{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:FLLQJRNC6C7EO4SZBIROZWJSC5","short_pith_number":"pith:FLLQJRNC","canonical_record":{"source":{"id":"1712.04024","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-11T21:02:17Z","cross_cats_sorted":[],"title_canon_sha256":"3ab4d6170a1c4cdc15ab19f4385a1fab6004f42a31f68d0464984faf8fd9f355","abstract_canon_sha256":"8d52816e8f71d79397d3b3bde4ee3879c4a41eb809b27a8f9658e615c59c9395"},"schema_version":"1.0"},"canonical_sha256":"2ad704c5a2f0be4772590a22ecd932174a1e85bb8e3009c6f5ecf8c90d5bfee5","source":{"kind":"arxiv","id":"1712.04024","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04024","created_at":"2026-05-18T00:28:09Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04024v1","created_at":"2026-05-18T00:28:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04024","created_at":"2026-05-18T00:28:09Z"},{"alias_kind":"pith_short_12","alias_value":"FLLQJRNC6C7E","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FLLQJRNC6C7EO4SZ","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FLLQJRNC","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:FLLQJRNC6C7EO4SZBIROZWJSC5","target":"record","payload":{"canonical_record":{"source":{"id":"1712.04024","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-11T21:02:17Z","cross_cats_sorted":[],"title_canon_sha256":"3ab4d6170a1c4cdc15ab19f4385a1fab6004f42a31f68d0464984faf8fd9f355","abstract_canon_sha256":"8d52816e8f71d79397d3b3bde4ee3879c4a41eb809b27a8f9658e615c59c9395"},"schema_version":"1.0"},"canonical_sha256":"2ad704c5a2f0be4772590a22ecd932174a1e85bb8e3009c6f5ecf8c90d5bfee5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:09.537391Z","signature_b64":"fnFZj0AludkhosGndiFrF2vOto6sdhM+wkKJqPuOFGmEngvoeO3nMEERu2OVNYIIoP7fcWIqS1AmOsvt/1vrBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ad704c5a2f0be4772590a22ecd932174a1e85bb8e3009c6f5ecf8c90d5bfee5","last_reissued_at":"2026-05-18T00:28:09.536641Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:09.536641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.04024","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":"2026-05-18T00:28:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fuBxujTDMLs4rx9Ont2qH26xzBnLUZWWz7YlUPtbcFeYP5MF9cMMgjemuDOyAF8UHcTmKOGONc06nQHJKPUuDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:35:05.704291Z"},"content_sha256":"804ec17085f4069a3ad9164d42a994a7d7e444e61717f8ef27e4aef8d04e6c02","schema_version":"1.0","event_id":"sha256:804ec17085f4069a3ad9164d42a994a7d7e444e61717f8ef27e4aef8d04e6c02"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:FLLQJRNC6C7EO4SZBIROZWJSC5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Differential Harnack Inequality for the Newell-Whitehead Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Derek Booth, Jack Burkart, Jason Snyder, Max Hallgren, Tom Stone, Xiaodong Cao, Zachary Munro","submitted_at":"2017-12-11T21:02:17Z","abstract_excerpt":"This paper will develop a Li-Yau-Hamilton type differential Harnack estimate for positive solutions to the Newell-Whitehead equation on $\\mathbb{R}^n$. We then use our LYH-differential Harnack inequality to prove several properties about positive solutions to the equation, including deriving a classical Harnack inequality, and characterizing standing solutions and traveling wave solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04024","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":"2026-05-18T00:28:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4erzx64YTyZirc/27n0qBvza8cw8KwXlGsMBa/J71qPNsaJCAiffWvy9yWI8olaKLaV2ft9ThKlZG1wvaVY8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:35:05.705004Z"},"content_sha256":"f81a8a24ecd7e296f53d576f4826baed3b4e0cb036f1a64bac3c20864ba2c0c1","schema_version":"1.0","event_id":"sha256:f81a8a24ecd7e296f53d576f4826baed3b4e0cb036f1a64bac3c20864ba2c0c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FLLQJRNC6C7EO4SZBIROZWJSC5/bundle.json","state_url":"https://pith.science/pith/FLLQJRNC6C7EO4SZBIROZWJSC5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FLLQJRNC6C7EO4SZBIROZWJSC5/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":"2026-05-26T12:35:05Z","links":{"resolver":"https://pith.science/pith/FLLQJRNC6C7EO4SZBIROZWJSC5","bundle":"https://pith.science/pith/FLLQJRNC6C7EO4SZBIROZWJSC5/bundle.json","state":"https://pith.science/pith/FLLQJRNC6C7EO4SZBIROZWJSC5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FLLQJRNC6C7EO4SZBIROZWJSC5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FLLQJRNC6C7EO4SZBIROZWJSC5","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":"8d52816e8f71d79397d3b3bde4ee3879c4a41eb809b27a8f9658e615c59c9395","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-11T21:02:17Z","title_canon_sha256":"3ab4d6170a1c4cdc15ab19f4385a1fab6004f42a31f68d0464984faf8fd9f355"},"schema_version":"1.0","source":{"id":"1712.04024","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04024","created_at":"2026-05-18T00:28:09Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04024v1","created_at":"2026-05-18T00:28:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04024","created_at":"2026-05-18T00:28:09Z"},{"alias_kind":"pith_short_12","alias_value":"FLLQJRNC6C7E","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FLLQJRNC6C7EO4SZ","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FLLQJRNC","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:f81a8a24ecd7e296f53d576f4826baed3b4e0cb036f1a64bac3c20864ba2c0c1","target":"graph","created_at":"2026-05-18T00:28:09Z","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":"This paper will develop a Li-Yau-Hamilton type differential Harnack estimate for positive solutions to the Newell-Whitehead equation on $\\mathbb{R}^n$. We then use our LYH-differential Harnack inequality to prove several properties about positive solutions to the equation, including deriving a classical Harnack inequality, and characterizing standing solutions and traveling wave solutions.","authors_text":"Derek Booth, Jack Burkart, Jason Snyder, Max Hallgren, Tom Stone, Xiaodong Cao, Zachary Munro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-11T21:02:17Z","title":"A Differential Harnack Inequality for the Newell-Whitehead Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04024","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":"sha256:804ec17085f4069a3ad9164d42a994a7d7e444e61717f8ef27e4aef8d04e6c02","target":"record","created_at":"2026-05-18T00:28:09Z","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":"8d52816e8f71d79397d3b3bde4ee3879c4a41eb809b27a8f9658e615c59c9395","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-11T21:02:17Z","title_canon_sha256":"3ab4d6170a1c4cdc15ab19f4385a1fab6004f42a31f68d0464984faf8fd9f355"},"schema_version":"1.0","source":{"id":"1712.04024","kind":"arxiv","version":1}},"canonical_sha256":"2ad704c5a2f0be4772590a22ecd932174a1e85bb8e3009c6f5ecf8c90d5bfee5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ad704c5a2f0be4772590a22ecd932174a1e85bb8e3009c6f5ecf8c90d5bfee5","first_computed_at":"2026-05-18T00:28:09.536641Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:09.536641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fnFZj0AludkhosGndiFrF2vOto6sdhM+wkKJqPuOFGmEngvoeO3nMEERu2OVNYIIoP7fcWIqS1AmOsvt/1vrBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:09.537391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.04024","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:804ec17085f4069a3ad9164d42a994a7d7e444e61717f8ef27e4aef8d04e6c02","sha256:f81a8a24ecd7e296f53d576f4826baed3b4e0cb036f1a64bac3c20864ba2c0c1"],"state_sha256":"62e0961a8de6c0e79a27f639d3d528800c7a43123c7c2483faf50685fb428cde"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ILoOLTu7nnV5Fr1hRDh3eDqTtgqxtLqQjydMv45FxorDL110TMtIZZ04RiNgpRJjryzwKLcvxMEvU4CYvRlZCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T12:35:05.708717Z","bundle_sha256":"bbbafa58e7473d5c083976e229fe7dfad2c71acf78fd76ca9df478af5192aa65"}}