ΛCE: A Dual‑Layer Model of Emergent Spacetime

ΛCE: A Dual‑Layer Model of Emergent Spacetime develops the ΛCE framework as a two‑tier ontology in which spacetime arises from the interaction between a continuous metric ladder and a discrete combinatorial ladder. The metric layer is defined by binary length‑doublings from the Planck scale to the particle horizon (~204 doublings), while the HU layer is generated by the volumetric 2³ recursion of the Holographic Unit (HU). Both ladders independently reach the cosmic scale of 10⁶1 in Planck units, but with distinct order‑unity prefactors: ~2. 7 for the metric ladder and exactly 3 for the HU ladder. ΛCE identifies the cosmological constant Λ as the curvature residue produced by this prefactor mismatch. This dual‑layer structure positions ΛCE within the broader emergent spacetime paradigm, aligning naturally with ideas from holography, entanglement‑driven geometry, and thermodynamic gravity while remaining compatible with general relativity at large scales. ΛCE provides a geometric, non‑fine‑tuned explanation for why Λ is extremely small yet non‑zero, without invoking vacuum energy, new fields, or modifications to GR. The paper reframes Λ not as a physical energy density but as a structural comparison between two independent scaling hierarchies — a geometric echo of emergence. v1