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Then there is a finite collection $\\mathcal{F}$ of spherical 3-orbifolds, such that $\\mathcal{O}$ is diffeomorphic to a (possibly infinite) orbifold connected sum of copies of members in $\\mathcal{F}$. This extends work of Perelman and Bessi$\\grave{e}$res-Besson-Maillot. The proof uses Ricci flow with surgery on complete 3-orbifolds, and are along the lines of the author's previous work on 4-orbifolds w"},"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":"1210.7331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-27T15:00:08Z","cross_cats_sorted":[],"title_canon_sha256":"340675aeae54f6ced69c518ecdaec61c1b84405ac8eeffc7d1c143f60cf864fc","abstract_canon_sha256":"52cb8b6d22c1af95b8ec80bce2857a1c412f16457413a76ac9aae784323a2d66"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:10.464011Z","signature_b64":"PqVJNzGlL+excgXsN9oEXIKRWf0PJ/5u/AulVB/JIRLiiB0Su8qGy0bt1IYevE4BYx3mPsc3flt0nLzMfzlLCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1768482f741a9bf529c195d6601d82b13d0ea410689c46b52f58406b0942d977","last_reissued_at":"2026-05-18T03:42:10.463109Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:10.463109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Three-orbifolds with positive scalar curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hong Huang","submitted_at":"2012-10-27T15:00:08Z","abstract_excerpt":"We prove the following result: Let $(\\mathcal{O},g_0)$ be a complete, connected 3-orbifold with uniformly positive scalar curvature, with bounded geometry, and containing no bad 2-suborbifolds. Then there is a finite collection $\\mathcal{F}$ of spherical 3-orbifolds, such that $\\mathcal{O}$ is diffeomorphic to a (possibly infinite) orbifold connected sum of copies of members in $\\mathcal{F}$. This extends work of Perelman and Bessi$\\grave{e}$res-Besson-Maillot. 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