{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:SQSPKL5TLOZLHKON6BJAV47TXZ","short_pith_number":"pith:SQSPKL5T","schema_version":"1.0","canonical_sha256":"9424f52fb35bb2b3a9cdf0520af3f3be63a7f86cbd44aa603095cdf381fd8098","source":{"kind":"arxiv","id":"1305.0485","version":3},"attestation_state":"computed","paper":{"title":"Liouville theorems for $f$-harmonic maps into Hadamard spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Bobo Hua, Chao Xia, Shiping Liu","submitted_at":"2013-05-02T15:44:52Z","abstract_excerpt":"In this paper, we study harmonic functions on weighted manifolds and harmonic maps from weighted manifolds into Hadamard spaces introduced by Korevaar and Schoen. We prove Liouville theorems for these harmonic maps with finite energy."},"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":"1305.0485","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-02T15:44:52Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"cff3e1e3aafd2de1803c89eca0f2bf113c69982dffe1d5bc3ddd945ed5d961b8","abstract_canon_sha256":"81a15940615a999d34d9c836966db75cde7143c89a1de9e007fc1976f8a33689"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:01.034359Z","signature_b64":"r1OT1q9XD1iKHF1z1xIlA80XuhbsBEKOI9vT1UJDwP+sN94WH50H93gf+Jg7EaSXAla1Z0qaGfLEq06WjAY8Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9424f52fb35bb2b3a9cdf0520af3f3be63a7f86cbd44aa603095cdf381fd8098","last_reissued_at":"2026-05-18T00:21:01.033863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:01.033863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Liouville theorems for $f$-harmonic maps into Hadamard spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Bobo Hua, Chao Xia, Shiping Liu","submitted_at":"2013-05-02T15:44:52Z","abstract_excerpt":"In this paper, we study harmonic functions on weighted manifolds and harmonic maps from weighted manifolds into Hadamard spaces introduced by Korevaar and Schoen. We prove Liouville theorems for these harmonic maps with finite energy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0485","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":"1305.0485","created_at":"2026-05-18T00:21:01.033939+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.0485v3","created_at":"2026-05-18T00:21:01.033939+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0485","created_at":"2026-05-18T00:21:01.033939+00:00"},{"alias_kind":"pith_short_12","alias_value":"SQSPKL5TLOZL","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"SQSPKL5TLOZLHKON","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"SQSPKL5T","created_at":"2026-05-18T12:27:59.945178+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/SQSPKL5TLOZLHKON6BJAV47TXZ","json":"https://pith.science/pith/SQSPKL5TLOZLHKON6BJAV47TXZ.json","graph_json":"https://pith.science/api/pith-number/SQSPKL5TLOZLHKON6BJAV47TXZ/graph.json","events_json":"https://pith.science/api/pith-number/SQSPKL5TLOZLHKON6BJAV47TXZ/events.json","paper":"https://pith.science/paper/SQSPKL5T"},"agent_actions":{"view_html":"https://pith.science/pith/SQSPKL5TLOZLHKON6BJAV47TXZ","download_json":"https://pith.science/pith/SQSPKL5TLOZLHKON6BJAV47TXZ.json","view_paper":"https://pith.science/paper/SQSPKL5T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.0485&json=true","fetch_graph":"https://pith.science/api/pith-number/SQSPKL5TLOZLHKON6BJAV47TXZ/graph.json","fetch_events":"https://pith.science/api/pith-number/SQSPKL5TLOZLHKON6BJAV47TXZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SQSPKL5TLOZLHKON6BJAV47TXZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SQSPKL5TLOZLHKON6BJAV47TXZ/action/storage_attestation","attest_author":"https://pith.science/pith/SQSPKL5TLOZLHKON6BJAV47TXZ/action/author_attestation","sign_citation":"https://pith.science/pith/SQSPKL5TLOZLHKON6BJAV47TXZ/action/citation_signature","submit_replication":"https://pith.science/pith/SQSPKL5TLOZLHKON6BJAV47TXZ/action/replication_record"}},"created_at":"2026-05-18T00:21:01.033939+00:00","updated_at":"2026-05-18T00:21:01.033939+00:00"}