DESI DR2 Phantom Crossing as an Apparent Effect of Irreversible Dark Energy–Dark Matter Interaction Along the Arrow of Time

This preprint is maintained as an archival record of an exploratory phenomenological branch developed during the early confrontation between the Cosmology of Time (CT) framework and the DESI DR2 apparent phantom-crossing signal. The original purpose of this paper was to investigate whether an irreversible Dark Energy → Dark Matter interaction, motivated by CT, could be reconstructed by standard Q = 0 late-time inference pipelines as an apparent phantom-like feature in w(z). In that exploratory formulation, the DESI DR2 crossing window was treated as a possible phenomenological target for a localized dark-sector drain near the deceleration–acceleration transition. Subsequent development of the minimal thermodynamic realization of CT, however, showed that this interpretation is not consistent with the canonical structure of the theory. In the later v3 formulation of the main framework, the thermodynamic Arrow of Time fixes the sign of the interaction term (Q > 0), and this in turn constrains the effective dark-energy behavior to remain in the quintessence-like regime, with w_eff ≥ -1 at background level. In other words, the minimal canonical CT framework formally excludes true phantom behavior. Accordingly, the primary phenomenological claim of the original version of this preprint is now superseded. From the perspective of the canonical CT baseline, the DESI DR2 phantom-like signal cannot be taken as evidence for a true physical phantom component generated by the theory. It must instead be interpreted either as:- a projection artefact of standard reconstruction parametrizations such as CPL,- a transient statistical anomaly in the current data,- or an indication of physics outside the minimal CT realization. This paper should therefore not be read as the canonical statement of the Cosmology of Time framework. It is better understood as an exploratory DESI-oriented branch written before the consolidation of the minimal thermodynamic baseline. Its remaining value is threefold:- it documents an important intermediate stage in the development of CT;- it preserves the observational motivation that helped clarify the theory’s falsifiability conditions;- and it records an alternative effective route that was later ruled out by the stronger thermodynamic structure of the canonical model. A key falsifiability condition of the minimal CT framework is now explicit: if future data robustly require genuine phantom behavior (w_eff < -1) as a physical component rather than a reconstruction artefact, then the minimal thermodynamic realization of CT is ruled out. This preprint is therefore preserved for transparency, continuity, and archival completeness, but its central DESI interpretation should be read in light of the later v3 formulation, which supersedes it at the level of canonical theory.