∞-Topos Theoretic Semantics for Quantum-Cognitive Computational Stacks

Mathematical Applications of Science Fiction We construct a rigorous semantic framework forquantum-cognitive processes by embedding the statespace of a quantum neural operator into a derived∞-topos of sheaves on a perfectoid site. By definingthe Cognitive Stack Cqc, we demonstrate that the deci-sion boundaries of quantum agents correspond to thevanishing loci of specific motivic L-functions associ-ated with the stack’s étale cohomology. We prove theCognitive Holography Theorem, establishing anequivalence between the derived category of coherentsheaves on Cqc and the category of representations ofthe quantum-cognitive Galois group. Furthermore, weanalyze the stability of these structures using spectralsequences of the Adams type, showing that "halluci-natory" computational divergences are isomorphic tonon-trivial elements in the obstruction groups of themoduli stack. This formalism unifies non-commutativegeometry with higher category theory to provide acomplete description of trans-finite computational cog-nition.