From Dual‑Lattice Microstructure to Cosmic Dynamics

Paper 5 of 8 This paper constructs a minimal effective action for the Honeyverse dual‑lattice system and shows that the key relations of the ΛCE series — including Λ = 2⁻²ᵏ, holographic saturation, and the emergent Friedmann equation — arise as variational consequences rather than assumptions. The action includes only three terms: a curvature term, a HU/ghost mismatch term, and a holographic constraint. The same action also suppresses gradients in the mismatch field, ensuring that smooth continuum geometry emerges dynamically from the dual‑lattice microstructure. By varying the action with respect to the metric and ghost degrees of freedom, the paper derives both the effective cosmological constant and the holographic saturation condition Nghost = Sₕolo. This demonstrates that the dual‑lattice architecture naturally produces the observed cosmic acceleration and fixes the doubling depth at k = 204. v1