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 PantheonFormula: 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 textCDM 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.