Information-Based Two-Phase Dark Sector Model: Unified Lagrangian, Derivation of the Coupling Constant, and Qualitative Analysis of Testability

We propose a phenomenological model in which dark matter and dark energy are two phases of a single informational scalar field Φ, coupled to the local entanglement entropy density S_ent through an alpine potential V(Φ) = Λ_Φ^4 [1 + cos(Φ/f_Φ)] + V_0. The unified Lagrangian contains a single dimensionless coupling constant α, which is derived from the central charge of a critical tensor network and is found to be of order unity: α = a/4 ~ O(1). The potential scales are fixed by the infrared cutoff of the information network: f_Φ ~ sqrt(M_Pl H_0) ~ 0.025 eV and Λ_Φ ~ 10^-3 eV. We show that for α ~ 1, laboratory signatures (anomalous decoherence, deviation from the Landauer principle) lie 5–10 orders of magnitude below the sensitivity of current experiments. The only principally testable arena is cosmology: an early dark energy component at z ~ 3000, a late-time deviation of w(z) from -1, a deviation of the growth rate fσ_8(z) from ΛCDM, a density-dependent phase transition rate Γ(ρ) ∝ ρ^n, and non-zero cross-correlations of the CMB at low multipoles l. No numerical MCMC fit has been performed and is left for future work. The work contains an explicit separation between what is derived and what is postulated, and an honest discussion of limitations.