ΛCE: The Cosmological Constant as a Prefactor Mismatch

This paper presents a complete derivation of the ΛCE (Lambda as a Categorization Error) framework, showing that the observed Planck‑unit magnitude of the cosmological constant arises from a geometric prefactor mismatch rather than a dynamical vacuum energy. The analysis begins with the HU midpoint‑truncation geometry, where each doubling step generates a combinatorial hierarchy of ghost degrees of freedom scaling as Ng (k) =b 2ᵏ. This structure is paired with the metric doubling hierarchy associated with the particle‑horizon scale, Nₘ (k) =a 2ᵏ, where the integer depth k corresponds to the causal size of the universe in Planck units. A central result of the paper is the Prefactor Invariance Theorem, which demonstrates that the ratio of ghost to metric prefactors, b/a, is invariant under cosmic expansion. Because both hierarchies share the same exponential factor 2ᵏ, the cosmological constant emerges as a pure prefactor mismatch, Λ ∝ (b²−a²) /a² yielding a constant Λ whose magnitude naturally matches the observed value ∼10^−122-123 in Planck units. The paper provides a unified, geometric explanation for the smallness and constancy of Λ, reframing the cosmological constant problem as a structural alignment between metric and combinatorial doubling scales rather than a fine‑tuning issue or vacuum‑energy discrepancy. v1