{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:LYWTYFX7X2ARLV3TCNPLZYDYIZ","short_pith_number":"pith:LYWTYFX7","canonical_record":{"source":{"id":"1805.05192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-11T11:27:36Z","cross_cats_sorted":[],"title_canon_sha256":"290410dedea47256bc2609539a996b78b7891f9a52cd055a5f0c4aba961d6b95","abstract_canon_sha256":"59dbc506c87e11d84ed194db8c205dfce6f3d2654b934d1c40d5be36cf9829eb"},"schema_version":"1.0"},"canonical_sha256":"5e2d3c16ffbe8115d773135ebce078465dea4c0b8d75aac63aa89a79ac0decc4","source":{"kind":"arxiv","id":"1805.05192","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.05192","created_at":"2026-05-18T00:16:03Z"},{"alias_kind":"arxiv_version","alias_value":"1805.05192v1","created_at":"2026-05-18T00:16:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.05192","created_at":"2026-05-18T00:16:03Z"},{"alias_kind":"pith_short_12","alias_value":"LYWTYFX7X2AR","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LYWTYFX7X2ARLV3T","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LYWTYFX7","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:LYWTYFX7X2ARLV3TCNPLZYDYIZ","target":"record","payload":{"canonical_record":{"source":{"id":"1805.05192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-11T11:27:36Z","cross_cats_sorted":[],"title_canon_sha256":"290410dedea47256bc2609539a996b78b7891f9a52cd055a5f0c4aba961d6b95","abstract_canon_sha256":"59dbc506c87e11d84ed194db8c205dfce6f3d2654b934d1c40d5be36cf9829eb"},"schema_version":"1.0"},"canonical_sha256":"5e2d3c16ffbe8115d773135ebce078465dea4c0b8d75aac63aa89a79ac0decc4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:03.706956Z","signature_b64":"nDkW5ImsZ5sbdb57NUYZRIPMlaoXDCLggGNIsSZqhfuno418NtAFCoEuAiEDpsOGk3g8MWWomlhLW3XC13CVBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e2d3c16ffbe8115d773135ebce078465dea4c0b8d75aac63aa89a79ac0decc4","last_reissued_at":"2026-05-18T00:16:03.706468Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:03.706468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.05192","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":"2026-05-18T00:16:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vOU7YK44K/GzBjgOs031IFPlZ59CpNT5nf1ENEZmoCyWz+yAdj+xj6zDH8bP7D7xVtY4x2pQPGny70a+7WqOAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:43:19.558199Z"},"content_sha256":"affda51580208103a8c7721c141d3bbf4d28f1fab1c63b2ff0881473d7874d35","schema_version":"1.0","event_id":"sha256:affda51580208103a8c7721c141d3bbf4d28f1fab1c63b2ff0881473d7874d35"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:LYWTYFX7X2ARLV3TCNPLZYDYIZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large Time Behavior and Convergence for the Camassa-Holm Equations with Fractional Laplacian Viscosity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Linghui Meng, Yong He, Zaihui Gan","submitted_at":"2018-05-11T11:27:36Z","abstract_excerpt":"In this paper, we consider the $n$-dimensional ($n=2,3$) Camassa-Holm equations with fractional Laplacian viscosity in the whole space. In stark contrast to the Camassa-Holm equations without any nonlocal effect, to our best knowledge, little has been known on the large time behavior and convergence for the nonlocal equations under study. We first study the large time behavior of solutions. We then discuss the relation between the equations under consideration and the imcompressible Navier-Stokes equations with fractional Laplacian viscosity (INSF). The main difficulty to achieve them lies in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05192","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":"2026-05-18T00:16:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+dKrK3e4YsonrAK/gXWHxbSCXSWrF69EXkwLDd+NczZfJ6E6ipKfvbodFAbmIPfHMX167ATnym1Yj8PXdXW6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:43:19.558663Z"},"content_sha256":"53198a24d59176c6f724714604593d29eb4c8aaab7b890c9890315a089eaf1d7","schema_version":"1.0","event_id":"sha256:53198a24d59176c6f724714604593d29eb4c8aaab7b890c9890315a089eaf1d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LYWTYFX7X2ARLV3TCNPLZYDYIZ/bundle.json","state_url":"https://