The Epoch Dependence

This is the central prediction of the paper. If you take nothing else from AP42, take this: the 68/27 split is not a constant. It is a snapshot. At different cosmic epochs the ratio is different — because the universe has been defragmenting for a different amount of time. The model predicts the dark-sector composition at every epoch:

z ≈ 5 (1.2 Gyr): DE 13.1%, DM 82.1%, Vis 4.8%, DE/DM 0.16.

z ≈ 2 (3.3 Gyr): DE 30.7%, DM 64.5%, Vis 4.8%, DE/DM 0.48.

z ≈ 1 (5.9 Gyr): DE 45.8%, DM 49.4%, Vis 4.8%, DE/DM 0.93.

z ≈ 0.5 (8.6 Gyr): DE 56.5%, DM 38.7%, Vis 4.8%, DE/DM 1.46.

z = 0, now (13.8 Gyr): DE 68.85%, DM 26.39%, Vis 4.76%, DE/DM 2.609.

The crossover — the epoch at which dark energy first exceeds dark matter — occurs at t ≈ 6.3 Gyr, corresponding to z ≈ 0.9.

4.1 — The coincidence problem dissolves

A persistent puzzle in cosmology: why are we living at the epoch where dark energy has only recently come to dominate? In ΛCDM this is a coincidence — there is no structural reason why the cosmological constant should be comparable to the matter density at this particular moment. In the defragmentation model there is no coincidence. The ratio changes continuously as defragmentation proceeds: dark matter dominated early (most content was still in process), dark energy dominates late (most content has completed processing). You are living at an unremarkable point on a monotonic curve. There is nothing special about z = 0 except that this is when you happen to be reading the clock.

4.2 — Comparison with ΛCDM

In standard ΛCDM, dark matter dilutes as (1+z)³ while dark energy density is constant; the DE = DM crossover occurs at z ≈ 0.38. In the defragmentation model, dark matter is being actively converted into dark energy through defragmentation; the crossover occurs at z ≈ 0.9 in the constant-feeding approximation. These differ. The defragmentation model predicts more dark matter at high redshift than ΛCDM, because it has a conversion mechanism ΛCDM lacks. This is observationally testable: precision measurements of the dark-matter fraction at z > 1 (weak lensing, BAO, CMB lensing) can distinguish the two models. This is flagged as KS-42.2.

ΛCDM is itself now under observational strain, and in a direction this model predicted. DESI DR2 (2025), combining three years of BAO with CMB and Type Ia supernovae, disfavours a constant Λ against an evolving dark energy (the w₀wₐCDM parameterisation) at 2.8–4.2σ depending on the supernova sample (2.8σ Pantheon+, 3.8σ Union3, 4.2σ DESY5; a principled combination of BAO and CMB alone gives 3.1σ), with the data preferring w₀ > −1 and wₐ < 0 — the quintom-B region, in which the equation of state was phantom (w < −1) in the past and quintessence-like (w > −1) today, with a phantom crossing near z ≈ 0.4–0.5. The best-fit point for the DESI+CMB+Pantheon+ combination sits near w₀ ≈ −0.84, wₐ ≈ −0.62. At least one analysis additionally reports a hint of a late-time interaction between dark energy and matter.

This cuts both ways for AP42, and honesty requires naming both. In support: an evolving dark sector with a late-time matter–dark-energy interaction is precisely this paper’s mechanism — dark matter (defragmentation in progress) is continuously converted into dark energy (the completed 1:1 reservoir). The coincidence-problem dissolution of section 4.1 lands in a far friendlier observational climate than “Planck 2018, ΛCDM” implies; the data have moved toward the kind of universe the defragmentation clock describes. In tension: the model’s effective equation of state is phantom in the past relaxing toward −1 (section 4.3), which matches DESI’s phantom-anchored early constraint and the wₐ < 0 trend but not, in the constant-feeding approximation, the present-day w₀ > −1 the late-universe data prefer. Whether that present-day crossing can be reached is owed to the feeding-rate history (D48), and is a live tension meanwhile. That confrontation is section 4.3 and the sharpened KS-42.2 and KS-42.4.

4.3 — The effective equation of state

DESI measures an effective equation of state under a non-interacting analysis: it fits w₀wₐCDM, in which the dark-energy density is assumed to evolve only through its own equation of state, with no source term. The defragmentation model is not that model — it is an interacting one, in which the dark-energy reservoir is continuously sourced by completed defragmentation. The two equations of state must therefore be distinguished, and the distinction is the prediction.

Intrinsically, each completed unit of reservoir is the substrate at rest: spatially uniform, non-diluting, negative-pressure — a cosmological-constant element with w = −1. But the reservoir as a whole is sourced. Its density does not merely fail to dilute; it grows, because content is continuously injected as defragmentation completes (section 1.2). An observer who fits a non-interacting model to a growing reservoir omits the source term, and the omission has a definite sign. From the continuity equation ρ̇ = −3H(1 + w)ρ, the inferred equation of state is 1 + w_eff = −ρ̇_DE / (3Hρ_DE). With the reservoir growing, ρ̇_DE > 0, so 1 + w_eff < 0: the inferred w_eff is below −1. A sourced, growing reservoir whose intrinsic state is w = −1 is read by the standard analysis as phantom.

This is not a defect; it is the section-4 epoch dependence written in the w-parameterisation, and it must be stated with its real limit. At early times the conversion rate is high relative to the small reservoir, ρ̇_DE/ρ_DE is large, and w_eff sits well below −1 — the phantom regime DESI’s CMB-anchored early-universe constraint prefers. As conversion saturates toward the present — most of the dark-sector content already completed — ρ̇_DE/ρ_DE shrinks and w_eff rises back toward −1 from below. The model therefore robustly predicts a phantom past (w_eff well below −1) relaxing toward −1 today, which matches DESI’s phantom-anchored early constraint and the rising trend wₐ < 0.

What the model does not do, in the constant-feeding approximation, is deliver a present-day crossing to w₀ > −1. A growing, non-diluting reservoir keeps ρ̇_DE > 0, so 1 + w_eff = −ρ̇_DE/(3Hρ_DE) < 0 at all times: w_eff stays ≤ −1 throughout, asymptoting to −1 rather than crossing it. Reaching the quintessence side that DESI’s central value (w₀ ≈ −0.84) prefers would require the reservoir density to decline at late times — the feeding rate falling faster than replenishment — which is exactly the feeding-rate history the constant-feeding model omits (D48). The match is therefore directional and bounded: the phantom past and the sign of wₐ are predicted from the same τ = (6/21) × t_H that fixes the partition; the present-day w₀, and whether it crosses −1 at all, are owed to D48. If the data settle firmly at w₀ > −1, that is a live tension for the constant-feeding model, not a confirmation of it — and the kill switch (KS-42.4) is written to say so. This is a sign-structure match on the phantom-past half, not a contour fit, and the paper claims no more.