{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:EZ3XF2PP3PNUE5ANCAO2DRSVNJ","short_pith_number":"pith:EZ3XF2PP","schema_version":"1.0","canonical_sha256":"267772e9efdbdb42740d101da1c6556a5fc5605706a9959644b98fb8daa00f86","source":{"kind":"arxiv","id":"1206.3756","version":1},"attestation_state":"computed","paper":{"title":"On the Cauchy problem for a Boussinesq type system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Felipe Linares, Jorge Drumond Silva, Mahendra Panthee","submitted_at":"2012-06-17T13:44:42Z","abstract_excerpt":"We consider the initial value problem (IVP) associated to a Boussinesq type system. After rewriting the system in an equivalent form of coupled KdV-type equations, we prove that this is locally well-posed in $(H^s(\\R^2))^4$, $s>3/2$, using sharp smoothing estimates. Consequently we obtain the local well-posedness result for the original system in $H^s\\times \\mathcal{V}^{s+1}$ for $s>3/2$ (see below for the definition of $\\mathcal{V}^{s}$)."},"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":"1206.3756","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-17T13:44:42Z","cross_cats_sorted":[],"title_canon_sha256":"7a939706be9ad872cc8da0bb77bc4f17e79af6697aa4d3a8e6d72fdea982680c","abstract_canon_sha256":"1ebb022aeec3e990522d51640252dc5880b8ac97bfe3f32e7599afff4d5fc8b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:18.826875Z","signature_b64":"/Tmz7lxx5v5UujlGBipQttuQiCOKSWL8n532XigMlIEId4VoGaYWyKjQiw1mDW4N5gL+nFE2ADnYEJvHGpb0Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"267772e9efdbdb42740d101da1c6556a5fc5605706a9959644b98fb8daa00f86","last_reissued_at":"2026-05-18T03:53:18.826259Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:18.826259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Cauchy problem for a Boussinesq type system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Felipe Linares, Jorge Drumond Silva, Mahendra Panthee","submitted_at":"2012-06-17T13:44:42Z","abstract_excerpt":"We consider the initial value problem (IVP) associated to a Boussinesq type system. After rewriting the system in an equivalent form of coupled KdV-type equations, we prove that this is locally well-posed in $(H^s(\\R^2))^4$, $s>3/2$, using sharp smoothing estimates. Consequently we obtain the local well-posedness result for the original system in $H^s\\times \\mathcal{V}^{s+1}$ for $s>3/2$ (see below for the definition of $\\mathcal{V}^{s}$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3756","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1206.3756","created_at":"2026-05-18T03:53:18.826378+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.3756v1","created_at":"2026-05-18T03:53:18.826378+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3756","created_at":"2026-05-18T03:53:18.826378+00:00"},{"alias_kind":"pith_short_12","alias_value":"EZ3XF2PP3PNU","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"EZ3XF2PP3PNUE5AN","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"EZ3XF2PP","created_at":"2026-05-18T12:27:04.183437+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/EZ3XF2PP3PNUE5ANCAO2DRSVNJ","json":"https://pith.science/pith/EZ3XF2PP3PNUE5ANCAO2DRSVNJ.json","graph_json":"https://pith.science/api/pith-number/EZ3XF2PP3PNUE5ANCAO2DRSVNJ/graph.json","events_json":"https://pith.science/api/pith-number/EZ3XF2PP3PNUE5ANCAO2DRSVNJ/events.json","paper":"https://pith.science/paper/EZ3XF2PP"},"agent_actions":{"view_html":"https://pith.science/pith/EZ3XF2PP3PNUE5ANCAO2DRSVNJ","download_json":"https://pith.science/pith/EZ3XF2PP3PNUE5ANCAO2DRSVNJ.json","view_paper":"https://pith.science/paper/EZ3XF2PP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.3756&json=true","fetch_graph":"https://pith.science/api/pith-number/EZ3XF2PP3PNUE5ANCAO2DRSVNJ/graph.json","fetch_events":"https://pith.science/api/pith-number/EZ3XF2PP3PNUE5ANCAO2DRSVNJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EZ3XF2PP3PNUE5ANCAO2DRSVNJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EZ3XF2PP3PNUE5ANCAO2DRSVNJ/action/storage_attestation","attest_author":"https://pith.science/pith/EZ3XF2PP3PNUE5ANCAO2DRSVNJ/action/author_attestation","sign_citation":"https://pith.science/pith/EZ3XF2PP3PNUE5ANCAO2DRSVNJ/action/citation_signature","submit_replication":"https://pith.science/pith/EZ3XF2PP3PNUE5ANCAO2DRSVNJ/action/replication_record"}},"created_at":"2026-05-18T03:53:18.826378+00:00","updated_at":"2026-05-18T03:53:18.826378+00:00"}