The Shattered Crystal Architecture: A Topological Grand Unified Theory — V20.1: Λ Magnitude Derivation

January 31, 2026Open Access

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Key Points

The aim is to derive the Λ magnitude within the framework of the Shattered Crystal Architecture, exploring fundamental parameters.
Derived the vacuum lattice formula Λ_k = 12π² M_Pl²/(2πk − θ⁽⁰⁾) using detailed topological constructs.
Provided GPU-based numerical predictions to test the derived integer-p structures and validate against existing data.
Utilized a taxonomical approach to refine the Addazi Higgs-curvature coupling and its application within the theoretical framework.
Identified Λ_k ∝ 1/k at large k with observed Λ requiring k_obs ≈ 10¹²².
Developed a falsifiable numerical prediction: p = 2 or p = 3 based on specific parameters related to the SCA.
Validated the SCA Hopfion-crystal vacuum as a realization of KV q-theory, reinforcing external frameworks supporting the findings.

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Investigates the Λ magnitude in foundational quantum theories, suggesting innovative implications for cosmology.

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Benjamin Wilbur (2026) studied this question.

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