{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:RXS7D6ZYJXDG54BOVDMAPDK6P7","short_pith_number":"pith:RXS7D6ZY","schema_version":"1.0","canonical_sha256":"8de5f1fb384dc66ef02ea8d8078d5e7ffe2860dcb59cf5ca2be0e14cd9f8def2","source":{"kind":"arxiv","id":"1902.00454","version":2},"attestation_state":"computed","paper":{"title":"Asymptotic dynamics for the small data weakly dispersive one-dimensional Hamiltonian ABCD system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chulkwang Kwak, Claudio Mu\\~noz","submitted_at":"2019-02-01T16:58:07Z","abstract_excerpt":"Consider the Hamiltonian $abcd$ system in one dimension, with data posed in the energy space $H^1\\times H^1$. This model, introduced by Bona, Chen and Saut, is a well-known physical generalization of the classical Boussinesq equations. The Hamiltonian case corresponds to the regime where $a,c<0$ and $b=d>0$. Under this regime, small solutions in the energy space are globally defined. A first proof of decay for this $2\\times 2$ system was given by the two authors and Poblete and Pozo, in a strongly dispersive regime, i.e. under essentially the conditions \\[ b=d > \\frac29, \\quad a,c<-\\frac1{18}."},"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":"1902.00454","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-01T16:58:07Z","cross_cats_sorted":[],"title_canon_sha256":"e127cc6f2d9098da9a77bcc74c82ff5c8ef13255e3491fb975423ec1e8311feb","abstract_canon_sha256":"0d48b586b903198bba220e5d01feb4e168058944c38656e5a796d372da5fb15f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:58.236273Z","signature_b64":"YQPjPB21cdr46aJag97zYuHeXnTc34e+xrPrwjyxQ/PnJB9Ax8LL/xkJIW6y07E6tcC+r+CjXYfooZEsEy8aCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8de5f1fb384dc66ef02ea8d8078d5e7ffe2860dcb59cf5ca2be0e14cd9f8def2","last_reissued_at":"2026-05-17T23:47:58.235872Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:58.235872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic dynamics for the small data weakly dispersive one-dimensional Hamiltonian ABCD system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chulkwang Kwak, Claudio Mu\\~noz","submitted_at":"2019-02-01T16:58:07Z","abstract_excerpt":"Consider the Hamiltonian $abcd$ system in one dimension, with data posed in the energy space $H^1\\times H^1$. This model, introduced by Bona, Chen and Saut, is a well-known physical generalization of the classical Boussinesq equations. The Hamiltonian case corresponds to the regime where $a,c<0$ and $b=d>0$. Under this regime, small solutions in the energy space are globally defined. A first proof of decay for this $2\\times 2$ system was given by the two authors and Poblete and Pozo, in a strongly dispersive regime, i.e. under essentially the conditions \\[ b=d > \\frac29, \\quad a,c<-\\frac1{18}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00454","kind":"arxiv","version":2},"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":"1902.00454","created_at":"2026-05-17T23:47:58.235940+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.00454v2","created_at":"2026-05-17T23:47:58.235940+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00454","created_at":"2026-05-17T23:47:58.235940+00:00"},{"alias_kind":"pith_short_12","alias_value":"RXS7D6ZYJXDG","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"RXS7D6ZYJXDG54BO","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"RXS7D6ZY","created_at":"2026-05-18T12:33:27.125529+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/RXS7D6ZYJXDG54BOVDMAPDK6P7","json":"https://pith.science/pith/RXS7D6ZYJXDG54BOVDMAPDK6P7.json","graph_json":"https://pith.science/api/pith-number/RXS7D6ZYJXDG54BOVDMAPDK6P7/graph.json","events_json":"https://pith.science/api/pith-number/RXS7D6ZYJXDG54BOVDMAPDK6P7/events.json","paper":"https://pith.science/paper/RXS7D6ZY"},"agent_actions":{"view_html":"https://pith.science/pith/RXS7D6ZYJXDG54BOVDMAPDK6P7","download_json":"https://pith.science/pith/RXS7D6ZYJXDG54BOVDMAPDK6P7.json","view_paper":"https://pith.science/paper/RXS7D6ZY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.00454&json=true","fetch_graph":"https://pith.science/api/pith-number/RXS7D6ZYJXDG54BOVDMAPDK6P7/graph.json","fetch_events":"https://pith.science/api/pith-number/RXS7D6ZYJXDG54BOVDMAPDK6P7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RXS7D6ZYJXDG54BOVDMAPDK6P7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RXS7D6ZYJXDG54BOVDMAPDK6P7/action/storage_attestation","attest_author":"https://pith.science/pith/RXS7D6ZYJXDG54BOVDMAPDK6P7/action/author_attestation","sign_citation":"https://pith.science/pith/RXS7D6ZYJXDG54BOVDMAPDK6P7/action/citation_signature","submit_replication":"https://pith.science/pith/RXS7D6ZYJXDG54BOVDMAPDK6P7/action/replication_record"}},"created_at":"2026-05-17T23:47:58.235940+00:00","updated_at":"2026-05-17T23:47:58.235940+00:00"}