Maximal Finite-Set Stabilizers in Thompson's Group T

Let D = Z[1/2]/Z be the dyadic circle and let T be Thompson's orientation-preserving circle group. We prove that, for every nonempty finite set A contained in D, its setwise stabilizer is a maximal proper subgroup of countably infinite index in T. If |A| = k, then Stab_T(A) is isomorphic to F^k semidirect C_k, equivalently the regular wreath product F wr C_k, where the cyclic group permutes the factors. Stabilizers with the same cardinality are conjugate, whereas those with distinct cardinalities are pairwise nonisomorphic. The proof establishes a general circular-order criterion: a group with the finite circular extension property acts primitively on the k-element subsets for every k. This yields a countably infinite family of maximal infinite-index subgroups and supplies examples requested in the 2024 AIM problem list on groups of dynamical origin. The theorem is apparently unrecorded in the literature checked; no absolute priority claim is made. This is an unrefereed preprint released for independent mathematical scrutiny. Publication on Zenodo does not constitute peer review. AI-assisted tools supported literature search, computation, proof auditing and manuscript preparation. The author remains responsible for the claims and final text. Corpus identifier: AIM-DYNAMICAL_SYSTEMS-0011. EulerSolve page: https://eulersolve.org/papers/aim-dynamical-systems-0011/