Cosmic Fixed-Point Einselection: Bootstrapping a Unique Final Boundary Condition via Time-Symmetric Quantum Darwinism

AbstractTime-symmetric and top-down approaches to quantum cosmology—most notably Aharonov’sTwo-State Vector Formalism (TSVF), Wheeler’s Participatory Anthropic Principle, andHawking-Hertog top-down cosmology—address the quantum measurement problem and cosmological fine-tuning by positing a post-selected final boundary state ⟨Φfinal| that constrainsthe early universe’s path integral. However, these frameworks face a persistent foundationalobjection: what selects the final boundary state itself? Postulating a hard-coded final microstate or an explicit teleological rule (such as “maximal integrated complexity”) merelytransfers the fine-tuning problem from the initial boundary (t = 0) to the asymptotic future (t → ∞). In this paper, we propose a non-teleological mechanism in which a uniquefinal boundary condition is dynamically bootstrapped into existence through TemporalQuantum Darwinism. Extending Zurek’s framework of Environment-Induced Superselection (einselection) and pointer-state proliferation to a bidirectional cosmic cavity, wemodel the initial and final boundaries not as externally imposed axioms, but as coupledmirrors in a time-symmetric resonant loop governed by a recursive fixed-point operator⟨Φ∗| = S[⟨Φ∗|]. We demonstrate that candidate cosmic histories dominated by intraenvironment thermal scrambling (Page-curve dynamics) fail to preserve orthogonal pointerrecords at the asymptotic horizon; consequently, their forward and backward propagatorsaccumulate random relative phases and destructively cancel out of the global WheelerDeWitt state (⟨Φscrambled|Ψ⟩ → 0). Conversely, histories whose fundamental constants support non-interacting “star-topology” broadcast channels (e.g., free-streaming photons andgravitons scattering off stable macroscopic structures) achieve massive pointer redundancy(Rδ ≫1). Because pointer states commute with the system-environment interaction Hamiltonian ([ ˆHint, ˆ Πk] = 0), they reflect coherently across the temporal cavity, amplifying viaspectral power iteration into a single, mode-locked 4D fixed-point eigenstate. This synthesis resolves the quantum measurement problem—accounting for the preferred pointerbasis, single-outcome realization without non-unitary collapse or Everettian branching, andthe Born rule—while demonstrating that complexity and observer-participancy emerge asstructural necessities for a quantum timeline to avoid destructive self-cancellation.