{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AHCLXXHDPGIYMPO3BIBURFCWMW","short_pith_number":"pith:AHCLXXHD","canonical_record":{"source":{"id":"1602.05347","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-17T09:33:24Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"bebd349fd5aaa000b1d5d2c18b812c3cb744f96717948f33d553b8c02ffc75c4","abstract_canon_sha256":"ac3c954867b24efd4558ce66e9e9589aff67e70400301956e31b9a917f6fd8e4"},"schema_version":"1.0"},"canonical_sha256":"01c4bbdce37991863ddb0a0348945665a2afd50598722211cbe07e8a8a90494a","source":{"kind":"arxiv","id":"1602.05347","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05347","created_at":"2026-05-18T01:10:45Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05347v3","created_at":"2026-05-18T01:10:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05347","created_at":"2026-05-18T01:10:45Z"},{"alias_kind":"pith_short_12","alias_value":"AHCLXXHDPGIY","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AHCLXXHDPGIYMPO3","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AHCLXXHD","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AHCLXXHDPGIYMPO3BIBURFCWMW","target":"record","payload":{"canonical_record":{"source":{"id":"1602.05347","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-17T09:33:24Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"bebd349fd5aaa000b1d5d2c18b812c3cb744f96717948f33d553b8c02ffc75c4","abstract_canon_sha256":"ac3c954867b24efd4558ce66e9e9589aff67e70400301956e31b9a917f6fd8e4"},"schema_version":"1.0"},"canonical_sha256":"01c4bbdce37991863ddb0a0348945665a2afd50598722211cbe07e8a8a90494a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:45.693268Z","signature_b64":"kgI4q2id8qlAM9Cgg4UyBSynNyXrPRwO/FxCZypwlBZyo6SiNT59LY0vEo+GSfgSs8p0E/6YVMyd+INoU8tlCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01c4bbdce37991863ddb0a0348945665a2afd50598722211cbe07e8a8a90494a","last_reissued_at":"2026-05-18T01:10:45.692882Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:45.692882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.05347","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:10:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vF0tFecNiqr/vVbGQjt37bVgXpg94pNvtgEKIiGgN/MrdqzeJ4XpM1bIllVGX2vjZzmIGWkM2Api3hsB+UQYCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T03:37:05.143076Z"},"content_sha256":"0d3f4709fc5ddcef212d19a53eac15c1078c391c115c492bced7e40e923712bf","schema_version":"1.0","event_id":"sha256:0d3f4709fc5ddcef212d19a53eac15c1078c391c115c492bced7e40e923712bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AHCLXXHDPGIYMPO3BIBURFCWMW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local Li-Yau's estimates on $RCD^*(K,N)$ metric measure 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":"2016-02-17T09:33:24Z","abstract_excerpt":"In this paper, we will study the (linear) geometric analysis on metric measure spaces. We will establish a local Li-Yau's estimate for weak solutions of the heat equation and prove a sharp Yau's gradient gradient for harmonic functions on metric measure spaces, under the Riemannian curvature-dimension condition $RCD^*(K,N).$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05347","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:10:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/iq8+2RCSNMjBmDDZBvUAwlcq1HFPxGXIhr7Ty6Ru/y9B4isYoZ49KWo1Lr8KGsxWTvHZDZ9p2xS+gnePGKODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T03:37:05.143436Z"},"content_sha256":"0ad147649a1367e7f4b0ec1a2bce7e914694a1d2dae25f39dad0391f50d8d12a","schema_version":"1.0","event_id":"sha256:0ad147649a1367e7f4b0ec1a2bce7e914694a1d2dae25f39dad0391f50d8d12a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AHCLXXHDPGIYMPO3BIBURFCWMW/bundle.json","state_url":"https://pith.science/pith/AHCLXXHDPGIYMPO3BIBURFCWMW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AHCLXXHDPGIYMPO3BIBURFCWMW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T03:37:05Z","links":{"resolver":"https://pith.science/pith/AHCLXXHDPGIYMPO3BIBURFCWMW","bundle":"https://pith.science/pith/AHCLXXHDPGIYMPO3BIBURFCWMW/bundle.json","state":"https://pith.science/pith/AHCLXXHDPGIYMPO3BIBURFCWMW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AHCLXXHDPGIYMPO3BIBURFCWMW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AHCLXXHDPGIYMPO3BIBURFCWMW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ac3c954867b24efd4558ce66e9e9589aff67e70400301956e31b9a917f6fd8e4","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-17T09:33:24Z","title_canon_sha256":"bebd349fd5aaa000b1d5d2c18b812c3cb744f96717948f33d553b8c02ffc75c4"},"schema_version":"1.0","source":{"id":"1602.05347","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05347","created_at":"2026-05-18T01:10:45Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05347v3","created_at":"2026-05-18T01:10:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05347","created_at":"2026-05-18T01:10:45Z"},{"alias_kind":"pith_short_12","alias_value":"AHCLXXHDPGIY","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AHCLXXHDPGIYMPO3","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AHCLXXHD","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:0ad147649a1367e7f4b0ec1a2bce7e914694a1d2dae25f39dad0391f50d8d12a","target":"graph","created_at":"2026-05-18T01:10:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we will study the (linear) geometric analysis on metric measure spaces. We will establish a local Li-Yau's estimate for weak solutions of the heat equation and prove a sharp Yau's gradient gradient for harmonic functions on metric measure spaces, under the Riemannian curvature-dimension condition $RCD^*(K,N).$","authors_text":"Hui-Chun Zhang, Xi-Ping Zhu","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-17T09:33:24Z","title":"Local Li-Yau's estimates on $RCD^*(K,N)$ metric measure spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05347","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0d3f4709fc5ddcef212d19a53eac15c1078c391c115c492bced7e40e923712bf","target":"record","created_at":"2026-05-18T01:10:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ac3c954867b24efd4558ce66e9e9589aff67e70400301956e31b9a917f6fd8e4","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-17T09:33:24Z","title_canon_sha256":"bebd349fd5aaa000b1d5d2c18b812c3cb744f96717948f33d553b8c02ffc75c4"},"schema_version":"1.0","source":{"id":"1602.05347","kind":"arxiv","version":3}},"canonical_sha256":"01c4bbdce37991863ddb0a0348945665a2afd50598722211cbe07e8a8a90494a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01c4bbdce37991863ddb0a0348945665a2afd50598722211cbe07e8a8a90494a","first_computed_at":"2026-05-18T01:10:45.692882Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:45.692882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kgI4q2id8qlAM9Cgg4UyBSynNyXrPRwO/FxCZypwlBZyo6SiNT59LY0vEo+GSfgSs8p0E/6YVMyd+INoU8tlCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:45.693268Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.05347","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d3f4709fc5ddcef212d19a53eac15c1078c391c115c492bced7e40e923712bf","sha256:0ad147649a1367e7f4b0ec1a2bce7e914694a1d2dae25f39dad0391f50d8d12a"],"state_sha256":"fc4c954fb1fb55185edb210aca53442b91f04055a8f9f23a5afb15c4b98fff67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SYkloAtEgxeoYK0nrLe6GyX7cXMnKFeJq7HexM69iJsEUUkdRRnHrZr1OPnmZODPfoFsFN0E8XR/QQ/hFkf9AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T03:37:05.145733Z","bundle_sha256":"75599f673ebfcf4167e4742fecbd7e3b343b9544a58ffc41d75a3bd8551f6232"}}