What question did this study set out to answer?

The paper aims to derive the ideal geometric fixed-point reading of the CKN holographic coefficient.

May 5, 2026Open Access

Paper I: A Geometric Fixed-Point Reading of the CKN Holographic Coefficient: C₁ = π²/ (16e²)

Key Points

The paper aims to derive the ideal geometric fixed-point reading of the CKN holographic coefficient.
Calculates a geometric fixed point using boundary-saturation unit (τ = 1) determined by the Bekenstein-Hawking entropy.
Derives the theoretical dark energy density fraction based on the fixed-point reading.
The derivation provides a holographic coefficient of C_1 = π²/(16e²).
Determines a dark energy density fraction of Ω_Λ^(fp) ≈ 0.6994 that is independent of H_0 and G.

Abstract

This paper derives the ideal de Sitter fixed-point reading of the Cohen-Kaplan-Nelson (CKN) holographic coefficient. By selecting the natural boundary-saturation unit (τ = 1) determined by the Bekenstein-Hawking entropy bound, the framework calculates a geometric fixed point of C₁ = π²/ (16e²). This derivation yields a theoretical dark energy density fraction of Ω_Λ^ (fp) ≈ 0. 6994, which is strictly independent of the Hubble constant (H₀) and the gravitational constant (G).

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