{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XRRXTUIRNX7OQXKXCSG6BXC344","short_pith_number":"pith:XRRXTUIR","canonical_record":{"source":{"id":"1803.10622","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-28T13:59:56Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"43ad6cffd5e1638a911e388dcd0077f096a73cd716d82ca70751c73e26d0a2d4","abstract_canon_sha256":"6b4ee4e32be759ae66b79b727a5da4bcb076e638895690143ee3e7ffcdc1075d"},"schema_version":"1.0"},"canonical_sha256":"bc6379d1116dfee85d57148de0dc5be7283c3586277160910af50acc0a0d7af9","source":{"kind":"arxiv","id":"1803.10622","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.10622","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"arxiv_version","alias_value":"1803.10622v1","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10622","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"pith_short_12","alias_value":"XRRXTUIRNX7O","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XRRXTUIRNX7OQXKX","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XRRXTUIR","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XRRXTUIRNX7OQXKXCSG6BXC344","target":"record","payload":{"canonical_record":{"source":{"id":"1803.10622","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-28T13:59:56Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"43ad6cffd5e1638a911e388dcd0077f096a73cd716d82ca70751c73e26d0a2d4","abstract_canon_sha256":"6b4ee4e32be759ae66b79b727a5da4bcb076e638895690143ee3e7ffcdc1075d"},"schema_version":"1.0"},"canonical_sha256":"bc6379d1116dfee85d57148de0dc5be7283c3586277160910af50acc0a0d7af9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:54.684076Z","signature_b64":"G7QAJ+Io6W8SSC/oLeCEO3a1wa0YbnQGaz0u0qGqIjKJKutpaKKu+MyS5GUaeOkBzN2ucvAn+2g2oOIvc7kICg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc6379d1116dfee85d57148de0dc5be7283c3586277160910af50acc0a0d7af9","last_reissued_at":"2026-05-18T00:19:54.683395Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:54.683395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.10622","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":"2026-05-18T00:19:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O+f7GFCR7U5Wa3Gbbx7Lg2407APkEovv+MlJrgIZ7TuywaaCRIsNH36HkqpkbRkyilwwGeofxF5Lr7sh6pPaCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T22:18:06.153893Z"},"content_sha256":"caad18cf0d765a7e06bcb0a8aa4daccedee06c123b9e13bc6b161c69859e7c4d","schema_version":"1.0","event_id":"sha256:caad18cf0d765a7e06bcb0a8aa4daccedee06c123b9e13bc6b161c69859e7c4d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XRRXTUIRNX7OQXKXCSG6BXC344","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New differential Harnack inequalities for nonlinear heat equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Jia-Yong Wu","submitted_at":"2018-03-28T13:59:56Z","abstract_excerpt":"We prove constrained trace, matrix and constrained matrix Harnack inequalities for the nonlinear heat equation $\\omega_t=\\Delta\\omega+a\\omega\\ln \\omega$ on closed manifolds. We also derive a new interpolated Harnack inequality for the equation $\\omega_t=\\Delta\\omega-\\omega\\ln\\omega+\\varepsilon R\\omega$ on closed surfaces under the $\\varepsilon$-Ricci flow. Finally we prove a new differential Harnack inequality for the equation $\\omega_t=\\Delta\\omega-\\omega\\ln\\omega$ under the Ricci flow without any curvature condition. Among these Harnack inequalities, the correction terms are all time-exponen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10622","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":"2026-05-18T00:19:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lahvkGpHY83zK/fEKfRu9vN9GGBaA1uIsJ5bv6YmifbjL1oPKbgx3eNTD86/9TqAMkZOBMMS/o85q7XLux+aDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T22:18:06.154239Z"},"content_sha256":"50080dda006ccefc1125aa66a5837f9d9fa258e0c90f8d012fe09e6dbc27fde6","schema_version":"1.0","event_id":"sha256:50080dda006ccefc1125aa66a5837f9d9fa258e0c90f8d012fe09e6dbc27fde6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XRRXTUIRNX7OQXKXCSG6BXC344/bundle.json","state_url":"https://pith