The code snippet demonstrates the Dual Sheet Model (DSM) incorporating real-world data and equations for dark energy studies.Real-world data for dark energy values and Hubble parameters are provided for analysis and comparison.The code includes interpolations, optimizations, and calculations of observables like effective w(z) and H(z).Functions for potentials, densities, Hubble parameters, derivatives, and chi-squared objective are defined and utilized.The code optimizes parameters for the DSM using the Nelder-Mead method and presents best-fit parameters lambda, m, and m_tilde.Simulations are run with the optimized parameters to compute w(z) and H(z) values for comparison with observational data.Plots are generated to show the results of w(z) and H(z) from the DSM simulation against observational data from DESI, CMB, Planck, and Union3.The plots illustrate the Dark Energy Equation of State and the Hubble Parameter comparison between DSM and observations.