Structural Concentration Test — Cross-Domain Summary (Ω)

Start here (30 sec):

▶ Run in Google Colab

Structural Concentration Test — Cross-Domain Summary (Ω)

This record provides a one-page summary of a minimal empirical observation:

Collapse-like events are not uniformly distributed.

Across domains, they concentrate in structurally defined high-Ω states under fixed definitions.

This is not a predictive model.

It is a structural concentration test.

Core definition:

Ω = I × G

Evaluation:

P(collapse | high Ω) vs P(collapse)

Key properties:

- Definitions are fixed ex-ante (no tuning)

- Collapse is defined independently of Ω (non-circular)

- Results are reported as conditional frequency, not timing prediction

- Reporting does not imply endorsement of a universal law

Domains included:

- Power systems (PJM electricity market)

- Finance (AAPL, BTC)

- Earthquakes (Japan)

- Weather (precipitation, Tokyo)

- Traffic (NYC, Chicago)

High-Ω definition:

- Power: top Ω regime (top 10%)

- Other domains: q(0.99)

Note:

High-Ω thresholds differ by domain and are not calibrated to be equal.

Each result reflects concentration within its own predefined extreme regime.

Reproducibility:

- Reproduction package (code + data):

  https://zenodo.org/records/19159664

- Minimal executable example (Colab):

  https://colab.research.google.com/drive/1FGu7_G1avub-0PUV6cpdox8cojuOvY9C

Additional notes:

- High-Ω is defined per domain and fixed before evaluation (ex-ante)

- In minimal reporting, collapse is treated as the event variable

- The objective is to provide a minimal, comparable reference across domains

Purpose:

To provide a minimal, cross-domain reference showing that collapse concentration can be observed under consistent structural definitions.

This record is a summary artifact.

It does not introduce new definitions beyond the minimal Ω framework.

Canonical structural overview:

https://zenodo.org/records/18296691