Functorial Classification of Non-Terrestrial Isomorphism Types: A Plethystic Approach to Xenobiological Taxonomy Utilizing the Cycle Index Series of Weighted Combinatorial Species

Mathematical Applications of Science Fiction We propose a rigorous categorical framework for the taxonomy of non-terrestrial biological entities (xenomorphs)where traditional Linnaean phylogenetics fails due to the absence of common ancestry. By modeling xenobio-logical structures as weighted combinatorial species F : Fin → Setω , we construct a functorial mapping fromthe category of isomorphism types of alien morphologies to the ring of formal power series via the CycleIndex Series ZF . We introduce the concept of Xenobiological Plethysm, denoted ⊛, to describe the modularcomposition of hyper-organismic structures. The central contribution of this monograph is the VoidwalkerIsomorphism Theorem, which establishes a necessary and sufficient condition for the structural equivalenceof two non-terrestrial entities based on the spectral properties of their associated cycle indices under ageneralized weighting function. Furthermore, we derive the asymptotic density of viable xenomorphs inthe limit of infinite biomass using analytic combinatorics and discuss the implications for the detection ofType-III civilizations.