A Hyperspherical Scalar–Topographic Framework for Late-Time Cosmological Anomalies

We present a cosmological framework in which spatial sections of the Universe are three-spheres S_3 (R_H) of large curvature radius R_H, and gravitational potentials arise from a scalar topographic field T(x)obeying a fourth-order elliptic equation. The emergent acceleration law a(x)=Q_1 T(x)+Q_2 (2_T (x)) introduces a harmonic-sensitive correction that modifies distance–redshift relations, induces low-redshift anisotropies, and generates a mild redshift dependence in the effective Hubble parameter. We show that three independent late-time anomalies—(i) BAO curvature constraints from DESI DR2, (ii) directional anisotropy in Pantheon+ supernovae, and (iii) reported evolution in H_0 (z)from cosmic chronometers and lensed supernovae—are simultaneously consistent with a single long-wavelength scalar mode. A falsifiable correlation between BAO scale shifts and supernova dipole amplitudes is derived, providing a sharp prediction for upcoming surveys. We confront the model with DESI DR2, Pantheon+, and H(z) data at the level of order-of-magnitude consistency, obtaining viable parameter ranges and identifying observational tests capable of ruling out the framework. This work offers a unified, falsifiable interpretation of several late-time cosmological anomalies without modifying early-Universe physics.