{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:M3DAF3LMC74D7ULLO6QI322P5X","short_pith_number":"pith:M3DAF3LM","schema_version":"1.0","canonical_sha256":"66c602ed6c17f83fd16b77a08deb4fedf1d42478d9788a068136e2e4d8e042ca","source":{"kind":"arxiv","id":"1711.11455","version":1},"attestation_state":"computed","paper":{"title":"On Warped Product Gradient Yamabe Soliton","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Levi Adriano, Romildo Pina, Willian I. Tokura","submitted_at":"2017-11-30T15:00:23Z","abstract_excerpt":"In this paper, we provide a necessary and sufficient conditions for the warped product $M=B\\times_f F$ to be a gradient Yamabe soliton when the base is conformal to an n-dimensional pseudo-Euclidean space, which are invariant under the action of an (n-1)-dimensional translation group, and the fiber F is scalar-constant. As application, we obtain solutions in steady case with fiber scalar-flat. Besides, on the warped product we consider the potential function as separable variables and obtain some characterization of the base and the fiber."},"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":"1711.11455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-11-30T15:00:23Z","cross_cats_sorted":[],"title_canon_sha256":"a5c038bf509f8d15814dd7b2e43f3407ee38851bbeaeaa3ecceebd5e4b9f177c","abstract_canon_sha256":"b481053581c366c5ef295cd9683317f75ee53a16e94893499bb366e575c89eb3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:11.549879Z","signature_b64":"iRL2+W7HJd3xpg10a1IMfhamwZnSH+BZv2ylXq4lZwKpKlcd45CYlHS8wPr5UUx26CjgB0jVGqeEmkQO8EoABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66c602ed6c17f83fd16b77a08deb4fedf1d42478d9788a068136e2e4d8e042ca","last_reissued_at":"2026-05-18T00:29:11.549203Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:11.549203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Warped Product Gradient Yamabe Soliton","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Levi Adriano, Romildo Pina, Willian I. Tokura","submitted_at":"2017-11-30T15:00:23Z","abstract_excerpt":"In this paper, we provide a necessary and sufficient conditions for the warped product $M=B\\times_f F$ to be a gradient Yamabe soliton when the base is conformal to an n-dimensional pseudo-Euclidean space, which are invariant under the action of an (n-1)-dimensional translation group, and the fiber F is scalar-constant. As application, we obtain solutions in steady case with fiber scalar-flat. Besides, on the warped product we consider the potential function as separable variables and obtain some characterization of the base and the fiber."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11455","kind":"arxiv","version":1},"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":"1711.11455","created_at":"2026-05-18T00:29:11.549304+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.11455v1","created_at":"2026-05-18T00:29:11.549304+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11455","created_at":"2026-05-18T00:29:11.549304+00:00"},{"alias_kind":"pith_short_12","alias_value":"M3DAF3LMC74D","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"M3DAF3LMC74D7ULL","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"M3DAF3LM","created_at":"2026-05-18T12:31:28.150371+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/M3DAF3LMC74D7ULLO6QI322P5X","json":"https://pith.science/pith/M3DAF3LMC74D7ULLO6QI322P5X.json","graph_json":"https://pith.science/api/pith-number/M3DAF3LMC74D7ULLO6QI322P5X/graph.json","events_json":"https://pith.science/api/pith-number/M3DAF3LMC74D7ULLO6QI322P5X/events.json","paper":"https://pith.science/paper/M3DAF3LM"},"agent_actions":{"view_html":"https://pith.science/pith/M3DAF3LMC74D7ULLO6QI322P5X","download_json":"https://pith.science/pith/M3DAF3LMC74D7ULLO6QI322P5X.json","view_paper":"https://pith.science/paper/M3DAF3LM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.11455&json=true","fetch_graph":"https://pith.science/api/pith-number/M3DAF3LMC74D7ULLO6QI322P5X/graph.json","fetch_events":"https://pith.science/api/pith-number/M3DAF3LMC74D7ULLO6QI322P5X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M3DAF3LMC74D7ULLO6QI322P5X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M3DAF3LMC74D7ULLO6QI322P5X/action/storage_attestation","attest_author":"https://pith.science/pith/M3DAF3LMC74D7ULLO6QI322P5X/action/author_attestation","sign_citation":"https://pith.science/pith/M3DAF3LMC74D7ULLO6QI322P5X/action/citation_signature","submit_replication":"https://pith.science/pith/M3DAF3LMC74D7ULLO6QI322P5X/action/replication_record"}},"created_at":"2026-05-18T00:29:11.549304+00:00","updated_at":"2026-05-18T00:29:11.549304+00:00"}