omega-library

Ω Claim Boundary

This document records the operational claim boundary for the historical V1 Ω framework and Execution Hub. It is not a theory paper. It is a reference for how historical V1 results should be interpreted after the 2026-05-31 empirical boundary clarification.

Boundary note: The earlier Ω-centered empirical layer should not be treated as current validation. Existing V1 materials remain historical, fixed, and Ω-centered. High ratio alone is not evidence. Future empirical claims require independent event labels, frozen definitions, anti-circularity review, sufficient support counts, and validation design before evaluation.

What historical V1 Ω evaluates

Historical V1 Ω evaluates whether independently defined events or states are structurally concentrated in high-Ω regimes under fixed definitions. This is a historical V1 comparison format, not current validation of Ω.

It supports reproducible comparison of:

What Ω does NOT claim

Ω does not claim:

These boundaries apply even when a historical V1 result shows strong concentration. High ratio alone is not evidence.

Fixed ex-ante definitions

Definitions should be fixed before interpreting results.

At minimum, this includes:

Post-hoc tuning should not be presented as a fixed Ω result.

Independent event definitions

Event definitions should be independent from Ω.

The event or collapse label should not be defined by the same Ω value that is later used to evaluate concentration.

This prevents circular interpretation.

Structural concentration only

Ω reports structural concentration.

It does not by itself explain mechanism, establish cause, select an optimal policy, or determine future events.

Open extensions

The historical V1 protocol does not claim prediction, causality, or intervention effects.

A possible future stage would require independent event labels, frozen definitions, anti-circularity review, sufficient support counts, and validation design before evaluation. It should not be treated as validated vNext work.

These extensions are outside the current minimal claim and may be pursued in future work by domain specialists, independent contributors, or the present author.

The historical V1 protocol only evaluates structural concentration: P(event high Ω) versus baseline P(event).

Null results are valid

Null, weak, or near-baseline results are valid outcomes.

A null result means the declared event did not concentrate in high-Ω states under the fixed definitions used in that run.

Null results should be reported when they are reproducible and clearly specified.

Reproducibility-first orientation

The Execution Hub is organized for reproducible execution, navigation, and result reporting.

Canonical public records remain on Zenodo where applicable. GitHub Pages and linked notebooks support execution, templates, issue reporting, and navigation.