The paper investigates the transition epoch in the universe's expansion, where dark energy begins to dominate over matter, using gamma-ray burst (GRB) correlations. The authors employ two model-independent approaches: direct expansion of the Hubble rate and expansion of the deceleration parameter around the transition redshift \( z_t \). To avoid the *circularity problem*, they calibrate the GRB correlations using Bézier interpolation of updated Hubble data. The GRB data sets are jointly fit with type Ia supernovae and baryonic acoustic oscillations through a Monte Carlo analysis. The results are consistent with the concordance model, with some exceptions. The study also examines the behavior of dark energy and the matter density \( \Omega_m \), finding that dark energy is compatible with a cosmological constant and \( \Omega_m \) is consistent with the Planck Collaboration values. The paper concludes by discussing the implications of these findings for the nature of dark energy and the universe's expansion.The paper investigates the transition epoch in the universe's expansion, where dark energy begins to dominate over matter, using gamma-ray burst (GRB) correlations. The authors employ two model-independent approaches: direct expansion of the Hubble rate and expansion of the deceleration parameter around the transition redshift \( z_t \). To avoid the *circularity problem*, they calibrate the GRB correlations using Bézier interpolation of updated Hubble data. The GRB data sets are jointly fit with type Ia supernovae and baryonic acoustic oscillations through a Monte Carlo analysis. The results are consistent with the concordance model, with some exceptions. The study also examines the behavior of dark energy and the matter density \( \Omega_m \), finding that dark energy is compatible with a cosmological constant and \( \Omega_m \) is consistent with the Planck Collaboration values. The paper concludes by discussing the implications of these findings for the nature of dark energy and the universe's expansion.