Why Λ = λ² - From Linear DOF Ratios to Holographic Curvature

Paper 2 of 8 This paper derives the central Honeyverse relation Λ = λ², where λ = 2⁻ᵏ is the HU/ghost degree‑of‑freedom ratio at doubling depth k. By showing how a linear mismatch in degrees of freedom produces an inverse‑square curvature term, the paper establishes the holographic scaling structure that underlies the entire ΛCE series (Lambda as Categorization Error). The analysis demonstrates that Λ is not an inserted constant but a geometric consequence of the dual‑lattice architecture. The HU lattice provides local metric structure, while the ghost lattice supplies a global relational reservoir whose exponential growth drives the curvature hierarchy. The resulting Λ term is shown to be a boundary‑level invariant tied to holographic saturation rather than a volume‑filling energy density. v1