.science/pith/XRRXTUIRNX7OQXKXCSG6BXC344/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XRRXTUIRNX7OQXKXCSG6BXC344/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":"2026-06-29T22:18:06Z","links":{"resolver":"https://pith.science/pith/XRRXTUIRNX7OQXKXCSG6BXC344","bundle":"https://pith.science/pith/XRRXTUIRNX7OQXKXCSG6BXC344/bundle.json","state":"https://pith.science/pith/XRRXTUIRNX7OQXKXCSG6BXC344/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XRRXTUIRNX7OQXKXCSG6BXC344/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XRRXTUIRNX7OQXKXCSG6BXC344","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":"6b4ee4e32be759ae66b79b727a5da4bcb076e638895690143ee3e7ffcdc1075d","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-28T13:59:56Z","title_canon_sha256":"43ad6cffd5e1638a911e388dcd0077f096a73cd716d82ca70751c73e26d0a2d4"},"schema_version":"1.0","source":{"id":"1803.10622","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.10622","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"arxiv_version","alias_value":"1803.10622v1","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10622","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"pith_short_12","alias_value":"XRRXTUIRNX7O","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XRRXTUIRNX7OQXKX","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XRRXTUIR","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:50080dda006ccefc1125aa66a5837f9d9fa258e0c90f8d012fe09e6dbc27fde6","target":"graph","created_at":"2026-05-18T00:19:54Z","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":"We prove constrained trace, matrix and constrained matrix Harnack inequalities for the nonlinear heat equation $\\omega_t=\\Delta\\omega+a\\omega\\ln \\omega$ on closed manifolds. We also derive a new interpolated Harnack inequality for the equation $\\omega_t=\\Delta\\omega-\\omega\\ln\\omega+\\varepsilon R\\omega$ on closed surfaces under the $\\varepsilon$-Ricci flow. Finally we prove a new differential Harnack inequality for the equation $\\omega_t=\\Delta\\omega-\\omega\\ln\\omega$ under the Ricci flow without any curvature condition. Among these Harnack inequalities, the correction terms are all time-exponen","authors_text":"Jia-Yong Wu","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-28T13:59:56Z","title":"New differential Harnack inequalities for nonlinear heat equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10622","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:caad18cf0d765a7e06bcb0a8aa4daccedee06c123b9e13bc6b161c69859e7c4d","target":"record","created_at":"2026-05-18T00:19:54Z","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":"6b4ee4e32be759ae66b79b727a5da4bcb076e638895690143ee3e7ffcdc1075d","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-28T13:59:56Z","title_canon_sha256":"43ad6cffd5e1638a911e388dcd0077f096a73cd716d82ca70751c73e26d0a2d4"},"schema_version":"1.0","source":{"id":"1803.10622","kind":"arxiv","version":1}},"canonical_sha256":"bc6379d1116dfee85d57148de0dc5be7283c3586277160910af50acc0a0d7af9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc6379d1116dfee85d57148de0dc5be7283c3586277160910af50acc0a0d7af9","first_computed_at":"2026-05-18T00:19:54.683395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:54.683395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G7QAJ+Io6W8SSC/oLeCEO3a1wa0YbnQGaz0u0qGqIjKJKutpaKKu+MyS5GUaeOkBzN2ucvAn+2g2oOIvc7kICg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:54.684076Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.10622","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caad18cf0d765a7e06bcb0a8aa4daccedee06c123b9e13bc6b161c69859e7c4d","sha256:50080dda006ccefc1125aa66a5837f9d9fa258e0c90f8d012fe09e6dbc27fde6"],"state_sha256":"e79752e81c1f2b47833a323141196a171015099ad176d873f2a1a6688747125f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FcNwLi/r8DjrCTtvWENM6LaKmSUSO//PURN7V1FdYjE3qDLUag/TsxjbuyQjWGaB1BGsg+a6NawyVj9QA3tmBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T22:18:06.156166Z","bundle_sha256":"e418f5088e1ce0386c3137f624082723f4b9f7b5b32d328b37f2c5d101e149cd"}}