This paper presents a finitary axiomatization of Arbitrary Social Announcement Logic (ASAL), a dynamic epistemic logic modeling belief diffusion in social networks. ASAL extends Social Announcement Logic (SAL) with arbitrary announcement operators, resembling those in Arbitrary Public Announcement Logic (APAL). Unlike APAL, ASAL is based on belief rather than knowledge and allows inconsistent beliefs and local information flow. While ASAL shares structural similarities with Boolean APAL (BAPAL), our approach differs by avoiding the necessity form technique and instead using a novel model transformation method. We prove the soundness of the finitary axiomatization, including a derivation rule for arbitrary announcements, and establish weak completeness via Henkin-style canonical models. Illustrative examples clarify the semantic distinctions from PAL-based systems and display the model transformation process. We conclude with potential extensions of ASAL and directions for future research.