting, and system-level aggregation.
