{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ERB5XWY6X43MYMXG2W4ADWCZMK","short_pith_number":"pith:ERB5XWY6","canonical_record":{"source":{"id":"1706.06249","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-20T03:02:25Z","cross_cats_sorted":[],"title_canon_sha256":"a503cebef28a66891e1d5c2e8c0561b16daf6a2539006563a1f8645c733d8e26","abstract_canon_sha256":"ff52a693366f6ce7e333df63c5c3f40dde05d9fb86fae13b861792dc8ebe380e"},"schema_version":"1.0"},"canonical_sha256":"2443dbdb1ebf36cc32e6d5b801d8596289a9fd528d63745ed337f34e96b79971","source":{"kind":"arxiv","id":"1706.06249","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.06249","created_at":"2026-05-18T00:42:03Z"},{"alias_kind":"arxiv_version","alias_value":"1706.06249v1","created_at":"2026-05-18T00:42:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06249","created_at":"2026-05-18T00:42:03Z"},{"alias_kind":"pith_short_12","alias_value":"ERB5XWY6X43M","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"ERB5XWY6X43MYMXG","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"ERB5XWY6","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ERB5XWY6X43MYMXG2W4ADWCZMK","target":"record","payload":{"canonical_record":{"source":{"id":"1706.06249","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-20T03:02:25Z","cross_cats_sorted":[],"title_canon_sha256":"a503cebef28a66891e1d5c2e8c0561b16daf6a2539006563a1f8645c733d8e26","abstract_canon_sha256":"ff52a693366f6ce7e333df63c5c3f40dde05d9fb86fae13b861792dc8ebe380e"},"schema_version":"1.0"},"canonical_sha256":"2443dbdb1ebf36cc32e6d5b801d8596289a9fd528d63745ed337f34e96b79971","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:03.786598Z","signature_b64":"CoEMreGRjCg1E9f59dBCk/i1TLAwipyu3KLyi54fG+Bmb6PKtZLnnchwTFnzVMtlK1Qwv4jCD5BqeCfGdospAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2443dbdb1ebf36cc32e6d5b801d8596289a9fd528d63745ed337f34e96b79971","last_reissued_at":"2026-05-18T00:42:03.785528Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:03.785528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.06249","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k4UXKyHgceDfyuDbb/EioyfeAIUWUjxs2sI0+zFbvqzadxHlRkd7gXMsYAdJjNZAwfECajXW1X3JF5ArqYAdBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:36:02.546731Z"},"content_sha256":"b151f05ffb3110a552264c668e79acde800777d6426f5c9268bf45cdf31f80d2","schema_version":"1.0","event_id":"sha256:b151f05ffb3110a552264c668e79acde800777d6426f5c9268bf45cdf31f80d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ERB5XWY6X43MYMXG2W4ADWCZMK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Li-Yau type gradient estimate of Li and Xu","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Chengjie Yu, Feifei Zhao, Zhigang Chen","submitted_at":"2017-06-20T03:02:25Z","abstract_excerpt":"In this paper, we obtain a Li-Yau type gradient estimate with time dependent parameter for positive solutions of the heat equation, so that the Li-Yau type gradient estimate of Li-Xu are special cases of the estimate. We also obtain improvements of Davies' Li-Yau type gradient estimate. The argument is different with those of Li-Xu and Qian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06249","kind":"arxiv","version":1},"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":"2026-05-18T00:42:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"18vt4k3AwfsJvRxcFlpNYpdtCQ9K3hVpmLW81FCU85yq4HqaIkVajwRwsUAiqQwBYE87Ce6D2oaByPevEAEFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:36:02.547484Z"},"content_sha256":"69625390e0ec72ec6f1c7ee9630df357bf1e01edc1c2901cc0d1c283a09a5708","schema_version":"1.0","event_id":"sha256:69625390e0ec72ec6f1c7ee9630df357bf1e01edc1c2901cc0d1c283a09a5708"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ERB5XWY6X43MYMXG2W4ADWCZMK/bundle.json","state_url":"https://pith.science/pith/ERB5XWY6X43MYMXG2W