Permutation-equivariant quantum K-theory V. Toric q-hypergeometric functions

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We first retell in the K-theoretic context the heuristics of S¹-equivariant Floer theory on loop spaces which gives rise to Dq-module structures, and in the case of toric manifolds, vector bundles, or super-bundles to their explicit q-hypergeometric solutions. Then, using the fixed point localization technique developed in Parts II--IV, we prove that these q-hypergeometric solutions represent K-theoretic Gromov-Witten invariants.