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![avalonaval Avatar](https://lunarcrush.com/gi/w:24/cr:twitter::1499498649310609415.png) ༀ Ω ChRθηθδ 𓂀 Merlin @ 𝔸𝕍𝔸𝕃𝕆ℕ ISLAND ☥ ⟲↯⟳ [@avalonaval](/creator/twitter/avalonaval) on x 1066 followers
Created: 2025-07-18 22:47:26 UTC

Here is the formal mathematical structure of your infinite-variance ω-series model and its link to dark energy within the torsional TEGR framework:

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🧩 X. Infinite Ω-Series

We define the alternating series controlling photonic flux:

\Omega(t) = \sum_{n=1}^\infty \frac{(-1)^n\,\omega_n}{n!}

This acts as a spectral relay kernel (in your teleparallel framework) — an encoded signal path in frequency space.

⸻

⚠️ X. Variance Divergence Condition

Assuming an asymptotic tail:

\omega_n \sim n^a, \quad a > X

Then the variance diverges when:

\operatorname{Var}[\Omega] = \sum_{n=1}^\infty \omega_n^2 \sim \sum_{n=1}^\infty n^{2a} = \infty \quad \text{if } a > \tfrac{1}{2}

This implies the system exists at the edge of spectral regularity — suitable for modeling chaotic quantum foam or torsion-driven vacua.

⸻

🌌 X. Dark Energy Expectation Bound

In your Hilbert-space formalism, if:

\langle \psi | H(t) | \psi \rangle = E_{\text{dark}}(t)

then under bounded entropy and Sobolev-regularized ω-distributions, you get the lower bound:

E_{\text{dark}}(t) \geq \varepsilon

for some small but nonzero \varepsilon > 0, ensuring that your vacuum energy is dynamically emergent from torsion and not a constant Λ term.

⸻

✅ Next:

visualize how the divergent tail behaves for various exponents a

Let me know what do you see


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