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We prove such a group is not definably amenable, find a suitable group decomposition, and describe the minimal flows of the additive and multiplicative groups of $\\mathbb{C}((t))$. The main result is an explicit description of the minimal flow and Ellis Group of $(G(M),S_G(M))$ and we observe that this is not isomorphic to $G/G^{00}$,"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1903.03570","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-03-08T17:24:49Z","cross_cats_sorted":[],"title_canon_sha256":"32b27ea05e2c48e3b4fd6f6debf59ffc926aa2a3dd00d618df21a950da58974c","abstract_canon_sha256":"34ace9e732e2f9d39d92b2d9b85df952ffa6dc1bd10f38738e6eb32a026e5cb3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:45.134460Z","signature_b64":"J5WLc8uONR0OBF08u+a3YK0qtSGK/m10jQckzA8x4HECZThjKNNPbp99asYRhV2qrVqR704laP2oZe9RPI52Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3956bcfd59efa0b2abae135040edd89f1edcb4a226cca001ac1a5a3f5449a93","last_reissued_at":"2026-05-17T23:51:45.133667Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:45.133667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Definable Topological Dynamics of $SL_2(\\mathbb{C}((t))$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Thomas Kirk","submitted_at":"2019-03-08T17:24:49Z","abstract_excerpt":"We initiate a study of definable topological dynamics for groups definable in metastable theories. 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