README: Transient Domain-Wall Model - Source Code v3Project Title: Transient Domain-Wall Networks from Spontaneous Symmetry Breaking: A Unified Solution to the Hubble Tension and Nanohertz Gravitational WavesAuthor: Ozan Altıntaş (Independent Researcher)ORCID: 0009-0001-0995-9811Date: March 16, 20261. OVERVIEWThis repository contains the Python scripts used to perform numerical simulations and generate the figures presented in the manuscript. The code calculates the expansion history of the universe under a transient domain-wall scaling regime and predicts the resulting stochastic gravitational-wave background (SGWB).2. IMPORTANT: FILE PATH WARNINGPlease Note: The current version of the script contains a hardcoded directory path for saving the generated figures:save_dir = r'C:\Users\ozan\Desktop\figure'Before running the script, you MUST update this line in the Python code to a valid directory on your local system (e.g., save_dir = './figures'). Otherwise, the script will attempt to write to a non-existent path and may return an OSError.3. FILE DESCRIPTIONSmain_simulation.py: The primary script containing the numerical solvers and plot generation for all 9 figures.figure1_expansion.pdf to figure9_cmb_imprint.pdf: The output files generated by the script (as seen in the manuscript).4. REQUIREMENTSTo run the simulations, you will need a Python 3.x environment with the following libraries:numpy (Numerical arrays and math functions)matplotlib (Plotting and visualization)os (Directory management)5. KEY FORMULAE IMPLEMENTEDExpansion Rate: Modified Friedmann equation incorporating the $\rho_{DW} \propto H$ term.GW Spectrum: Analytical modeling of the domain-wall decay signal centered in the nanohertz band.Parameter Space: Constraints from CMB (Planck), BBN, and PTA (NANOGrav/EPTA) observations.6. CONTACTFor technical inquiries or collaboration requests regarding the numerical implementation, please contact the author at: bukagi@gmail.com