Knowledge base · SIGMA Engine
Concepts library
The mathematical and financial concepts powering the SIGMA engine. Each carries a formal definition, its formula, historical examples, and live readings across 22 countries.
Hurst Exponent
The Hurst Exponent (H) measures trend persistence in financial time series. H > 0.5 indicates persistent trending behavi…
Hawkes Process
A Hawkes process is a self-exciting point process where each event increases the probability of future events. In financ…
R₀ Financial Contagion Number
R₀_financial is the financial contagion reproduction number — the expected number of secondary country crises caused by …
Early Warning Signal (EWS)
An Early Warning Signal (EWS) is a mathematically-derived indicator that a financial system is approaching a critical tr…
Regime Transition
A regime transition in financial systems is an abrupt shift from one quasi-stable state to another — from "stable" to "a…
Markov Chain Risk Modeling
Markov Chain risk modeling represents financial systems as probabilistic state machines where the current state determin…
Noosphere Score (SIGMA)
The Noosphere Score (SIGMA) is a deterministic, multi-layer mathematical risk score from 0 to 100 that measures systemic…
Minsky Cycle
The Minsky Cycle is a three-phase model of financial fragility developed by economist Hyman Minsky. Phase 1 (Hedge): bor…
Sovereign Default
A sovereign default occurs when a national government fails to meet its debt obligations — either through non-payment, r…
Minsky Moment
The Minsky Moment is the sudden transition from financial stability to crisis — the point at which market participants s…
Phantom Consensus
Phantom Consensus is the systematic divergence between official/public narrative and the underlying mathematical risk si…
Carry Trade & Currency Risk
A carry trade borrows in a low-interest currency and invests in a high-interest currency, creating systemic fragility wh…
Sudden Stop — Capital Flow Reversal
A sudden stop occurs when foreign capital inflows abruptly cease, forcing a country to rapidly adjust its current accoun…
Yield Curve Inversion — The Recession Predictor
Yield curve inversion — when short-term interest rates exceed long-term rates — has preceded every US recession for 50 y…
Dutch Disease — Resource Curse Economics
Dutch disease occurs when a natural resource boom drives currency appreciation that destroys a country's non-resource ex…
Original Sin — External Debt in Foreign Currency
"Original sin" in economics describes the inability of developing countries to borrow internationally in their own curre…
Fiscal Multiplier — When Government Spending Amplifies or Destroys
The fiscal multiplier measures how much GDP changes per unit of government spending. In crisis periods, multipliers can …
Contagion Risk
Financial contagion is the cross-border or cross-market transmission of financial shocks beyond what fundamentals justif…
Percolation Threshold
The percolation threshold is the critical network connectivity level above which stress can propagate across an entire f…
Balance of Payments Crisis
A balance of payments crisis occurs when a country cannot finance its current account deficit — running out of foreign e…
See it live
These concepts are running live across 22 countries.
Every SIGMA score is computed from the concepts above — SHA-256-anchored and verifiable.