Skip to content
Structural Selection
Part VIAppendix2 min read·391 words

Appendix Y — Horizon Robustness and Memory Persistence

Reading widthWidth
Text sizeText

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 γ\gamma was simulated using identical numerical parameters, except for the total integration length. Three horizons were employed:

160,000,320,000,640,000  steps.160{,}000,\quad 320{,}000,\quad 640{,}000 \;\text{steps}.

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 L\langle |L| \rangle 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 L\langle |L| \rangle measured at 160k, 320k, and 640k simulation steps. For runs classified as ‘ORBIT‘, the qualitative magnitude of L\langle |L| \rangle 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-γ\gamma and high-γ\gamma cases.

\beginfigure[H]

[figure: see original PDF]

Figure: Angular momentum persistence across horizons. Low-γ\gamma runs exhibit sustained L\langle |L| \rangle across increasing simulation time, while high-γ\gamma 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.

Source: 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  -