A Quantum Darwinist Completion of Hawking–Hertog Top-Down Cosmology: Closing the Cosmic Self-Bootstrapping Loop on I+

Companion Addendum to the Time-Symmetric Quantum Darwinism (TSQD) Quintet (Papers I–V) The foundational mechanisms required to explain how a single classical history emerges from a closed quantum universe have historically developed across four separate theoretical domains: (i) the Two-State Vector Formalism (TSVF) of Aharonov, Bergmann, and Lebowitz, which anchors quantum reality between initial and final boundary states; (ii) Zurek's Quantum Darwinism, which establishes how classical pointer states survive environmental decoherence through redundant photon broadcasts; (iii) the horizon subsystem and fast-scrambling theorems of Page, Sekino, and Susskind; and (iv) the Top-Down Cosmology of Hawking and Hertog (arXiv:hep-th/0602091, arXiv:1707.07702), which demonstrates that bulk cosmic histories α are selected retro-causally by boundary conditions on a late-time surface S (the de Sitter Future Conformal Boundary I+). Yet each pillar stopped short of a closed, autonomous circuit: Aharonov and Hawking–Hertog required an external agent or manual anthropic projection P_β(S) to specify the final boundary state, while Zurek's Quantum Darwinism operated strictly forward in time. In this companion note to the Time-Symmetric Quantum Darwinism (TSQD) series (Papers I–V), we isolate the novel synthesis that unites these four pillars into a parameter-free cosmic self-bootstrapping loop. By modifying Equations (6)–(9) of Hawking and Hertog (2006) with the self-selecting horizon fixed-point functional <Φ*| = S[<Φ*|] on I+, we demonstrate three core results:1. Exact ABL Isomorphism (Proposition 3.1): Identifying Hawking and Hertog's late-time boundary projector P_β(S) on I+ with a self-consistent boundary bra <Φ*| reduces their Equation (9) directly to the Aharonov–Bergmann–Lebowitz (ABL) Two-State transition probability, while preserving local Born-rule causality via coarse-grained ABL degeneracy cancellation (Paper III).2. Single-Threshold Return-Stroke Lock-In (Paper IV v1.2): Because the de Sitter horizon radiates thermal Gibbons–Hawking noise (n_GH ~ 1) and acts as a fast scrambler, unmodulated thermal starlight (n_star ≈ 0.067 << 1) and localized sub-horizon broadcasts (f_A < 1/2) are thermally erased on I+. Surviving erasure requires a finite "return-stroke pulse" of full 4π horizon saturation (A_H = 12π/Λ ≈ 3.2 × 10^53 m^2, f_A -> 1) by a phase-coherent laser state (N_mode >> 1) at the freeze-out flux φ_crit ~ 1 photon·m^(-2)·s^(-1) sustained across the Hubble horizon freeze-out window (Δτ_stroke ~ H_inf^(-1)), demanding a real-time stellar fusion power P_crit(Λ) = 12π φ_crit hν_0 / Λ ≈ 3.83 × 10^26 W (1.0 L_sun). Once this finite pulse crosses the event horizon R_H, it freezes permanently into I+, locking <Φ*| and retro-causally selecting the evolutionary trajectory ("stepped leader") that engineered it.3. The Cosmological Constant Lower Bound (Paper V v1.1): Because evolving the biological bootloader requires Δτ_bio ≈ 4.5 Gyr plus the main-sequence return-stroke fuel window (τ_MS ≥ 10 Gyr)—capping the bolometric luminosity of any biologically viable host star at L_max,bio ≈ 1.0 L_sun—equating P_crit(Λ) = L_max,bio places a hard lower bound on dark energy at Λ_min = 12π φ_crit hν_0 / L_sun ≈ 1.1 × 10^(-52) m^(-2) (Λ_min * l_P^2 ≈ 2.9 × 10^(-122)) without manual anthropic tuning.