Fisher Matrix Forecasts for the SV0 Dark Energy Model: Distinguishing Structural and Phenomenological Phantom Crossings in the Stage-IV Era (Preprint)

The Signed-Volume (SV0) dark energy model has been shown to provide a structurally guaranteed phantom crossing without the divergence issues inherent to the Chevallier-Polarski-Linder (CPL) parametrization. In this paper, we perform a Fisher matrix forecast to determine how well future Stage-IV surveys (such as DESI DR3, Euclid, and Rubin) will constrain the SV0 model parameters and its crossing redshift (z_c). Using projected 1% uncertainties on the Hubble parameter and angular diameter distance across 0 < z < 2, we find that Stage-IV data will constrain the crossing redshift to σ(z_c) ≈ 0.008. Crucially, while the CPL parametrization yields a broader and highly correlated uncertainty σ(z_c) ≈ 0.025, the SV0 prediction remains sharp and robust. This sharpness provides a distinct observational signature that will allow Stage-IV surveys to decisively distinguish the structural crossing of SV0 from the phenomenological crossing of CPL. Data Availability:The Python (NumPy) code used to generate these forecasts is publicly available on Zenodo at: https://doi.org/10.5281/zenodo.24035597 References:[1] M. U. Sandaruwan, "Structurally Guaranteed Phantom Crossing in a Signed-Volume Effective Fluid..." (2026). Zenodo: https://doi.org/10.5281/zenodo.24026844[2] M. U. Sandaruwan, "Microphysical Origin of the Algebraic Phantom Crossing..." (2026). Zenodo: https://doi.org/10.5281/zenodo.24032977[3] M. U. Sandaruwan, "Covariant Formulation of the Signed-Volume Effective Fluid..." (2026). Zenodo: https://doi.org/10.5281/zenodo.24033838[4] M. U. Sandaruwan, "Gauge-Invariant Cosmological Perturbations in the SV0 Dark Energy Model..." (2026). Zenodo: https://doi.org/10.5281/zenodo.24034927[5] M. U. Sandaruwan, "Dynamical Systems Analysis of the Signed-Volume Dark Energy Model..." (2026). Zenodo: https://doi.org/10.5281/zenodo.24035268