Statistical convergence within octonion metric structures

This paper investigates statistical convergence and completeness within the framework of octonion-valued metric spaces (OVMSs). By equipping the algebra of octonions with a suitable partial order, we extend classical notions of convergence, Cauchy sequences, and statistical density to the non-associative setting of octonions. Several fundamental properties are established, highlighting the interaction between statistical convergence and completeness in OVMSs. Our findings show that statistical convergence implies statistical Cauchy behaviour in these spaces, and conditions under which statistical completeness is achieved are clarified. The study not only generalizes conventional metric spaces but also reveals the structural impact of octonions' non-associativity on convergence theory. Potential implications for both pure mathematics and applied areas such as physics, control theory, and artificial intelligence are discussed.