{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:YKZRKMPQKN2SJLQQAGDV6TGCBV","short_pith_number":"pith:YKZRKMPQ","schema_version":"1.0","canonical_sha256":"c2b31531f0537524ae1001875f4cc20d40270038eaf81a3aa0b6c5dd341dae49","source":{"kind":"arxiv","id":"1805.06039","version":3},"attestation_state":"computed","paper":{"title":"On sharp global well-posedness and Ill-posedness for a fifth-order KdV-BBM type equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mahendra Panthee, Xavier Carvajal","submitted_at":"2018-05-15T21:34:02Z","abstract_excerpt":"We consider the Cauchy problem associated to the recently derived higher order hamiltonian model for unidirectional water waves and prove global existence for given data in the Sobolev space $H^s$, $s\\geq 1$. We also prove an ill-posedness result by showing that the flow-map is not continuous if the given data has Sobolev regularity $s< 1$. The results obtained in this work are sharp."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1805.06039","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-15T21:34:02Z","cross_cats_sorted":[],"title_canon_sha256":"141a0b93816d8d6dcd31b8bf45a499ca88c294cfaafb678ae3e2dc5a48d46d41","abstract_canon_sha256":"17567e0d3da4c1ff38e62e3016b6c3542347e406d699894bbf9e315964ae6dd7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:15.451305Z","signature_b64":"mSPLvmBZLlo/QBt6reeDVhdjLSCdDRyfflp3hg6Z13rZ+A7viRhHSQqCdQXrD2XQmKQ+rSyMQHzoOvngofEEAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2b31531f0537524ae1001875f4cc20d40270038eaf81a3aa0b6c5dd341dae49","last_reissued_at":"2026-05-17T23:42:15.450638Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:15.450638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On sharp global well-posedness and Ill-posedness for a fifth-order KdV-BBM type equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mahendra Panthee, Xavier Carvajal","submitted_at":"2018-05-15T21:34:02Z","abstract_excerpt":"We consider the Cauchy problem associated to the recently derived higher order hamiltonian model for unidirectional water waves and prove global existence for given data in the Sobolev space $H^s$, $s\\geq 1$. We also prove an ill-posedness result by showing that the flow-map is not continuous if the given data has Sobolev regularity $s< 1$. The results obtained in this work are sharp."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06039","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1805.06039","created_at":"2026-05-17T23:42:15.450735+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.06039v3","created_at":"2026-05-17T23:42:15.450735+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.06039","created_at":"2026-05-17T23:42:15.450735+00:00"},{"alias_kind":"pith_short_12","alias_value":"YKZRKMPQKN2S","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_16","alias_value":"YKZRKMPQKN2SJLQQ","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_8","alias_value":"YKZRKMPQ","created_at":"2026-05-18T12:33:04.347982+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YKZRKMPQKN2SJLQQAGDV6TGCBV","json":"https://pith.science/pith/YKZRKMPQKN2SJLQQAGDV6TGCBV.json","graph_json":"https://pith.science/api/pith-number/YKZRKMPQKN2SJLQQAGDV6TGCBV/graph.json","events_json":"https://pith.science/api/pith-number/YKZRKMPQKN2SJLQQAGDV6TGCBV/events.json","paper":"https://pith.science/paper/YKZRKMPQ"},"agent_actions":{"view_html":"https://pith.science/pith/YKZRKMPQKN2SJLQQAGDV6TGCBV","download_json":"https://pith.science/pith/YKZRKMPQKN2SJLQQAGDV6TGCBV.json","view_paper":"https://pith.science/paper/YKZRKMPQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.06039&json=true","fetch_graph":"https://pith.science/api/pith-number/YKZRKMPQKN2SJLQQAGDV6TGCBV/graph.json","fetch_events":"https://pith.science/api/pith-number/YKZRKMPQKN2SJLQQAGDV6TGCBV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YKZRKMPQKN2SJLQQAGDV6TGCBV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YKZRKMPQKN2SJLQQAGDV6TGCBV/action/storage_attestation","attest_author":"https://pith.science/pith/YKZRKMPQKN2SJLQQAGDV6TGCBV/action/author_attestation","sign_citation":"https://pith.science/pith/YKZRKMPQKN2SJLQQAGDV6TGCBV/action/citation_signature","submit_replication":"https://pith.science/pith/YKZRKMPQKN2SJLQQAGDV6TGCBV/action/replication_record"}},"created_at":"2026-05-17T23:42:15.450735+00:00","updated_at":"2026-05-17T23:42:15.450735+00:00"}