The Fibonacci-Tetrahedral Lattice: A Unified Geometric Origin for Dark Matter and Dark Energy

This paper proposes the Fibonacci-Tetrahedral Lattice (FTL), a discrete geometric substrate forthe vacuum derived from an E8-to-3D projection. By treating space as a quasicrystalline packingrather than a smooth continuum, we identify a foundational ‘Information-Ontology’ where the 8Dlattice serves as the geometric source and 3D reality is the projected result. We demonstrate that thetransition from 8D symmetry to 3D packing necessitates a 7.356◦ topological deficit (the AristotleGap). This geometric frustration manifests macroscopically as an entropic pressure, providing a zero-parameter resolution to galactic rotation curves (“Dark Matter”) without requiring new particles.Furthermore, by applying Holographic Scaling (N 2/3) to the lattice nodes, we resolve the “VacuumCatastrophe,” deriving an observed energy density of ≈ 10−27.33 kg/m3 (matching Λ) from thetheoretical Planck baseline.