Model–Independent Reconstruction and Observational Diagnostics of f(𝒯 ,ℬ) Gravity

In this study, we investigate the late–time cosmological behaviour of a modified teleparallel gravity model described by an arbitrary function of the torsion scalar [Formula: see text] and the boundary term [Formula: see text], namely [Formula: see text] gravity. Unlike dynamical [Formula: see text] theories, the inclusion of the boundary term restores a continuous bridge between curvature and torsion based formulations and provides a richer geometric structure capable of driving cosmic acceleration. To explore the observational viability of this theory, we adopted a model–independent approach based on a logarithmic parametrization of the Hubble function and employed using OHD, DESI DR2, and Pantheon[Formula: see text] supernova datasets. The modified field equations yield the effective energy density and pressure terms to construct a complete set of cosmological diagnostics, including the effective equation of state, adiabatic sound speed, energy conditions, [Formula: see text] evolutionary plane, deceleration parameter, statefinder pairs [Formula: see text] and [Formula: see text], and the [Formula: see text] diagnostic. Our results show that the reconstructed effective equation of state remains slightly below the cosmological constant boundary, indicating a mild phantom-like behaviour compatible with recent low-redshift observations. The deceleration parameter confirms a persistent late-time acceleration, whereas the energy conditions behave consistently with an accelerating universe. The [Formula: see text] and statefinder trajectories reveal clear deviations from [Formula: see text]CDM yet evolve towards its fixed points at [Formula: see text], demonstrating dynamical compatibility with observational data. Overall, the [Formula: see text] framework exhibits physically viable and observationally consistent geometrically induced dark-energy behaviour, suggesting that torsion–boundary couplings may serve as a promising alternative to conventional dark-energy models.