Domain Translation Guide for Ω = I × G A Minimal Implementation Specification for Cross-Domain Collapse Analysis

This document provides a minimal specification for translating the Ω (Omega) framework across domains.

The guide defines a fixed implementation structure:

- Ω is not directly observable.

To make it testable, it is decomposed into:

- Structure (I)

- Direction (G)

and defined as:

- Ω = I × G

- event = Ω > q(0.995)

- collapse defined as a single observable variable (independent of Ω)

The threshold q = 0.995 is a reference standard for cross-domain comparability.  

In execution, q_threshold may vary depending on data distribution.

Constraint:

- Within each test, definitions (I, G, q_threshold, collapse) are fixed before evaluation and not modified.

Initial definitions may be simple or provisional; only post hoc modification is restricted.

This establishes a consistent structural interface for constructing Ω using domain-relevant variables.

It enables:

- Reproducible collapse analysis

- Cross-domain comparability

- Independent implementation across systems

The guide includes:

- A fixed core framework

- A step-by-step implementation procedure

- Domain translation examples (healthcare, finance, power systems, ecology)

- Minimum data requirements

This is a structural specification, not a predictive model.

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Test Ω on your own data.

For reporting results, see:

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