{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:VW23VSUGO6ZNLVGSAF6DNJZK3I","short_pith_number":"pith:VW23VSUG","schema_version":"1.0","canonical_sha256":"adb5baca8677b2d5d4d2017c36a72ada20337d17425f7101b9c718e8206dcb37","source":{"kind":"arxiv","id":"1012.4233","version":3},"attestation_state":"computed","paper":{"title":"Yau's gradient estimates on Alexandrov spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Hui-Chun Zhang, Xi-Ping Zhu","submitted_at":"2010-12-20T03:15:56Z","abstract_excerpt":"In this paper, we establish a Bochner type formula on Alexandrov spaces with Ricci curvature bounded below. Yau's gradient estimate for harmonic functions is also obtained on Alexandrov spaces."},"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":"1012.4233","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-20T03:15:56Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"86855485a31f0380876f92b3c967c2c5ce81eda7ffa0279ac91ceaf33d617155","abstract_canon_sha256":"618d74f5f69f4640fc93d3bf70ba0f58547abd6903dde70b572be165d96ea1c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:59.934847Z","signature_b64":"kvll1e5Ri3mGe3xZYCVLZLfYm2KCdpwMDGmdMWpGN4/4H2LV6PY2OakxejA8w039rJYriC8Z7VC2IcQznPCBDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adb5baca8677b2d5d4d2017c36a72ada20337d17425f7101b9c718e8206dcb37","last_reissued_at":"2026-05-18T04:00:59.934213Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:59.934213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Yau's gradient estimates on Alexandrov spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Hui-Chun Zhang, Xi-Ping Zhu","submitted_at":"2010-12-20T03:15:56Z","abstract_excerpt":"In this paper, we establish a Bochner type formula on Alexandrov spaces with Ricci curvature bounded below. Yau's gradient estimate for harmonic functions is also obtained on Alexandrov spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4233","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":"1012.4233","created_at":"2026-05-18T04:00:59.934305+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.4233v3","created_at":"2026-05-18T04:00:59.934305+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4233","created_at":"2026-05-18T04:00:59.934305+00:00"},{"alias_kind":"pith_short_12","alias_value":"VW23VSUGO6ZN","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"VW23VSUGO6ZNLVGS","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"VW23VSUG","created_at":"2026-05-18T12:26:15.391820+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/VW23VSUGO6ZNLVGSAF6DNJZK3I","json":"https://pith.science/pith/VW23VSUGO6ZNLVGSAF6DNJZK3I.json","graph_json":"https://pith.science/api/pith-number/VW23VSUGO6ZNLVGSAF6DNJZK3I/graph.json","events_json":"https://pith.science/api/pith-number/VW23VSUGO6ZNLVGSAF6DNJZK3I/events.json","paper":"https://pith.science/paper/VW23VSUG"},"agent_actions":{"view_html":"https://pith.science/pith/VW23VSUGO6ZNLVGSAF6DNJZK3I","download_json":"https://pith.science/pith/VW23VSUGO6ZNLVGSAF6DNJZK3I.json","view_paper":"https://pith.science/paper/VW23VSUG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.4233&json=true","fetch_graph":"https://pith.science/api/pith-number/VW23VSUGO6ZNLVGSAF6DNJZK3I/graph.json","fetch_events":"https://pith.science/api/pith-number/VW23VSUGO6ZNLVGSAF6DNJZK3I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VW23VSUGO6ZNLVGSAF6DNJZK3I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VW23VSUGO6ZNLVGSAF6DNJZK3I/action/storage_attestation","attest_author":"https://pith.science/pith/VW23VSUGO6ZNLVGSAF6DNJZK3I/action/author_attestation","sign_citation":"https://pith.science/pith/VW23VSUGO6ZNLVGSAF6DNJZK3I/action/citation_signature","submit_replication":"https://pith.science/pith/VW23VSUGO6ZNLVGSAF6DNJZK3I/action/replication_record"}},"created_at":"2026-05-18T04:00:59.934305+00:00","updated_at":"2026-05-18T04:00:59.934305+00:00"}