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We give a description of all possible connected conformal holonomy groups which act transitively on the M\\\"obius sphere $S^{p,q}$, the homogeneous model space for conformal structures of signature $(p,q)$. The main part of this description is a list of all such groups which also act irreducibly on $\\R^{p+1,q+1}$. For the rest, we show that they must be compact and act de"},"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":"1107.0617","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-04T13:14:21Z","cross_cats_sorted":[],"title_canon_sha256":"1b602fe17114460ff073466f4d34225bad28523dacd54563128f735bb2c423b4","abstract_canon_sha256":"d6dd3a8b54c8ed693339e1f3172b15b0b26467f0e2d82658f63e7f6cdadada24"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:53.690717Z","signature_b64":"/tlb5/n0kFA0/7z+LBqnhFvU888yd2jNCZixJtifXo4Q3nOIvJ0dzHm439WzoWkzFIDrs2i0MlD/HhlJxDH6Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"786ec826d2956e1aad1de540d792fe5ea70236f69a79ba76b8a3ce8f9b5c919c","last_reissued_at":"2026-05-18T04:18:53.690306Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:53.690306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transitive conformal holonomy groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jesse Alt","submitted_at":"2011-07-04T13:14:21Z","abstract_excerpt":"For $(M,[g])$ a conformal manifold of signature $(p,q)$ and dimension at least three, the conformal holonomy group $\\mathrm{Hol}(M,[g]) \\subset O(p+1,q+1)$ is an invariant induced by the canonical Cartan geometry of $(M,[g])$. 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