The Homogeneity Threshold

How AI Precision Creates Systemic Fragility

Paper II in the Applied Probabilistic Systems Series

Jason Gething · FishIntel Global Ltd. · February 2026

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Core Result

Improving AI accuracy in adaptive systems monotonically increases the probability of catastrophic cascade failure:

h(q) = τ₀q^γ / (τ₀q^γ + (1−r)τₚ)

The critical diversity threshold required to prevent cascade:

φ*(q, h*) = 1 − √(h* / h(q))

Key Findings

• 31/31 robustness configurations pass monotonicity
• h(1) = 0.741 — maximum homogeneity at full AI quality
• φ = 17.8%* — diversity required at maximum AI quality
• 0% safeguard success when q > 0.6
• 106 cascade events in baseline simulation (N=1,000, T=10,000)

Reproduce the Figure

pip install numpy matplotlib
python generate_paper_ii_hero.py

Citation

Gething, J. (2026b). The Homogeneity Threshold: How AI Precision Creates Systemic Fragility. FishIntel Global Working Paper.

Series

• Paper I: Uncertainty Axioms (Gething, 2026a)
• Paper II: The Homogeneity Threshold (this repo)
• Paper III: Forthcoming

License

MIT