New expansion rate anomalies at characteristic redshifts geometrically determined using DESI-DR2 BAO and DES-SN5YR observations.

We perform a model-independent reconstruction of the cosmic distances using the Multi-Task Gaussian Process (MTGP) framework as well as knot-based spline techniques with DESI-DR2 BAO and DES-SN5YR datasets. We calibrate the comoving sound horizon at the baryon drag epoch $r_d$ to the Planck value, ensuring consistency with early-universe physics. With the reconstructed cosmic distances and their derivatives, we obtain seven characteristic redshifts in the range $0.3 \leq z \leq 1.7$. We derive the normalized expansion rate of the Universe $E(z)$ at these redshifts. Our findings reveal a significant deviations of approximately $4$ to 5$\sigma$ from the Planck 2018 $\Lambda$CDM predictions, particularly pronounced in the redshift range $z \sim 0.35$-0.55. These anomalies are consistently observed across both reconstruction methods and combined datasets, indicating robust late-time tensions in the expansion rate of the Universe and which are distinct from the existing ``Hubble Tension''. This could signal new physics beyond the standard cosmological framework at this redshift range. Our findings underscore the role of characteristic redshifts as sensitive indicators of expansion rate anomalies and motivate further scrutiny with forthcoming datasets from DESI-5YR BAO, Euclid, and LSST. These future surveys will tighten constraints and will confirm whether these late-time anomalies arise from new fundamental physics or unresolved systematics in the data.