{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:U77NVNRF6EK24MXRBQUXM6IWQA","short_pith_number":"pith:U77NVNRF","canonical_record":{"source":{"id":"1004.4840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-04-27T15:52:19Z","cross_cats_sorted":[],"title_canon_sha256":"8ceaf06aa5cf5936c8b04db38ec17989a9c1c4b2f99723c0ca4fc7bdca755c45","abstract_canon_sha256":"7a814653c0eca3023c557d49492cbc6850e53f455ce7c9589500a48271f2ff16"},"schema_version":"1.0"},"canonical_sha256":"a7fedab625f115ae32f10c297679168004dbfc85e2a533612c46049dcbec8045","source":{"kind":"arxiv","id":"1004.4840","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.4840","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"arxiv_version","alias_value":"1004.4840v1","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.4840","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"pith_short_12","alias_value":"U77NVNRF6EK2","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"U77NVNRF6EK24MXR","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"U77NVNRF","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:U77NVNRF6EK24MXRBQUXM6IWQA","target":"record","payload":{"canonical_record":{"source":{"id":"1004.4840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-04-27T15:52:19Z","cross_cats_sorted":[],"title_canon_sha256":"8ceaf06aa5cf5936c8b04db38ec17989a9c1c4b2f99723c0ca4fc7bdca755c45","abstract_canon_sha256":"7a814653c0eca3023c557d49492cbc6850e53f455ce7c9589500a48271f2ff16"},"schema_version":"1.0"},"canonical_sha256":"a7fedab625f115ae32f10c297679168004dbfc85e2a533612c46049dcbec8045","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:15.802785Z","signature_b64":"bJ3rYDUfRXENG+d4DVFjV0v0TZymjZS/yr58EviBtd9rZNRe8L513+m+Zt6E2WFlsxBqmlSSB4flaz+/NKuKDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7fedab625f115ae32f10c297679168004dbfc85e2a533612c46049dcbec8045","last_reissued_at":"2026-05-18T02:24:15.802150Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:15.802150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.4840","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":"2026-05-18T02:24:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4LZtKhLYOsz+56IlyLqB1CcCEHt5seF24QOocYqR4GcmFs4m4lgPwYtekA/xba9MEyTrDvgyGS/hhS3pTjTnBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:45:47.909357Z"},"content_sha256":"3bf6c7ecdd0dd3b1834fbe4cca4535d66d7b38581ce471ae75dd0fd0bc5a7f99","schema_version":"1.0","event_id":"sha256:3bf6c7ecdd0dd3b1834fbe4cca4535d66d7b38581ce471ae75dd0fd0bc5a7f99"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:U77NVNRF6EK24MXRBQUXM6IWQA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp differential estimates of Li-Yau-Hamilton type for positive $(p,p)$-forms on K\\\"ahler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Lei Ni, Yanyan Niu","submitted_at":"2010-04-27T15:52:19Z","abstract_excerpt":"In this paper we study the heat equation (of Hodge-Laplacian) deformation of $(p, p)$-forms on a K\\\"ahler manifold. After identifying the condition and establishing that the positivity of a $(p, p)$-form solution is preserved under such an invariant condition we prove the sharp differential Harnack (in the sense of Li-Yau-Hamilton) estimates for the positive solutions of the Hodge-Laplacian heat equation. We also prove a nonlinear version coupled with the K\\\"ahler-Ricci flow and some interpolating matrix differential Harnack type estimates for both the K\\\"ahler-Ricci flow and the Ricci flow."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.4840","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":"2026-05-18T02:24:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/nXUUrv91hgN/TN6GwjthmYPqlDHloux3TQQZOjDYkujk7nOigFbujWiJ5ikR55DOyTyGl/k1Np/Lc5pshFTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:45:47.909938Z"},"content_sha256":"a2aadff1a51a7d5707e9d6c112d1c1e2d7a2c4b1302d807a13e02c09c7ec9d71","schema_version":"1.0","event_id":"sha256:a2aadff1a51a7d5707e9d6c112d1c1e2d7a2c4b1302d807a13e02c09c7ec9d71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U77NVNRF6EK24MXRBQUXM6IWQA/bundle.json","state_url":"https://pith.science