DERIVED FUKAYA CATEGORIES OF LEGENDRIAN VOID-TETHERS: OBSTRUCTIONS TO SYMPLECTIC FILLING IN RETRO-CAUSAL CONTACT ORBIFOLDS VIA INSTANTON FLOER HOMOLOGY

Mathematical Applications of Science Fiction We construct the derived Fukaya category associated with a class of Legendrian submanifolds, referred to as Void-Tethers, situated within a retrocausal contact orbifold. We show that the existence of a closed timelike Reeb orbit produces a nonvanishing deformation in the A-infinity structure of the category, described by a modular obstruction class in the second Hochschild cohomology group. By coupling this structure with the instanton Floer homology of the orbifold’s singular locus, we prove that if the Chronos curvature of the void-tether is strictly positive, then the contact orbifold admits no exact symplectic filling. This result provides a resolution of the generalized filling conjecture under boundary conditions that violate acausality.