{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:NUQE5PWAPJ6NO5YIYYWGSULGN6","short_pith_number":"pith:NUQE5PWA","schema_version":"1.0","canonical_sha256":"6d204ebec07a7cd77708c62c6951666fb9da5529ff906f6829a9b153a4c67809","source":{"kind":"arxiv","id":"2502.06793","version":2},"attestation_state":"computed","paper":{"title":"Barycenter curvature-dimension condition for extended metric measure spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Bang-Xian Han, Deng-Yu Liu, Zhuo-Nan Zhu","submitted_at":"2025-01-27T02:51:09Z","abstract_excerpt":"In this survey, we introduce a new curvature-dimension condition for extended metric measure spaces, called Barycenter-Curvature Dimension condition BCD, from the perspective of Wasserstein barycenter."},"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":"2502.06793","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-01-27T02:51:09Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"51c52df07e76028201ba53dd30065388f86e8ced6b7659da25d40e96bb37bcbc","abstract_canon_sha256":"32aecb2f1ce448a391a199594a6789c92b0bce3ff05242fc497be6dd59ee33cc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:23:23.340565Z","signature_b64":"vdfSCOlHzlTYyjLhDRcNNZOl7XYn2TOudu4xqqizzA/FxnFNvR6FJuOXz/3s1bHQpSqrTJV8Lufy5LR1pL5qBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d204ebec07a7cd77708c62c6951666fb9da5529ff906f6829a9b153a4c67809","last_reissued_at":"2026-07-05T11:23:23.340052Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:23:23.340052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Barycenter curvature-dimension condition for extended metric measure spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Bang-Xian Han, Deng-Yu Liu, Zhuo-Nan Zhu","submitted_at":"2025-01-27T02:51:09Z","abstract_excerpt":"In this survey, we introduce a new curvature-dimension condition for extended metric measure spaces, called Barycenter-Curvature Dimension condition BCD, from the perspective of Wasserstein barycenter."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06793","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.06793/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2502.06793","created_at":"2026-07-05T11:23:23.340115+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.06793v2","created_at":"2026-07-05T11:23:23.340115+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.06793","created_at":"2026-07-05T11:23:23.340115+00:00"},{"alias_kind":"pith_short_12","alias_value":"NUQE5PWAPJ6N","created_at":"2026-07-05T11:23:23.340115+00:00"},{"alias_kind":"pith_short_16","alias_value":"NUQE5PWAPJ6NO5YI","created_at":"2026-07-05T11:23:23.340115+00:00"},{"alias_kind":"pith_short_8","alias_value":"NUQE5PWA","created_at":"2026-07-05T11:23:23.340115+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.06518","citing_title":"Absolute continuity of generalized Wasserstein barycenters of finitely many measures","ref_index":27,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NUQE5PWAPJ6NO5YIYYWGSULGN6","json":"https://pith.science/pith/NUQE5PWAPJ6NO5YIYYWGSULGN6.json","graph_json":"https://pith.science/api/pith-number/NUQE5PWAPJ6NO5YIYYWGSULGN6/graph.json","events_json":"https://pith.science/api/pith-number/NUQE5PWAPJ6NO5YIYYWGSULGN6/events.json","paper":"https://pith.science/paper/NUQE5PWA"},"agent_actions":{"view_html":"https://pith.science/pith/NUQE5PWAPJ6NO5YIYYWGSULGN6","download_json":"https://pith.science/pith/NUQE5PWAPJ6NO5YIYYWGSULGN6.json","view_paper":"https://pith.science/paper/NUQE5PWA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.06793&json=true","fetch_graph":"https://pith.science/api/pith-number/NUQE5PWAPJ6NO5YIYYWGSULGN6/graph.json","fetch_events":"https://pith.science/api/pith-number/NUQE5PWAPJ6NO5YIYYWGSULGN6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NUQE5PWAPJ6NO5YIYYWGSULGN6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NUQE5PWAPJ6NO5YIYYWGSULGN6/action/storage_attestation","attest_author":"https://pith.science/pith/NUQE5PWAPJ6NO5YIYYWGSULGN6/action/author_attestation","sign_citation":"https://pith.science/pith/NUQE5PWAPJ6NO5YIYYWGSULGN6/action/citation_signature","submit_replication":"https://pith.science/pith/NUQE5PWAPJ6NO5YIYYWGSULGN6/action/replication_record"}},"created_at":"2026-07-05T11:23:23.340115+00:00","updated_at":"2026-07-05T11:23:23.340115+00:00"}