Operadic Deformations of Xenosemiotic Fusion Categories and the Cohomological Classification of Exolingual Representation Spectra

Mathematical Applications of Science Fiction We present a rigorous foundational framework for the deformation theory of xenosemiotic fusioncategories, treating them as algebras over a specific E∞-operad encoding the syntax of non-Euclideanlinguistic structures. By constructing the Hochschild-Davydov-Yetter cohomology complex for a rigidmonoidal category C enriched over a trans-finite field K, we derive the governing Maurer-Cartanequations for infinitesimal deformations. The central result of this manuscript establishes a canonicalisomorphism between the moduli space of exolingual representation spectra and the hypercohomologyof a sheaf of L∞-algebras defined on the Grothendieck site of the category. We further prove thatobstructions to the quantization of semantic ambiguity vanish if and only if the underlying fusion ringadmits a unitary structure compatible with the Drinfeld associator. This work provides the necessarymathematical infrastructure for interpreting high-entropy signals from extra-dimensional intelligences.