{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:WWXTTGTDH6B7QU2M4TLDYIBVR4","short_pith_number":"pith:WWXTTGTD","schema_version":"1.0","canonical_sha256":"b5af399a633f83f8534ce4d63c20358f30f46a1e308cfea7d935fe9205e507ce","source":{"kind":"arxiv","id":"1307.3627","version":3},"attestation_state":"computed","paper":{"title":"Liouville type theorems for transversally harmonic and biharmonic maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Min Joo Jung, Seoung Dal Jung","submitted_at":"2013-07-13T07:53:41Z","abstract_excerpt":"We study the Liouville type theorems for transversally harmonic and biharmonic maps on foliated Riemannian manifolds"},"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":"1307.3627","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-13T07:53:41Z","cross_cats_sorted":[],"title_canon_sha256":"e649142719de31ef5159d2e6e7b35ec80ef8541f366952cfa18027a4ef03ea29","abstract_canon_sha256":"7732bd2872c30f8b293100a866d4c6b518ecc750bfd0ee906e788563e5d3b603"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:44.039620Z","signature_b64":"5El1ahqVCmoB+ulzRV3QRsmdUQAC5/2FeDknCivAzi2Gu6o8KEF2rxNFgt60Va/pUnyhC/Kh17FcSVKEELTKCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5af399a633f83f8534ce4d63c20358f30f46a1e308cfea7d935fe9205e507ce","last_reissued_at":"2026-05-18T01:11:44.039289Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:44.039289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Liouville type theorems for transversally harmonic and biharmonic maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Min Joo Jung, Seoung Dal Jung","submitted_at":"2013-07-13T07:53:41Z","abstract_excerpt":"We study the Liouville type theorems for transversally harmonic and biharmonic maps on foliated Riemannian manifolds"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3627","kind":"arxiv","version":3},"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":"1307.3627","created_at":"2026-05-18T01:11:44.039344+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.3627v3","created_at":"2026-05-18T01:11:44.039344+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3627","created_at":"2026-05-18T01:11:44.039344+00:00"},{"alias_kind":"pith_short_12","alias_value":"WWXTTGTDH6B7","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"WWXTTGTDH6B7QU2M","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"WWXTTGTD","created_at":"2026-05-18T12:28:06.772260+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/WWXTTGTDH6B7QU2M4TLDYIBVR4","json":"https://pith.science/pith/WWXTTGTDH6B7QU2M4TLDYIBVR4.json","graph_json":"https://pith.science/api/pith-number/WWXTTGTDH6B7QU2M4TLDYIBVR4/graph.json","events_json":"https://pith.science/api/pith-number/WWXTTGTDH6B7QU2M4TLDYIBVR4/events.json","paper":"https://pith.science/paper/WWXTTGTD"},"agent_actions":{"view_html":"https://pith.science/pith/WWXTTGTDH6B7QU2M4TLDYIBVR4","download_json":"https://pith.science/pith/WWXTTGTDH6B7QU2M4TLDYIBVR4.json","view_paper":"https://pith.science/paper/WWXTTGTD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.3627&json=true","fetch_graph":"https://pith.science/api/pith-number/WWXTTGTDH6B7QU2M4TLDYIBVR4/graph.json","fetch_events":"https://pith.science/api/pith-number/WWXTTGTDH6B7QU2M4TLDYIBVR4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WWXTTGTDH6B7QU2M4TLDYIBVR4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WWXTTGTDH6B7QU2M4TLDYIBVR4/action/storage_attestation","attest_author":"https://pith.science/pith/WWXTTGTDH6B7QU2M4TLDYIBVR4/action/author_attestation","sign_citation":"https://pith.science/pith/WWXTTGTDH6B7QU2M4TLDYIBVR4/action/citation_signature","submit_replication":"https://pith.science/pith/WWXTTGTDH6B7QU2M4TLDYIBVR4/action/replication_record"}},"created_at":"2026-05-18T01:11:44.039344+00:00","updated_at":"2026-05-18T01:11:44.039344+00:00"}