{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DN6EX3VA2FXFF2YMKHQCSW7T56","short_pith_number":"pith:DN6EX3VA","schema_version":"1.0","canonical_sha256":"1b7c4beea0d16e52eb0c51e0295bf3ef8a233d4ee1be368cc81b483e33720e7a","source":{"kind":"arxiv","id":"1506.03800","version":2},"attestation_state":"computed","paper":{"title":"A warped product version of the Cheeger-Gromoll splitting theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"William Wylie","submitted_at":"2015-06-11T19:51:04Z","abstract_excerpt":"We prove a new generalization of the Cheeger-Gromoll splitting theorem where we obtain a warped product splitting under the existence of a line. The curvature condition in our splitting is a curvature dimension inequality of the form $CD(0,1)$. Even though we have to allow warping in our splitting, we are able to recover topological applications. In particular, for a smooth compact Riemannian manifold admitting a density which is $CD(0,1)$, we show that the fundamental group of $M$ is the fundamental group of a compact manifold with nonnegative sectional curvature. If the space is also locally"},"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":"1506.03800","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-06-11T19:51:04Z","cross_cats_sorted":[],"title_canon_sha256":"b550d948438dcbf85dc57c799e93bd62609ba3b5396d07ac29e2a82fc1ec2a49","abstract_canon_sha256":"f92ad9e269340de525fc719710740ce623c425f53373aca18afecdb26a9c06ef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:43.833222Z","signature_b64":"d7oEmIIj1fMX3lZG7u+uHYYlOWS5Qgi+cVSFYxI8xi//5LdV6GEs5X6H7bPSOb6GLIDQu6wmgzskTmH5Z1k+Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b7c4beea0d16e52eb0c51e0295bf3ef8a233d4ee1be368cc81b483e33720e7a","last_reissued_at":"2026-05-18T01:11:43.832900Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:43.832900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A warped product version of the Cheeger-Gromoll splitting theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"William Wylie","submitted_at":"2015-06-11T19:51:04Z","abstract_excerpt":"We prove a new generalization of the Cheeger-Gromoll splitting theorem where we obtain a warped product splitting under the existence of a line. The curvature condition in our splitting is a curvature dimension inequality of the form $CD(0,1)$. Even though we have to allow warping in our splitting, we are able to recover topological applications. In particular, for a smooth compact Riemannian manifold admitting a density which is $CD(0,1)$, we show that the fundamental group of $M$ is the fundamental group of a compact manifold with nonnegative sectional curvature. If the space is also locally"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03800","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":"1506.03800","created_at":"2026-05-18T01:11:43.832951+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.03800v2","created_at":"2026-05-18T01:11:43.832951+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03800","created_at":"2026-05-18T01:11:43.832951+00:00"},{"alias_kind":"pith_short_12","alias_value":"DN6EX3VA2FXF","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DN6EX3VA2FXFF2YM","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DN6EX3VA","created_at":"2026-05-18T12:29:17.054201+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/DN6EX3VA2FXFF2YMKHQCSW7T56","json":"https://pith.science/pith/DN6EX3VA2FXFF2YMKHQCSW7T56.json","graph_json":"https://pith.science/api/pith-number/DN6EX3VA2FXFF2YMKHQCSW7T56/graph.json","events_json":"https://pith.science/api/pith-number/DN6EX3VA2FXFF2YMKHQCSW7T56/events.json","paper":"https://pith.science/paper/DN6EX3VA"},"agent_actions":{"view_html":"https://pith.science/pith/DN6EX3VA2FXFF2YMKHQCSW7T56","download_json":"https://pith.science/pith/DN6EX3VA2FXFF2YMKHQCSW7T56.json","view_paper":"https://pith.science/paper/DN6EX3VA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.03800&json=true","fetch_graph":"https://pith.science/api/pith-number/DN6EX3VA2FXFF2YMKHQCSW7T56/graph.json","fetch_events":"https://pith.science/api/pith-number/DN6EX3VA2FXFF2YMKHQCSW7T56/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DN6EX3VA2FXFF2YMKHQCSW7T56/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DN6EX3VA2FXFF2YMKHQCSW7T56/action/storage_attestation","attest_author":"https://pith.science/pith/DN6EX3VA2FXFF2YMKHQCSW7T56/action/author_attestation","sign_citation":"https://pith.science/pith/DN6EX3VA2FXFF2YMKHQCSW7T56/action/citation_signature","submit_replication":"https://pith.science/pith/DN6EX3VA2FXFF2YMKHQCSW7T56/action/replication_record"}},"created_at":"2026-05-18T01:11:43.832951+00:00","updated_at":"2026-05-18T01:11:43.832951+00:00"}