pith.science/pith/LYWTYFX7X2ARLV3TCNPLZYDYIZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LYWTYFX7X2ARLV3TCNPLZYDYIZ/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":"2026-05-26T04:43:19Z","links":{"resolver":"https://pith.science/pith/LYWTYFX7X2ARLV3TCNPLZYDYIZ","bundle":"https://pith.science/pith/LYWTYFX7X2ARLV3TCNPLZYDYIZ/bundle.json","state":"https://pith.science/pith/LYWTYFX7X2ARLV3TCNPLZYDYIZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LYWTYFX7X2ARLV3TCNPLZYDYIZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LYWTYFX7X2ARLV3TCNPLZYDYIZ","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":"59dbc506c87e11d84ed194db8c205dfce6f3d2654b934d1c40d5be36cf9829eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-11T11:27:36Z","title_canon_sha256":"290410dedea47256bc2609539a996b78b7891f9a52cd055a5f0c4aba961d6b95"},"schema_version":"1.0","source":{"id":"1805.05192","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.05192","created_at":"2026-05-18T00:16:03Z"},{"alias_kind":"arxiv_version","alias_value":"1805.05192v1","created_at":"2026-05-18T00:16:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.05192","created_at":"2026-05-18T00:16:03Z"},{"alias_kind":"pith_short_12","alias_value":"LYWTYFX7X2AR","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LYWTYFX7X2ARLV3T","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LYWTYFX7","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:53198a24d59176c6f724714604593d29eb4c8aaab7b890c9890315a089eaf1d7","target":"graph","created_at":"2026-05-18T00:16:03Z","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 consider the $n$-dimensional ($n=2,3$) Camassa-Holm equations with fractional Laplacian viscosity in the whole space. In stark contrast to the Camassa-Holm equations without any nonlocal effect, to our best knowledge, little has been known on the large time behavior and convergence for the nonlocal equations under study. We first study the large time behavior of solutions. We then discuss the relation between the equations under consideration and the imcompressible Navier-Stokes equations with fractional Laplacian viscosity (INSF). The main difficulty to achieve them lies in ","authors_text":"Linghui Meng, Yong He, Zaihui Gan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-11T11:27:36Z","title":"Large Time Behavior and Convergence for the Camassa-Holm Equations with Fractional Laplacian Viscosity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05192","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:affda51580208103a8c7721c141d3bbf4d28f1fab1c63b2ff0881473d7874d35","target":"record","created_at":"2026-05-18T00:16:03Z","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":"59dbc506c87e11d84ed194db8c205dfce6f3d2654b934d1c40d5be36cf9829eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-11T11:27:36Z","title_canon_sha256":"290410dedea47256bc2609539a996b78b7891f9a52cd055a5f0c4aba961d6b95"},"schema_version":"1.0","source":{"id":"1805.05192","kind":"arxiv","version":1}},"canonical_sha256":"5e2d3c16ffbe8115d773135ebce078465dea4c0b8d75aac63aa89a79ac0decc4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e2d3c16ffbe8115d773135ebce078465dea4c0b8d75aac63aa89a79ac0decc4","first_computed_at":"2026-05-18T00:16:03.706468Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:03.706468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nDkW5ImsZ5sbdb57NUYZRIPMlaoXDCLggGNIsSZqhfuno418NtAFCoEuAiEDpsOGk3g8MWWomlhLW3XC13CVBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:03.706956Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.05192","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:affda51580208103a8c7721c141d3bbf4d28f1fab1c63b2ff0881473d7874d35","sha256:53198a24d59176c6f724714604593d29eb4c8aaab7b890c9890315a089eaf1d7"],"state_sha256":"39d6bf0d6c54c6a1750857b3acd67c32e55fd090ee157763586119bd2b3558c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ovln0PN+FrTbKrHoEcwAbsdp7jOjBGXoCC0DJQ1XOqa7mtjlzvM5WJnn878kz6kzhZX6aCELIzRN/3ie5aQ/AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T04:43:19.561437Z","bundle_sha256":"b4b3d4ec2da4b2dc4c8c8cab3d227fe389f65f509f0912fa123afa1a901d2c62"}}