Agent-based simulations validating the axiomatic framework for risk, prediction, and systemic stability.
Companion simulation package for "The First Principles of Uncertainty: A Unified Axiomatic Framework for Risk, Prediction, and Systemic Stability" — Paper III in the Applied Probabilistic Systems series.
The paper identifies five axiomatic properties of uncertainty — Irreducibility (Knight 1921), Reflexivity (Soros 1987), Non-Stationarity (Minsky 1992), Emergent Coupling (Mandelbrot 1963), and Requisite Diversity (Holling 1973) — and demonstrates that their unification into a single deductive system produces seven theorems with consequences no prior framework has derived.
This code validates the theorems computationally through agent-based simulation.
| Simulation | Validates | Key Result |
|---|---|---|
| Precision-Fragility Paradox | Theorem 6 (Axioms II + V) | Inverted-U: shared knowledge improves stability to a point, then destroys it |
| Calibration Decay | Theorem 3 (Axioms I + III) | Prediction error grows unpredictably. Decay rate is itself non-stationary |
| Diversification Failure | Theorem 4 (Axiom IV) | Portfolio diversification benefit collapses from 0.95 to near zero under stress |
| Coupling Cascade | Axiom IV | Non-linear phase transition: isolated failures become systemic cascades |
| Endogenous Feedback | Theorem 2 (Axiom II) | Risk estimates feeding back into reality amplify volatility ~86% |
Theorems 1, 5, and 7 are validated by logical argument in the paper rather than simulation.
# Install dependencies
pip install numpy matplotlib scipy
# Run all simulations
python uncertainty_simulations.py
# Run a specific theorem
python uncertainty_simulations.py --theorem 6
# Export publication-quality figures
python uncertainty_simulations.py --export
# Custom parameters
python uncertainty_simulations.py --agents 1000 --trials 100 --seed 42The code includes production-ready implementations of three core metrics defined in the paper:
- DDR (Distributional Drift Rate) — speed of distributional change
- BHI (Behavioural Homogeneity Index) — agent response similarity
- CII (Coupling Intensity Index) — cross-factor correlation intensity
All simulations use numpy.random.default_rng with explicit seed control. Default seed is 42. Results are deterministic for any given configuration.
| Paper | Title | Date |
|---|---|---|
| I | The Reflexive Stagnation Trap | December 2025 |
| II | The Homogeneity Threshold | January 2026 |
| III | The First Principles of Uncertainty | February 2026 |
All papers at jasongething.substack.com
Gething, J. (2026). "The First Principles of Uncertainty: A Unified Axiomatic
Framework for Risk, Prediction, and Systemic Stability." FishIntel Global,
Applied Probabilistic Systems Working Paper Series, Paper III.
Jason Gething — Founder, FishIntel Global
MIT — see LICENSE