Appendix Z — Stability Statistics and Validator Summary

\labelapp:stability_statistics

This appendix provides a purely statistical summary of the simulation outcomes. All results reported here are derived directly from the validator CSV output and the automated verification report.

No interpretation or theoretical inference is introduced.

Definition of Stability

A run is classified as stable (‘ORBIT‘) if and only if:

• the validator phase label is ‘ORBIT‘ or ‘ORBITAL‘,
• angular momentum $\langle |L| \rangle$ is finite,
• non-monotonic radial motion is detected.

This definition is applied uniformly across all dissipation values, realizations, and horizons.

Stability Fraction Across Dissipation

Figure ‘§fig:stability_fraction‘ shows the fraction of runs classified as ‘ORBIT‘ as a function of the dissipation parameter $\gamma$.

\beginfigure[H]

[figure: see original PDF]

Figure: Stability fraction versus dissipation. Each point represents the fraction of runs classified as ‘ORBIT‘ across all realizations and horizons for a fixed $\gamma$. \labelfig:stability_fraction \endfigure

Coverage of the Parameter Scan

The dataset includes:

• Multiple dissipation values spanning low to high $\gamma$,
• Three independent realizations per $\gamma$,
• Three simulation horizons per realization.

In total, the validator processed $95$ independent simulation logs.

Validator Summary

The automated validator report confirms that:

• stable classifications are consistent across horizons,
• apparent short-horizon stability that fails under extension is systematically excluded,
• no additional stable regimes are detected outside the reported range.

All statistics reported in this appendix are reproducible by re-running the parsing and validation scripts on the raw analysis logs.

Scope of the Appendix

This appendix provides only numerical counts, fractions, and classifications. It does not:

• assign physical meaning,
• propose mechanisms,
• extrapolate beyond the measured data.

End of Appendix Z.