Appendix Y — Horizon Robustness and Memory Persistence
Appendix Y — Horizon Robustness and Memory Persistence
\labelapp:horizon_robustness
This appendix examines the temporal robustness of the observed dynamical behavior. Its sole purpose is to establish that the reported regimes are not artifacts of finite simulation time, numerical transients, or horizon truncation.
No interpretation of the origin or meaning of the observed persistence is introduced here. Only direct comparisons across simulation horizons are reported.
Multi-Horizon Protocol
Each dissipation value was simulated using identical numerical parameters, except for the total integration length. Three horizons were employed:
All diagnostics reported in this appendix are computed independently for each horizon and each realization (‘rep‘).
Horizon Robustness of Angular Momentum
Figure ‘§fig:horizon_robustness‘ shows the mean angular momentum as a function of simulation horizon for representative runs across the parameter scan.
\beginfigure[H]
[figure: see original PDF]
Figure: Horizon robustness test. Mean angular momentum measured at 160k, 320k, and 640k simulation steps. For runs classified as ‘ORBIT‘, the qualitative magnitude of persists under horizon extension. \labelfig:horizon_robustness \endfigure
The data show that extending the simulation horizon:
- does not induce numerical divergence,
- does not force a transition to collapse,
- does not suppress angular momentum on short timescales.
Angular Momentum Persistence
Figure ‘§fig:L_persistence‘ compares angular-momentum persistence for representative low- and high- cases.
\beginfigure[H]
[figure: see original PDF]
Figure: Angular momentum persistence across horizons. Low- runs exhibit sustained across increasing simulation time, while high- runs remain suppressed. \labelfig:L_persistence \endfigure
No evidence is observed for rapid decay of angular momentum solely as a function of integration time.
Orbital Memory Distribution
Figure ‘§fig:orbital_memory‘ shows the distribution of completed orbital cycles across all runs classified as ‘ORBIT‘.
\beginfigure[H]
[figure: see original PDF]
Figure: Distribution of orbital memory. The number of completed orbital cycles varies across realizations, indicating history dependence, while remaining bounded and non-divergent under horizon extension. \labelfig:orbital_memory \endfigure
The persistence of orbital motion across extended horizons demonstrates that the observed behavior is not a transient produced by short integration windows.
Scope of the Appendix
This appendix establishes only that:
- the observed behavior survives horizon extension,
- angular momentum does not collapse immediately with time,
- orbital motion is not a finite-time artifact.
No physical interpretation or causal explanation is implied.
End of Appendix Y.
Gravity as a Temporally Closed Dynamical Phase/38_Appendix Y — Horizon Robustness and Memory Persistence.tex in the verified v2 revision. Found an issue with this section? Submit a criticism.Cite this section
Plain text
Hassan, A. (2026). Appendix Y — Horizon Robustness and Memory Persistence. In Gravity as a Temporally Closed Dynamical Phase, The Complete Structural Selection Corpus. Nuronova Genix Corp. https://structuralselection.org/book/appendix/appendix-y-horizon-robustness-and-memory-persistence
BibTeX
@incollection{hassan2026appendixyhorizonrobu,
author = {Hassan, Akram},
title = {Appendix Y — Horizon Robustness and Memory Persistence},
booktitle = {The Complete Structural Selection Corpus},
publisher = {Nuronova Genix Corp},
year = {2026},
url = {https://structuralselection.org/book/appendix/appendix-y-horizon-robustness-and-memory-persistence}
}RIS
TY - CHAP AU - Hassan, Akram TI - Appendix Y — Horizon Robustness and Memory Persistence T2 - The Complete Structural Selection Corpus PB - Nuronova Genix Corp PY - 2026 UR - https://structuralselection.org/book/appendix/appendix-y-horizon-robustness-and-memory-persistence ER -