∞-Topos Theoretic Semantics for Quantum-Cognitive Computational Stacks
Year: 2025
Type: article
Abstract: 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.
Authors: Revista, Zen, MFC, 10
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7117877684
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