4ADWCZMK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ERB5XWY6X43MYMXG2W4ADWCZMK/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":"2026-06-01T00:36:02Z","links":{"resolver":"https://pith.science/pith/ERB5XWY6X43MYMXG2W4ADWCZMK","bundle":"https://pith.science/pith/ERB5XWY6X43MYMXG2W4ADWCZMK/bundle.json","state":"https://pith.science/pith/ERB5XWY6X43MYMXG2W4ADWCZMK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ERB5XWY6X43MYMXG2W4ADWCZMK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ERB5XWY6X43MYMXG2W4ADWCZMK","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":"ff52a693366f6ce7e333df63c5c3f40dde05d9fb86fae13b861792dc8ebe380e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-20T03:02:25Z","title_canon_sha256":"a503cebef28a66891e1d5c2e8c0561b16daf6a2539006563a1f8645c733d8e26"},"schema_version":"1.0","source":{"id":"1706.06249","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.06249","created_at":"2026-05-18T00:42:03Z"},{"alias_kind":"arxiv_version","alias_value":"1706.06249v1","created_at":"2026-05-18T00:42:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06249","created_at":"2026-05-18T00:42:03Z"},{"alias_kind":"pith_short_12","alias_value":"ERB5XWY6X43M","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"ERB5XWY6X43MYMXG","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"ERB5XWY6","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:69625390e0ec72ec6f1c7ee9630df357bf1e01edc1c2901cc0d1c283a09a5708","target":"graph","created_at":"2026-05-18T00:42:03Z","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 obtain a Li-Yau type gradient estimate with time dependent parameter for positive solutions of the heat equation, so that the Li-Yau type gradient estimate of Li-Xu are special cases of the estimate. We also obtain improvements of Davies' Li-Yau type gradient estimate. The argument is different with those of Li-Xu and Qian.","authors_text":"Chengjie Yu, Feifei Zhao, Zhigang Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-20T03:02:25Z","title":"On the Li-Yau type gradient estimate of Li and Xu"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06249","kind":"arxiv","version":1},"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:b151f05ffb3110a552264c668e79acde800777d6426f5c9268bf45cdf31f80d2","target":"record","created_at":"2026-05-18T00:42:03Z","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":"ff52a693366f6ce7e333df63c5c3f40dde05d9fb86fae13b861792dc8ebe380e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-20T03:02:25Z","title_canon_sha256":"a503cebef28a66891e1d5c2e8c0561b16daf6a2539006563a1f8645c733d8e26"},"schema_version":"1.0","source":{"id":"1706.06249","kind":"arxiv","version":1}},"canonical_sha256":"2443dbdb1ebf36cc32e6d5b801d8596289a9fd528d63745ed337f34e96b79971","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2443dbdb1ebf36cc32e6d5b801d8596289a9fd528d63745ed337f34e96b79971","first_computed_at":"2026-05-18T00:42:03.785528Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:03.785528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CoEMreGRjCg1E9f59dBCk/i1TLAwipyu3KLyi54fG+Bmb6PKtZLnnchwTFnzVMtlK1Qwv4jCD5BqeCfGdospAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:03.786598Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.06249","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b151f05ffb3110a552264c668e79acde800777d6426f5c9268bf45cdf31f80d2","sha256:69625390e0ec72ec6f1c7ee9630df357bf1e01edc1c2901cc0d1c283a09a5708"],"state_sha256":"57671cd293443331cb5ce97f6718a2a619ff993f68b67f277ecddc62d27a4523"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vc6ZDqdWTfZuXeEpqgr0BwMiSWOPCtojxAtIEkTUrAjWrIEj4xCrpX1BUUNClTLLH7sH7f9yLc9ReOKaa0cYBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T00:36:02.551729Z","bundle_sha256":"5dc88a3399eab2f8402ff18e4f9317b7e57a2d8049bc315ca309bebe8dc8ca5f"}}