Reproducibility Package for Structural Collapse and the Ω State Variable

Boundary note: This record should be read as a historical V1 / methodological record, not as current validation, proof of Ω, or cross-domain empirical confirmation. Some wording below reflects the original V1 framing and should be interpreted under this boundary. High ratio alone is not evidence. The current empirical boundary is defined in: VOT Empirical Layer Boundary Note: Ω-Centered Validation Not Currently Supported — https://zenodo.org/records/20474232

Reproducibility Package for Structural Collapse and the Ω State Variable

Collapse-related events concentrate in the highest Ω regime (top 1%).

→ ~10x higher than baseline.

Run directly in Google Colab:

[Main reproduction — PJM]

https://colab.research.google.com/drive/12xUug2YZ4Xfr79uhI5c70y2HEGRLUv-H

[Quick test — AAPL]

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

[Additional example — BTC (may require retry due to data fetch)]

https://colab.research.google.com/drive/1tWsSTveyDj-rLUHXpZkULAA04gOM-KZE

Reproduced in real-world power system data (PJM).

Ω = I × G

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What this shows:

- collapse-related events are not distributed uniformly

- a direction-based variable (Ω) isolates a high-event regime

- this structure is testable and falsifiable

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Package contents:

- PDF (definitions, pipeline)

- Colab notebook (reproduce_omega_pjm_fixed.ipynb)

- Dataset (rt_hrl_lmps.csv)

Data period: March 1, 2025 – March 1, 2026 (PJM RT LMP, hourly)

Event threshold: 0.998 (independent of Ω)

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After reproduction:

- apply Ω to your domain

- test alternative Ω constructions

- test alternative structural definitions

Try Ω on your own data:

Minimal CSV Template:

https://zenodo.org/records/20309117

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Minimal report format:

domain / data / definition of collapse / P(collapse | high Ω) / baseline P(collapse)

https://github.com/onsenojisan/omega-repro/issues/new?template=report.md

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Related:

- Domain Translation Guide:

https://zenodo.org/records/19199493

- Execution Protocol:

https://zenodo.org/records/19324740

- Cross-domain structural concentration study:

https://zenodo.org/records/20045831

- Execution and reproducibility hub:

https://onsenojisan.github.io/omega-library/