Thermodynamic fate of the universe in the Page Wootters mechanism and Fisher Bures geometry

The Vacuum Time Geometry (VTG) framework derived in Paper I 1, Paper II 2, Paper III 3, and refined in the UV by Paper 2-AF 4 and Paper 4 5, identifies the quantum vacuum as the universal Page Wootters clock and the spacetime metric as the Fisher Bures pullback of the vacuum entanglement map λ : M4 → M, where M = Sp(56,R)/U(28). The fermion sector is supplied bythe Howe dual-pair completion GF = O(9, 3) 6. We address the destiny of the universe in this framework. Four results are established. First, the master equation Δt := tPΔS/˜η (which defines the local proper-time interval Δt in terms of vacuum-clock entropy production), combined with the Erker Huber bound ΔS ≥ 0 and the non-existence of a UV fixed point at finite coupling (asymptotic freedom proved by Paper 2-AF and verified by five independent methods in Paper 4), implies that the universe cannot bounce: the destiny is monotonic Big Freeze. Second, the dissolution of the dark sectors within VTG (dark energy as scalar curvature of M, dark matter as ∇˜η from internal modes) removes any fluid capable of doing positive work against the second law; the question of whether the observed acceleration is real or apparent becomes empirically open. We argue thatthe natural reading is apparent acceleration via Wiltshire-style backreaction with ΛFB subdominant, and we present the empirical case grounded in recent Pantheon+ analyses and the DESI DR1/DR2 hints of dynamical dark energy. Third, the endpoint of the cosmological ow is the unique U(N)-invariant pure state at the Fock face o ∈M, the maximal-coherence configuration of the vacuum. This is the structural description; the operational consequence is the degeneration of the Page Wootters clock POVM. We show that the apparent paradox of thermodynamic entropy growing while ending at a pure state is dissolved by distinguishing three perspective-dependent entropies in the sense of Höhn Smith Lock relational dynamics 7: total state entropy (constant in zero, trivially), clock-system entanglement entropy (decreasing structurally), and thermodynamicentropy (monotone non-decreasing). Fourth, the atemporal nature of the Page Wootters constraint, combined with the generic bilaterality of the support of |Ψ⟩ ∈ ker( ˆ CH) (verified numerically on Haar-uniform samples), and the C-conjugation O(9, 3) → O(3, 9) acting on the fermionic dual partner, exhibits a structural identication of two QRF perspectives on the same atemporal state. The cyclic structure is relational, not temporal, and operationally one-sided: the C-conjugate perspective is inaccessible from ours; whether it corresponds to a physically existing other universe is a question outside the empirical content of the framework. We discuss how the value of ΛFB in the present aeon may be inherited from the thermodynamics of the previous Big Freeze, dissolving the cosmological-constant problem without anthropics or landscape. The framework yields a coherentpicture initial state, intermediate dynamics, late-time fate, and structural continuation through C without bounce, without ination as additional input, without dark energy as uid, and without claims about observable consequences of other aeons. All claims are tied to specific falsifiers: detection of a primordial bounce signature, of stable cosmic defects with non-trivial homotopy, of an EW vacuum tunneling event in the cosmological timescale hierarchy, or of an Etherington-relation violation above ∼ 10−32, would each refute the framework.