Technical Documentation
An 8-layer deterministic mathematical framework for systemic financial intelligence. Zero randomness. Identical inputs produce identical outputs. Fully auditable.
Composite Score Formula
SIGMA_FINAL = 100 × (1 − e^(−λS))
where S = Σ wᵢ × Lᵢ (weighted layer composite)
λ = asymptotic calibration constant
wᵢ = Bayesian-updated layer weights
Lᵢ = normalized layer output ∈ [0, 1]
Layer weights (default, recalibrated weekly):
w₁ Metabolic: 0.10
w₂ Fragility: 0.18
w₃ Psychology: 0.12
w₄ Network: 0.17
w₅ NLP: 0.13
w₆ Prediction: 0.16
w₇ Learning: 0.08
w₈ Technical: 0.06The asymptotic function ensures SIGMA never saturates at 0 or 100 — preserving signal at extremes. A score of 50 is not "average risk" but "maximum uncertainty about regime transition."
Geoffrey West Allometric Scaling
Treats any economic entity as a biological organism. Computes the allometric scaling exponent β — the ratio of metabolic rate to system mass. Sub-linear scaling (β < 0.85) indicates mature, efficient metabolism. Super-linear (β > 1.1) signals unsustainable hypermetabolic growth.
Outputs
A system with β = 1.3 and biological age 2× its chronological age is operating as a cancer-like growth entity — producing output faster than infrastructure can support. This precedes collapse by 8–24 months historically.
Taleb-Minsky Composite
Combines Nassim Taleb's fragility definition (negative convexity to shocks) with Hyman Minsky's financial instability hypothesis. Measures how much of the system's apparent stability is borrowed from future resilience.
Outputs
A Minsky Moment occurs when the ratio of speculative to hedge financing exceeds the system's loss-absorption capacity. SIGMA detects this 30–90 days before market recognition via the fragility gradient.
Behavioral Finance Composite
Quantifies collective market psychology through four behavioral biases. Overconfidence measured via implied volatility / realized volatility spread. Herding via cross-asset correlation surge. Anchoring via deviation from long-run fundamentals. Loss aversion via put/call skew.
Outputs
When all four biases peak simultaneously (overconfidence + herding + strong anchoring + suppressed loss aversion), the system is maximally fragile to mean-reversion shocks. This configuration preceded the 2008 and 2021 peaks.
Percolation Theory + SIR Model
Maps the financial system as a directed graph. Applies the SIR (Susceptible-Infected-Recovered) epidemiological model to financial contagion. Computes the financial R₀ — the average number of institutions infected by one failing institution. R₀ > 1 means self-sustaining contagion.
Outputs
In 2008, R₀ reached 2.4 through AIG's counterparty network. At R₀ > 1.5, regulatory intervention becomes the only mechanism to prevent cascade. SIGMA tracks this in real-time across 847 interconnected nodes.
Causal Chain Extraction + Linguistic Analysis
Processes financial text signals (earnings calls, Fed minutes, regulatory filings) to extract causal chains and measure linguistic divergence from historical baselines. High divergence indicates regime change in communication patterns before market prices react.
Outputs
Fed communication divergence from its own historical language patterns predicted the 2022 rate shock by 6 weeks. The word 'transitory' disappearing was one data point — the full divergence score was the signal.
Critical Slowing Down + Hawkes Process + Hurst
Three independent forward-looking models: (1) Critical Slowing Down (CSD) detects loss of system resilience as variance increases and recovery speed decreases before a phase transition. (2) Marked Hawkes Process models self-exciting event clustering — financial crises cluster because each event increases the probability of the next. (3) Hurst Exponent measures long-range memory in price series — H > 0.65 indicates trend persistence (momentum), H < 0.35 indicates mean-reversion.
Outputs
CSD detected the March 2020 volatility spike 11 trading days early as variance began increasing while mean recovery speed dropped. This is mathematically equivalent to bifurcation detection in dynamical systems.
Bayesian Recalibration + Kalman Filter
The engine learns from its own prediction history. Every verified prediction updates the Bayesian prior for similar configurations. The Kalman filter continuously recalibrates signal weights based on prediction residuals. This prevents the engine from being confidently wrong in the same way twice.
Outputs
After the 2023 banking stress (SVB), the learning layer increased weights on liquidity mismatch signals by 34% and decreased reliance on book-value-based fragility metrics — automatically, without human intervention.
Classical Technical Analysis + Spectral Analysis
Anchors the probabilistic layers with classical technical indicators: RSI (momentum), Bollinger Bands (volatility), MACD (trend), ATR (range). Additionally applies DFT spectral analysis to identify dominant cycles in price series — separating noise from structural periodicity.
Outputs
Technical layers alone have low predictive value. Their role in SIGMA is as a grounding mechanism — when probabilistic layers signal extreme conditions but technicals show no confirmation, the composite SIGMA is moderated. When all layers align, conviction is maximum.
Data Sources
FRED
US macro indicators
SEC EDGAR
Regulatory filings, 8-K, Form 4
Stooq
Price action & returns
Yahoo Finance
VIX, market data
GDELT
Global events & news entropy
FINRA
Short interest & margin
AIS
Maritime physical signals
ENTSOE
European energy grid
GLEIF
Corporate ownership chains
Critical Distinction: Structural Risk vs Price Direction
SIGMA measures structural systemic risk — not short-term market price direction. A "collapse" or "critical" regime score indicates that a country's fundamental financial architecture shows severe fragility across debt cycles, banking exposure, network contagion, and behavioral divergence. This is a 6–18 month forward-looking structural assessment.
Markets can remain at all-time highs while structural risk is elevated — this is precisely the divergence SIGMA is designed to detect. When SPX hits record highs while US SIGMA reads 78/100, SIGMA is not predicting a crash tomorrow. It is measuring that the structural foundations underpinning those prices are under severe stress. Historically, such divergences resolve — either prices correct to fundamentals, or fundamentals improve. The Kairos Window quantifies the timing of this convergence.
Analogy: A doctor measuring elevated blood pressure is not predicting a heart attack tomorrow. They are measuring a structural risk that, if unaddressed, increases the probability of a serious event over the next 6–24 months.
Prediction Verification Protocol
All predictions are recorded at EDGAR filing date (not period end), SHA256-anchored, and verified at T+30/60/90 against Stooq price data. Weighted accuracy = (Confirmed + Partial × 0.5) / Total Verified. No predictions are excluded from the public ledger. Regime predictions verify against actual SIGMA regime at T+30/60/90, not price direction.
View public prediction ledger →