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Abstract

We present version 10 of the Toroidal Recoherence Cycle (CRT) model, a framework in which thepresent accelerated expansion of the universe arises from the decoherence of spin-network degreesof freedom located on the cosmological event horizon. This paper has two principal contributions.First, we validate the structural form of the CRT entropy ansatz using a concrete bipartite spin-chain toy model: a horizon subsystem of nA qubits coupled to a bulk bath of nB qubits through atime-decaying interaction J(t) ∝ e−γt, which mimics the dilution of the cosmic matter background.Partial tracing over the bulk yields a reduced density matrix whose entanglement entropy saturatesin a logistic-like fashion, matching the phenomenological form assumed in CRT. Second, we presenta corrected and dimensionless-reformulated integrator (inherited from v9.1) that eliminates anIEEE 754 overflow present in earlier versions and produces numerically stable predictions: w0 =−0.979 ± 0.02 and ρΛ = (5.94 ± 0.2) × 10−27 kg m−3. We are careful to distinguish what CRTpredicts from what it fits: two of the four effective parameters are constrained by matching ρΛ andw0 to observation, so the model has no genuine predictive excess at this stage. The present valuew0 = −0.979 is consistent with desi DR2 [6] at approximately 1.6σ, though CRT resides near thecosmological-constant end of the DESI preferred band, not at its dynamical-dark-energy center.A systematic microscopic derivation — via isolated quantum horizon formalism, Chern-Simonsmicrostate counting, and spin-foam decoherence rates — is outlined as a four-phase program; thepresent paper constitutes Phase 0 of that program.

We present version 9.1 of the Toroidal Recoherence Cycle (CRT) model, introducing a mobility-dependent saturation mechanism that dynamically freezes the comoving period L(t) at late times.This revision incorporates three principal advances: (i) a rigorous convexity argument for theeective entropy parametrization, treated explicitly as a phenomenological working hypothesis;(ii) a self-consistent justication of the mode truncation via holographic suppression factors; and(iii) a corrected coupled cosmological integrator reformulated in dimensionless variables to eliminatethe double-precision arithmetic overow present in v8. All dynamical equations are derived froman eective parameterization of the Lindblad entropy; no direct derivation from Loop QuantumGravity (LQG) is claimed at this stage. The model predicts a present-day vacuum energy densityρΛ(L0) = (5.35 ± 0.4) × 10−27 kg m−3 and an equation-of-state parameter w0 = −0.977 ± 0.03.This value is statistically consistent with recent desi DR2 measurements (wdesi0 = −0.76 ± 0.13) atthe ∼ 1.6σ level, a dramatic improvement over the 4σ tension in v8, establishing CRT as a viableframework for interacting dark energy