Low-redshift-agnostic BAO Constraints on Binned Dark-energy Density Evolution from DESI DR1 and DR2

We present a low-redshift-agnostic compression of anisotropic baryon acoustic oscillation (BAO) distances to constrain the normalized dark-energy density evolution, $X(z)\equiv \rho_{\rm DE}(z)/\rho_{\rm DE}(0)$, above the lowest BAO redshift node $z_1$. Standard BAO summaries include the transverse comoving distance $D_{\rm M}/r_{\rm d}$, which depends on the integral of $H^{-1}(z)$ from $z=0$ to $z$ and therefore mixes the expansion history at $z<z_1$ with the higher-redshift signal. We instead replace the set $D_{\rm M}(z_i)/r_{\rm d}$ by adjacent increments $\Delta D_{\rm M}(z_i,z_{i+1})/r_{\rm d}$ while retaining the radial distances $D_{\rm H}(z_i)/r_{\rm d}$. The mapping is linear, so the covariance propagates exactly. This compression intentionally removes one absolute transverse-distance mode, namely the additive contribution to $D_{\rm M}/r_{\rm d}$ below the first BAO node, and preserves the remaining information relevant to reconstructing the expansion history above $z_1$. Applied to DESI DR1 and DR2 anisotropic BAO measurements, the method yields almost uncorrelated constraints on piecewise-constant interval parameters $X_j$. In this sense, the compressed likelihood provides a conservative band-power-like estimate of dark-energy evolution: each interval is constrained mainly by BAO information from its own redshift range, while one nonlocal transverse mode and stronger global assumptions are deliberately projected out or marginalized over. Because our baseline analysis also marginalizes over bin-local matter-density and distance-scale parameters with broad external priors, the resulting $X_j$ constraints should be interpreted as a low-redshift-agnostic BAO baseline rather than as a fully prior-free reconstruction. All bins are consistent with $X=1$ within current uncertainties.