Foundational Consistency of Time-Symmetric Quantum Darwinism: Global Boundary Linearity, Lorentz-Invariant Proper-Time Action, Inflaton Resonance, and Born-Rule Recovery

In two preceding papers (DOIs: 10.5281/zenodo.23572180 and 10.5281/zenodo.23677536), we introduced Cosmic Fixed-Point Einselection—demonstrating that the universe bootstraps a unique final boundary condition <Phi*| = S[<Phi*|] via Time-Symmetric Quantum Darwinism (TSQD)—and proved that this non-degenerate eigenstate resolves the Fermi Paradox via a winner-take-all first-passage "return stroke" bounded by an inflationary search space of N_min ~ 1/p_total ~ 10^22 stars (N_e ~ 60 e-folds). In this companion note, we establish the strict mathematical consistency of this framework against four foundational no-go theorems in quantum mechanics and relativistic cosmology. First, we prove that the recursive boundary operator S completely bypasses Gisin's non-linear signaling theorem: because S acts solely as a global asymptotic boundary-value solver while leaving interior dynamics U(t, t_0) strictly linear and unitary, local spacelike no-signaling is preserved identically. Second, we resolve the relativistic foliation problem by formulating the amplification weight Lambda_i as a diffeomorphism-invariant functional of proper time tau_i integrated along causal diamonds terminating on the future conformal boundary (I^+). Third, we eliminate apparent fine-tuning between early-universe inflation (t ~ 10^-32 s) and late-time biological evolution by treating the inflaton duration N_e as a quantum superposition whose fundamental cavity resonance peaks at lambda = N * p_total ~ 1. Fourth, we prove an ABL Degeneracy Theorem demonstrating that while post-selection enforces P -> 1 across prehistoric evolutionary bottlenecks, coarse-grained symmetry of <Phi*| across microscopic laboratory degrees of freedom cancels the post-selection factor today, recovering the exact standard Born rule P(a_k) = |<a_k|psi>|^2.