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April 11, 20260 citationsOpen Access

The Dark Energy 6/7 Factor from Face Laplacian Topology

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LMLuke Martin

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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Cite This Study

Luke Martin (2026) studied this question.

synapsesocial.com/papers/69d9e64e78050d08c1b769d8https://doi.org/10.5281/zenodo.19483955
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