{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:7Y7H5CTKNHHVYV3QKHBMIJZCCU","short_pith_number":"pith:7Y7H5CTK","schema_version":"1.0","canonical_sha256":"fe3e7e8a6a69cf5c577051c2c42722150b2ad82a411c3a93bc62a6bf26752917","source":{"kind":"arxiv","id":"1112.3637","version":2},"attestation_state":"computed","paper":{"title":"Topology of steady and expanding gradient Ricci solitons via f-harmonic maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Giona Veronelli, Michele Rimoldi","submitted_at":"2011-12-15T20:24:42Z","abstract_excerpt":"In this paper we give some results on the topology of manifolds with $\\infty$-Bakry-\\'Emery Ricci tensor bounded below, and in particular of steady and expanding gradient Ricci solitons. To this aim we clarify and further develop the theory of f-harmonic maps from non-compact manifolds into non-positively curved manifolds. Notably, we prove existence and vanishing results which generalize to the weighted setting part of Schoen and Yau's theory of harmonic maps."},"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":"1112.3637","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-15T20:24:42Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"c079b8b213010335c17ea178b1868f73fd477c4e1da2f9a802b82fc6a0b2f3a7","abstract_canon_sha256":"1a85bfa7af6c5ed03273c65658bae0e5b82dd36b83aefa2e4b932cd92fd22947"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:45.586469Z","signature_b64":"uZzKkAT732xHUSgCls2edJyxK93e09AEjbFFtDf0Jc2eYYL+ixoVrdZ3g/gpcqrayfueHRIJZgf47UWnYwEwAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe3e7e8a6a69cf5c577051c2c42722150b2ad82a411c3a93bc62a6bf26752917","last_reissued_at":"2026-05-18T00:00:45.586053Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:45.586053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topology of steady and expanding gradient Ricci solitons via f-harmonic maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Giona Veronelli, Michele Rimoldi","submitted_at":"2011-12-15T20:24:42Z","abstract_excerpt":"In this paper we give some results on the topology of manifolds with $\\infty$-Bakry-\\'Emery Ricci tensor bounded below, and in particular of steady and expanding gradient Ricci solitons. To this aim we clarify and further develop the theory of f-harmonic maps from non-compact manifolds into non-positively curved manifolds. Notably, we prove existence and vanishing results which generalize to the weighted setting part of Schoen and Yau's theory of harmonic maps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3637","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1112.3637","created_at":"2026-05-18T00:00:45.586125+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.3637v2","created_at":"2026-05-18T00:00:45.586125+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3637","created_at":"2026-05-18T00:00:45.586125+00:00"},{"alias_kind":"pith_short_12","alias_value":"7Y7H5CTKNHHV","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"7Y7H5CTKNHHVYV3Q","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"7Y7H5CTK","created_at":"2026-05-18T12:26:22.705136+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7Y7H5CTKNHHVYV3QKHBMIJZCCU","json":"https://pith.science/pith/7Y7H5CTKNHHVYV3QKHBMIJZCCU.json","graph_json":"https://pith.science/api/pith-number/7Y7H5CTKNHHVYV3QKHBMIJZCCU/graph.json","events_json":"https://pith.science/api/pith-number/7Y7H5CTKNHHVYV3QKHBMIJZCCU/events.json","paper":"https://pith.science/paper/7Y7H5CTK"},"agent_actions":{"view_html":"https://pith.science/pith/7Y7H5CTKNHHVYV3QKHBMIJZCCU","download_json":"https://pith.science/pith/7Y7H5CTKNHHVYV3QKHBMIJZCCU.json","view_paper":"https://pith.science/paper/7Y7H5CTK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.3637&json=true","fetch_graph":"https://pith.science/api/pith-number/7Y7H5CTKNHHVYV3QKHBMIJZCCU/graph.json","fetch_events":"https://pith.science/api/pith-number/7Y7H5CTKNHHVYV3QKHBMIJZCCU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7Y7H5CTKNHHVYV3QKHBMIJZCCU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7Y7H5CTKNHHVYV3QKHBMIJZCCU/action/storage_attestation","attest_author":"https://pith.science/pith/7Y7H5CTKNHHVYV3QKHBMIJZCCU/action/author_attestation","sign_citation":"https://pith.science/pith/7Y7H5CTKNHHVYV3QKHBMIJZCCU/action/citation_signature","submit_replication":"https://pith.science/pith/7Y7H5CTKNHHVYV3QKHBMIJZCCU/action/replication_record"}},"created_at":"2026-05-18T00:00:45.586125+00:00","updated_at":"2026-05-18T00:00:45.586125+00:00"}