Resolving the Triad of Quantum Cosmological Pathologies via Everettian Horizon Projection: The Boltzmann Brain Paradox, the Past Hypothesis, and the Measure Problem in Time-Symmetric Quantum Darwinism

Standard Lambda-CDM and inflationary quantum cosmology face a triad of deeply interconnected foundational pathologies when embedded in an unconstrained Everettian universal wavefunction Psi: (1) the Cosmological Measure Problem, in which eternal inflation and unitary branching generate infinite state norms (infinity/infinity) requiring arbitrary geometric cutoffs; (2) the Boltzmann Brain Paradox, in which asymptotic de Sitter thermal fluctuations (T_GH = hbar * H_0 / 2*pi*k_B) nucleate transient, disembodied observers vastly outnumbering biological observers evolved from a Big Bang; and (3) the Past Hypothesis, which must postulate an unexplained, exponentially fine-tuned low-entropy boundary condition (S_0 much less than S_max) at t = 0 to generate the Second Law of Thermodynamics. In this paper, building on the Everettian formulation of Time-Symmetric Quantum Darwinism (TSQD) established in our recent companion works (doi:10.5281/zenodo.24054298 and doi:10.5281/zenodo.24054876), we prove that all three pathologies are simultaneously resolved by a single physical operator: the asymptotic de Sitter horizon classicality projector Pi_cl(I+) = Theta(f_A - 1/2). First, we show that because each static de Sitter causal patch possesses a strictly finite Gibbons-Hawking horizon Hilbert-space dimension dim(H_I+) = exp(S_dS) approx exp(3 x 10^122), the trace norm Tr(Pi_cl * rho_patch) provides a natural, cutoff-free ultraviolet and infrared regulator for Everettian probabilities. Second, we prove that transient vacuum or thermal fluctuations (Boltzmann Brains) capture a negligible horizon redundancy fraction (f_A_BB approx 10^-120, well below 1/2) and are annihilated identically by Pi_cl(I+), never achieving macroscopic pointer-state objectivity. Third, we prove that crossing the f_A = 1/2 Page-curve threshold via a coherent 1 L_sun stellar beacon requires a sustained free-energy cascade, which top-down projects the universal wavefunction exclusively onto initial branches with low Weyl curvature and low initial entropy (S_0 much less than S_dS), deriving the Past Hypothesis and the thermodynamic arrow of time directly from horizon classicality selection.