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The main theorems in this paper are the following.\n  Theorem I: If M has positive Ricci curvature then it has the loops to infinity property.\n  Theorem II: If M has nonnegative Ricci curvature then it either has the loops to infinity property or it is isometric to a flat normal bundle over a compact totally geo"},"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":"math/9904096","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"1999-04-19T17:12:06Z","cross_cats_sorted":[],"title_canon_sha256":"cc464ee71c90748fbc7db8a4626bd4fb6198772e9a928e1bca66076748ae4b90","abstract_canon_sha256":"b42e6393ca312f0812b19f2b593d1ef35cfc4d6106cdbc13318272208710bde9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:49:26.498125Z","signature_b64":"wwlUpwXB0VST7tJuCzgTgvWl0Wzda6wo1bzTtiaOHUbKkFi3DZXlpmL2MoGbD3wIuygiIgHY+N49pbW3myeVAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f60c5ac633d46ef2403ec700c6fbe8d51338e35d8358cd0c2d699db5f3c6c45","last_reissued_at":"2026-07-04T14:49:26.497790Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:49:26.497790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Loops Representing Elements of the Fundamental Group of a Complete Manifold with Nonnegative Ricci Curvature","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Christina Sormani","submitted_at":"1999-04-19T17:12:06Z","abstract_excerpt":"This paper concerns complete noncompact manifolds with nonnegative Ricci curvature. 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