ΛCE: The Cosmological Constant as a Categorization Error

This paper presents the foundational argument of the ΛCE (Lambda as a Categorization Error) framework: that the cosmological constant Λ is not a physical energy density of the vacuum, but a mis‑assigned geometric prefactor arising from the interaction between two fundamentally different scaling systems. The work introduces the Honeycomb Unit (HU), a dual‑lattice pre‑geometric structure composed of a rigid tetrahedral metric scaffold and a flexible octahedral ghost‑lattice. Through repeated HU‑doubling, the model generates a scale hierarchy in which the metric and combinatorial lattices diverge exponentially, producing an apparent vacuum curvature term when interpreted through classical GR. The paper demonstrates that Λ emerges not from quantum fields or vacuum fluctuations, but from a bookkeeping mismatch between metric volume scaling and combinatorial degree‑of‑freedom scaling. This reframes the cosmological constant problem as a categorization error rather than a physical fine‑tuning puzzle. The ΛCE framework naturally reproduces the observed magnitude of Λ after 204 HU doublings, aligns with holographic saturation at the cosmic horizon, and resolves the 120‑orders‑of‑magnitude discrepancy without introducing new physics or adjustable parameters. The paper concludes by outlining observational consequences, including early‑epoch structure formation signatures, ghost‑lattice tension effects, and scale‑dependent curvature behavior that distinguishes ΛCE from ΛCDM. v1