/pith/U77NVNRF6EK24MXRBQUXM6IWQA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U77NVNRF6EK24MXRBQUXM6IWQA/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":"2026-06-07T10:45:47Z","links":{"resolver":"https://pith.science/pith/U77NVNRF6EK24MXRBQUXM6IWQA","bundle":"https://pith.science/pith/U77NVNRF6EK24MXRBQUXM6IWQA/bundle.json","state":"https://pith.science/pith/U77NVNRF6EK24MXRBQUXM6IWQA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U77NVNRF6EK24MXRBQUXM6IWQA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:U77NVNRF6EK24MXRBQUXM6IWQA","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":"7a814653c0eca3023c557d49492cbc6850e53f455ce7c9589500a48271f2ff16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-04-27T15:52:19Z","title_canon_sha256":"8ceaf06aa5cf5936c8b04db38ec17989a9c1c4b2f99723c0ca4fc7bdca755c45"},"schema_version":"1.0","source":{"id":"1004.4840","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.4840","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"arxiv_version","alias_value":"1004.4840v1","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.4840","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"pith_short_12","alias_value":"U77NVNRF6EK2","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"U77NVNRF6EK24MXR","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"U77NVNRF","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:a2aadff1a51a7d5707e9d6c112d1c1e2d7a2c4b1302d807a13e02c09c7ec9d71","target":"graph","created_at":"2026-05-18T02:24:15Z","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 study the heat equation (of Hodge-Laplacian) deformation of $(p, p)$-forms on a K\\\"ahler manifold. After identifying the condition and establishing that the positivity of a $(p, p)$-form solution is preserved under such an invariant condition we prove the sharp differential Harnack (in the sense of Li-Yau-Hamilton) estimates for the positive solutions of the Hodge-Laplacian heat equation. We also prove a nonlinear version coupled with the K\\\"ahler-Ricci flow and some interpolating matrix differential Harnack type estimates for both the K\\\"ahler-Ricci flow and the Ricci flow.","authors_text":"Lei Ni, Yanyan Niu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-04-27T15:52:19Z","title":"Sharp differential estimates of Li-Yau-Hamilton type for positive $(p,p)$-forms on K\\\"ahler manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.4840","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":"sha256:3bf6c7ecdd0dd3b1834fbe4cca4535d66d7b38581ce471ae75dd0fd0bc5a7f99","target":"record","created_at":"2026-05-18T02:24:15Z","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":"7a814653c0eca3023c557d49492cbc6850e53f455ce7c9589500a48271f2ff16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-04-27T15:52:19Z","title_canon_sha256":"8ceaf06aa5cf5936c8b04db38ec17989a9c1c4b2f99723c0ca4fc7bdca755c45"},"schema_version":"1.0","source":{"id":"1004.4840","kind":"arxiv","version":1}},"canonical_sha256":"a7fedab625f115ae32f10c297679168004dbfc85e2a533612c46049dcbec8045","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7fedab625f115ae32f10c297679168004dbfc85e2a533612c46049dcbec8045","first_computed_at":"2026-05-18T02:24:15.802150Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:15.802150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bJ3rYDUfRXENG+d4DVFjV0v0TZymjZS/yr58EviBtd9rZNRe8L513+m+Zt6E2WFlsxBqmlSSB4flaz+/NKuKDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:15.802785Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.4840","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3bf6c7ecdd0dd3b1834fbe4cca4535d66d7b38581ce471ae75dd0fd0bc5a7f99","sha256:a2aadff1a51a7d5707e9d6c112d1c1e2d7a2c4b1302d807a13e02c09c7ec9d71"],"state_sha256":"24684cb55dbe30140be38bca1c76eee46842f0eea942c25668895045a75abe6d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D1yRaz5kTps/KrMw5NKxPDTQ5xqqsCM84AJMdLuSJoPoWrdra4ywwQFxxOYhs3v1zbSTJIM+Ho6sq2flPIHdAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T10:45:47.912618Z","bundle_sha256":"26a044e2f8c297415b65f79ee25c99dadb0bc2b817b5ae11931755a7d944a456"}}