10. Validation and Large-Scale Parameter Scans

10.1 Big Orbit Validator Architecture

To distinguish transient dynamics from genuine gravitational phases, a dedicated validation framework was constructed: the Big Orbit Validator.

Rather than relying on isolated simulations, the validator executes structured ensembles spanning:

• Multiple values of the damping parameter $\gamma$,
• Independent realizations with controlled perturbations,
• Multiple temporal horizons for each configuration.

Each individual run consists of:

1. Full numerical integration of the inertial emergent gravity equations,
2. Post hoc extraction of observable diagnostics,
3. Phase classification using orbit count, radial oscillation amplitude, and angular momentum persistence.

All outputs are recorded in audit-grade artifacts:

• Raw spatiotemporal field histories,
• Structured analysis summaries,
• Aggregated tables spanning repeats and horizons.

This architecture ensures that phase identification is objective, algorithmic, and independent of visual inspection or single-run behavior.

10.2 Horizon Scaling ($\times1$, $\times2$, $\times4$)

A central ambiguity in dynamical systems is the misclassification of long-lived transients as stable behavior. To eliminate this risk, each parameter configuration is evaluated across multiple temporal horizons.

Let $T_0$ denote a baseline integration time. For each configuration, simulations are performed at:

A phase classification is accepted only if it remains invariant under horizon extension.

This test directly probes the temporal-closure hypothesis:

• Genuine gravitational phases persist under horizon extension,
• Spurious oscillations decay or collapse as integration time increases.

Horizon scaling therefore functions as a necessary condition for identifying temporally closed dynamics rather than finite-time artifacts.

10.3 Repeatability and Phase Robustness

To assess sensitivity to initial histories, each parameter set is evaluated under multiple controlled repeats.

Repeatability is enforced through:

• Explicit random-seed control,
• Small spatial shifts of initial density profiles,
• Sub-threshold stochastic perturbations.

Gravitational phases are observed to remain stable across repeats whenever temporal closure is achieved. In contrast, non-gravitational regimes exhibit either monotonic collapse or rapid divergence across realizations.

Operationally, phase robustness is defined as:

This criterion separates structural dynamics from numerical sensitivity and precludes interpretations based on fine-tuned initial conditions.

10.4 Statistical Consistency and Mixed Outcomes

For each fixed value of $\gamma$, results are aggregated across all repeats and horizons.

The validator computes:

• Counts of orbital, collapsing, and flyby outcomes,
• Orbit occurrence frequencies,
• Phase distributions across histories.

Let $\{s_i\}$ denote the set of phase outcomes for fixed $\gamma$. The dominant phase is defined as:

Crucially, the data reveal that for certain values of $\gamma$ (notably $\gamma \approx 0.014$), no single phase dominates. Instead, both orbital and collapsing outcomes occur under identical control parameters but differing system histories.

This behavior demonstrates that:

• Phase existence is not uniquely determined by $\gamma$,
• No force-law or static threshold can predict gravitational behavior,
• Temporal history is an essential degree of freedom.

These mixed regimes are documented in detail in Appendix E and constitute direct empirical evidence for gravity as a conditionally realized, temporally closed phase.

Having established reproducibility, horizon stability, and statistical structure, the framework can now be compared to existing theories. The following section situates these results relative to Newtonian gravity, modified gravity proposals, and general relativity.