Deriving the Holographic Dark Energy IR Cutoff from Interior Observer Thermodynamics

Holographic Dark Energy (HDE) has used the future event horizon R_eh as its infrared cutoff since Li (2004) without providing a physical explanation for this choice. This paper derives that choice from first principles by applying the Cohen-Kaplan-Nelson (CKN) entropic bound to an interior observer whose gravitational termination scale is R_eh rather than a local Schwarzschild radius. The derivation is motivated by the algebraic equivalence of the Friedmann equation and the Schwarzschild horizon condition — confirmed by CMB flatness measurements — and leads naturally to the Temporal Compression framework: the proposal that the observable universe exists within the interior of a black hole. The framework is encoded as a thawing hilltop quintessence scalar field and constrained by a full Boltzmann-integrated MCMC analysis using CLASS, against BAO distance measurements (BOSS DR12, eBOSS, DESI Year 1), Pantheon+ Type Ia supernovae, and Planck 2018 CMB distance priors. The Boltzmann-constrained posterior yields w₀ = −0.937 ± 0.006 (68% CI: [−0.944, −0.932]), φ₀ = 0.378 ± 0.070 M_Pl, μ = 1.176 ± 0.189 M_Pl, and H₀ = 69.87 ± 0.32 km/s/Mpc. The value w = −1.000 lies outside the 95% credible interval of the TC posterior, and the prediction constitutes a falsifiable test against DESI Year 5. A new branch of the framework reinterprets Hawking radiation as the physical manifestation of the temporal differential at the black hole boundary — a result mathematically latent in the standard Hawking derivation.