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Deriving the cosmological constant suppression factor 6/7 from the topology of the face adjacency Laplacian.

April 11, 2026Open Access

The Dark Energy 6/7 Factor from Face Laplacian Topology

Key Points

Deriving the cosmological constant suppression factor 6/7 from the topology of the face adjacency Laplacian.
Utilized topology of the truncated octahedron
Identified inert modes using rank-nullity
Analyzed bipartiteness with spectral graph theory
Calculated propagating modes from the face and Euler characteristics
Derived the suppression factor of 6/7
Calculated the cosmological constant density ρ_Λ as 5.849×10⁻²⁷ kg/m³
Achieved a value within 0.47% of Planck 2018 measurements
No free parameters were included in the model

Abstract

Derives the cosmological constant suppression factor 6/7 as a Tier 1 theorem from the topology of the face adjacency Laplacian of the truncated octahedron. Two inert modes — A₁g (zero mode, connectivity) and A₂u (maximum mode, bipartiteness of the cube graph Q₃) — are identified via rank-nullity and spectral graph theory respectively. The remaining (F−χ) /F = 12/14 = 6/7 propagating modes set the ratio ρ_Λ/ρ₀. Result: ρ_Λ = 5. 849×10⁻²⁷ kg/m³, 0. 47% from Planck 2018. Zero free parameters.

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Luke Martin

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The Dark Energy 6/7 Factor from Face Laplacian Topology

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