This paper presents a study using Crossing Statistics to reconstruct the expansion history of the universe and the properties of dark energy, leveraging DESI Data Release 1 (DR1) Baryon Acoustic Oscillation (BAO) data combined with different supernova compilations (PantheonPlus, Union3, and DES-SN5YR) and Planck Cosmic Microwave Background (CMB) observations. The authors employ a model-agnostic approach, using Chebyshev polynomials to expand the equation of state \( w(z) \) and the effective dark energy density \( f_{\text{DE}}(z) \). The results suggest an evolving and emergent behavior of dark energy, with a negligible presence at \( z \geq 1 \), and a cosmological constant lying outside the 95% confidence intervals for some redshift ranges. The findings are consistent with the conventional \( w_0 - w_a \) dark energy equation of state parametrization reported in the DESI Key Cosmology paper. The study also provides constraints on the Hubble constant \( H_0 r_d \) and supports the idea of a slowing down of cosmic acceleration at low redshifts. The results add to the understanding of dark energy behavior and provide a model-agnostic reconstruction framework.This paper presents a study using Crossing Statistics to reconstruct the expansion history of the universe and the properties of dark energy, leveraging DESI Data Release 1 (DR1) Baryon Acoustic Oscillation (BAO) data combined with different supernova compilations (PantheonPlus, Union3, and DES-SN5YR) and Planck Cosmic Microwave Background (CMB) observations. The authors employ a model-agnostic approach, using Chebyshev polynomials to expand the equation of state \( w(z) \) and the effective dark energy density \( f_{\text{DE}}(z) \). The results suggest an evolving and emergent behavior of dark energy, with a negligible presence at \( z \geq 1 \), and a cosmological constant lying outside the 95% confidence intervals for some redshift ranges. The findings are consistent with the conventional \( w_0 - w_a \) dark energy equation of state parametrization reported in the DESI Key Cosmology paper. The study also provides constraints on the Hubble constant \( H_0 r_d \) and supports the idea of a slowing down of cosmic acceleration at low redshifts. The results add to the understanding of dark energy behavior and provide a model-agnostic reconstruction framework.