The central core theory establishes that the organization of a social representation depends on a distinction between central and peripheral cognitions. Only the first ones are considered as particularly linked to the group identity. Previous works showed that, contrary to peripheral cognitions, central cognitions are subject to social valorization within the group. The present contribution aimed to conceptually replicate this finding, and to explore new hypotheses. We implemented two self-presentation paradigms (N = 161 and N = 183) using two different measures of adherence to social representation’s cognitions. The previous results related to the social value of central cognitions were replicated twice in a row. However, both studies also highlighted the social value of peripheral cognitions and of the adherence to the social representation in its entirety. These results constitute interesting theoretical advancements, especially in the study of the articulation between social representations and social identity.