This brief analysis presents observations intended to support the development of a non-standard cosmological model. The project, named "4-Sphere", and currently under development, operates within the framework of Special Relativity.The Apparent magnitude m, as measure of the brightness of a star, is decisive, together with the Absolute magnitude M, for the correct calculation of the Distance Modulus.The Distance Modulus = m - M, indeed, is related to the Luminosity distance d by m — M = 5 log(d) - 5 (d in Parsec) from which some verifications of a Cosmological model are then derived. Contrary to what one might think, the determination of the Apparent magnitude depends on the hypothesized model used. If no Galactic Recession is foreseen, its value coincides with the observed one. However, if the existence of a recession is hypothesized, additional conversions are necessary.This work considers Special Relativity (SR) as the framework for such calculations. Assuming the star is not at rest relative to the observer (an essential condition for the relevance of this analysis), the apparent magnitude calculated in SR assumes a distinct logical weight compared to that obtained based on hypothetical models.Specifically, the calculation based on SR can be used to verify the validity of a model (the intrinsic validity of SR is not in question). Conversely, to avoid a vicious circle, calculations based on hypotheses can only falsify the very model that generated them or serve to determine its parameters.In order to make the new K correction practical, an attempt was made to develop a simple corrective factor for the transformation of the Distance Modulus. This would have allowed us to exploit the extensive database of existing supernova observations, converting the distance modulus used in the FLRW model into its equivalent in SR. The last paragraph, however, explains the reasons why such a conversion is deemed impractical.