This paper investigates whether the observed horizon‑doubling depth k≈204 is a contingent feature of the present cosmic epoch or a structurally forced outcome of the ΛCE (Λ Cosmological Emergence) framework. By analyzing the dual‑layer relationship between the particle horizon and the Holographic Unit (HU) lattice boundary, the paper demonstrates that the value k=204 emerges naturally from the intersection of geometric scaling, causal structure, and the present‑epoch value of the particle horizon radius Rₚh (t₀) ; as 10⁶1 Planck units. The work introduces the Dual‑Layer Horizon‑Matching Theorem, showing that the metric horizon depth and the combinatorial HU depth converge at the same exponential scale as they grow in parallel over time. This establishes that k=204 is not a universal constant but an epoch‑dependent alignment between geometric and causal layers of the ΛCE model. The result clarifies the role of horizon matching in emergent spacetime, strengthens the interpretation of Λ as a categorization error, and provides a clean explanation for why the present universe exhibits a doubling depth near 204. This paper is part of the ongoing ΛCE series exploring geometric, combinatorial, and emergent‑spacetime interpretations of the cosmological constant. v1
R J M W Howard (Mon,) studied this question.