The Entropy Clock Universe: The dark sector as the zero-energy residual of gravitational entropy — a falsifiable model

We propose a cosmological model in which the dark sector is the zero-energy residual of gravitational entropy. A single vacuum term (the model's dark energy) follows Penrose's gravitational-entropy indicator, the ratio of Weyl to Ricci curvature, used here as a timing signal we call the clock; fit to DESI DR2 baryon acoustic oscillations, DES-SN5YR supernovae and the Planck acoustic scale, it reaches Δχ² ≈ −28 relative to ΛCDM, matching the two-parameter w0–wa fit with no free parameter beyond ΛCDM's h. The model reads global zero energy (E=0) through unimodular gravity, where the cosmological term is a vacuum energy fixed by the net energy exchanged with matter. Unimodular consistency requires this vacuum to be spatially uniform to about one part in 10^8, so the vacuum can respond only to a globally averaged quantity. While the Weyl-to-Ricci ratio rises, dark matter gives up energy to the vacuum; while it falls, the vacuum releases energy to a stiff helicity-0 mode. E=0 fixes how much vacuum energy exists; gravitational entropy fixes when it changes. The reference model predicts a dark-sector density peak at z ≈ 0.9 (an inferred equation of state that still crosses w = −1 near z ≈ 0.5, tracking DESI), about 7% dark-matter conversion, and ~5% excess growth today. That growth excess (S8 ≈ 0.85) is the model's one distinctive perturbation signature and its sharpest vulnerability: at face value ~1.5σ above the least-discrepant weak-lensing surveys, eased further by their mutual scatter and by baryonic-feedback degeneracy; the same enhanced growth raises CMB lensing by only ~2%, within Planck's precision. Euclid and Rubin will be decisive. Twelve physically motivated alternatives, including a local-Hamiltonian shear clock, fall short on the same data, most by tens to more than 1,000 units of χ². The clock's coarse-graining mass is fixed from the galaxy cooling limit (t_cool = t_ff, 1.26×10^12 solar masses), an independent physical scale rather than a fitted one; with ε=1 from a boundary condition, the model then has no free parameter beyond ΛCDM's h and gives Δχ² ≈ −28.4, on a broad plateau in the clock scale. The linear, constant-coefficient coupling is derived, not adopted: the unimodular structure makes the vacuum an integration constant (fixing the coefficient), and its lossless response makes it a state function of the clock (fixing linearity); the squared alternative exhausts dark matter and an H²-weighted equipartition form fails by more than 7×10^4 in χ². What is left unexplained is why the horizon medium is so nearly lossless — at least ten times less than KSS saturation.