A Structural Failure-Mode Transition in Coupled Systems

Code and data for "Why Fixed Protections Fail Under Rising Coordination: A Structural Failure-Mode Transition in Coupled Systems" (Chowon Jung, submitted to Nature Communications).

What's here

• manuscript/ — paper, supplementary information, cover letter, arXiv metadata, and bibliography.
• simulation/ — Python scripts and outputs for the minimal Curie–Weiss model, the L1–L3 ablation cascade, the six-topology agent-based extension, the dynamic-coupling sweep, the active-stabilizer experiment, the sensitivity analyses, and the alternative-model-class sweep.
• empirical/ — Python scripts and outputs for the financial (S&P 500), cryptocurrency, AI-coupling (AlpacaEval), and political-science (V-Dem) analyses, plus per-analysis result writeups.
• REPRODUCIBILITY.md — full manifest mapping every figure and headline number to the script that produced it.

Headline finding

As coupling rises in a coordinated system, the type of failure transitions from fragmentation (uncoordinated disorder) to rigidity (synchronized lock-in on the wrong branch). In 22 years of S&P 500 sector data the empirical type-composition curve correlates with the model's prediction at Spearman ρ = +0.93. The framework also predicts the same regime in cryptocurrency markets (64% of windows supercritical vs ~25% for equities) and locates frontier AI in the regime where passive protections decay.

The underlying scaling law: a fixed stabilizer field h opposing coupling J loses effectiveness as h/J² with an irreducible residual at high coupling. The pattern survives across alternative bistable model classes (Curie–Weiss, voter, Kuramoto, cubic Landau), six network topologies, and two empirical domains.

Reproducing the results

See REPRODUCIBILITY.md for the full script-by-script manifest. Quick start:

# Simulation results (no external data needed)
python simulation/scripts/run_sweep.py
python simulation/scripts/network_abm.py
python simulation/scripts/sensitivity_sweep.py
python simulation/scripts/alternative_class_sweep.py

# Empirical results (see REPRODUCIBILITY.md for one-time data setup)
python empirical/scripts/diversification_failure.py
python empirical/scripts/tail_risk_frequency.py
python empirical/scripts/rigidity_fragmentation.py
python empirical/scripts/crypto_extension.py
python empirical/scripts/ai_coupling_direct.py

Python 3.13 with numpy, pandas, matplotlib, scipy, statsmodels, yfinance, sentence-transformers, and networkx.

License

Code: MIT (see LICENSE). Data redistributed in empirical/data/ is subject to upstream licenses (V-Dem CC-BY 4.0; AlpacaEval Apache 2.0). Financial and FRED data are not redistributed; download instructions are in REPRODUCIBILITY.md.

Citation

Jung, C. Why Fixed Protections Fail Under Rising Coordination:
A Structural Failure-Mode Transition in Coupled Systems.
Manuscript submitted to Nature Communications (2026).

Contact

Issues, reproductions, or alternative analyses → open an issue in this repository.