This analysis focuses on the critical point that could refute the fundamental assumptions of this alternative cosmological model to the standard one. The project, named "4-Sphere" and currently under development, operates within the framework of Special Relativity. Following [viXra:2207.0051] and [viXra:2208.0040] this work concerns the validation of a supernova, suggesting that the dismissal of a Doppler-type redshift interpretation for Galactic Recession may warrant further reconsideration. Starting from data of a Supernova Ia (SN) at High-Redshift, the discussion also emphasizes the simplicity of the model in calculating the quantities involved, even if the right tools are lacking.The validation desired is carried out on the Luminosity distance, comparing its value calculated from the Redshift z of a star with that derived by its Distance modulus. Typically, this is achieved by having access to observational data concerning a Supernova Ia explosion.Then, starting from the results achieved in [viXra:2208.0040] the discussion begins with how to get the Absolute magnitude and to use the K-correction. We will also speak of Extinction. All this is mainly done with Photometry. Our first result is good. The SN Luminosity distance of 1,320 Mpc calculated by 4-Sphere has been confirmed with an accuracy of 96.5% (pretty good). FLRW provides approximately double the distance.Checking the correct application of least squares method is detailed in[viXra:2208.0040], here I supply an Excel spreadsheet for independent verification of the calculations. This method allows for direct confirmation (the values are easily identifiable). I have uploaded the Excel file on my OSF project Files tab.