Renormalized Spectral Deficits and Horizon Capacity: A Casimir-Inspired Route to Holographic Dark Energy in the Entropic Ledger Framework

We reformulate the Casimir/dark-energy analogy within the Entropic Ledger Framework by replacing the naive plate-to-horizon substitution with a covariant, renormalized spectral construction. Rather than treating the Hubble radius as a literal conducting boundary, we define a horizon-dependent spectral deficit for quantum fields on FLRW causal domains and regularize it using heat-kernel and zeta-function methods, computing it explicitly for a conformally coupled scalar on the static de Sitter patch. The resulting effective dark sector takes the form ρ_DE(L) = 3η M_P² L⁻² + κ_C L⁻⁴ + ρ_dyn, where the leading L⁻² term follows from horizon area-law capacity and the Gibbons-Hawking temperature, the L⁻⁴ term is a genuine Casimir-like correction, and ρ_dyn encodes time-dependent Bogoliubov particle production. We show that the future event horizon yields a Li-type holographic dark-energy sector with a derived evolving equation of state, while the Casimir correction is suppressed by (ℓ_p/L)² ≈ 10⁻¹²² at the present horizon scale. We quantify the predicted equation-of-state drift Δw ~ O(10⁻³) against projected DESI and Euclid sensitivity and estimate the holographic noise power spectral density.