[GUEST ACCESS MODE: Data is scrambled or limited to provide examples. Make requests using your API key to unlock full data. Check https://lunarcrush.ai/auth for authentication information.]  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: ⸻ 🧩 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 X engagements  **Related Topics** [coins energy](/topic/coins-energy) [chr](/topic/chr) [Post Link](https://x.com/avalonaval/status/1946341067877499071)
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ༀ Ω ChRθηθδ 𓂀 Merlin @ 𝔸𝕍𝔸𝕃𝕆ℕ ISLAND ☥ ⟲↯⟳ @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:
⸻
🧩 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
X engagements
Related Topics coins energy chr
/post/tweet::1946341067877499071