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Structural Selection
Definition N.2In a file corrected during the v2 audit

Definition N.2 — Stability

Formal statement

A universe Ui\mathcal{U}_i is stable if and only if there exists a nonempty interval Ii⊂(0,∞)I_i \subset (0,\infty) such that for all γ∈Ii\gamma \in I_i and for all admissible ω∈Ωtest\omega \in \Omega_{\mathrm{test}}, the following hold:

∀γ∈Ii, ∀ω:  {C(γ,ω)=1(temporal closure)⟨∣L∣⟩(γ,ω)≥Lcrit(inertial storage)Δrosc(γ,ω;T)>0(non-monotonicity)R(γ;Ωtest)=1(history robustness)\boxed{ \forall \gamma\in I_i,\ \forall \omega:\; \begin{cases} \mathcal{C}(\gamma,\omega)=1 & \text{(temporal closure)}\\ \langle |L|\rangle(\gamma,\omega) \ge L_{\mathrm{crit}} & \text{(inertial storage)}\\ \Delta r_{\mathrm{osc}}(\gamma,\omega;T) > 0 & \text{(non-monotonicity)}\\ \mathcal{R}(\gamma;\Omega_{\mathrm{test}})=1 & \text{(history robustness)} \end{cases} }

All quantities above are directly logged by the numerical pipeline and validated across repeat runs and horizon extensions.

Source

Appendix N: The Finite Cardinality of Stable Universes — Gravity as a Temporally Closed Dynamical Phase

Gravity as a Temporally Closed Dynamical Phase/29_Appendix N — Finite Number of Stable Universes.tex

Revision history

This source file received at least one correction during the v2 audit — see the changelog for the exact change; not every statement in the file was necessarily the one corrected.

Read this result in context on its source chapter page, or submit a criticism if you believe this statement, as given, is incomplete or incorrect.