{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZPNA6LE2VJIXMAYMCZYJ3CMZ3M","short_pith_number":"pith:ZPNA6LE2","schema_version":"1.0","canonical_sha256":"cbda0f2c9aaa5176030c16709d8999db3b9e89631ddf395bcc91d73947214279","source":{"kind":"arxiv","id":"1710.08380","version":2},"attestation_state":"computed","paper":{"title":"The Cauchy problem for a family of two-dimensional fractional Benjamin-Ono equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eddye Bustamante, Jorge Mej\\'ia, Jos\\'e Jim\\'enez Urrea","submitted_at":"2017-10-23T16:54:02Z","abstract_excerpt":"In this work we prove that the initial value problem (IVP) associated to the fractional two-dimensional Benjamin-Ono equation $$\\left. \\begin{array}{rl} u_t+D_x^{\\alpha} u_x +\\mathcal Hu_{yy} +uu_x &=0,\\qquad\\qquad (x,y)\\in\\mathbb R^2,\\; t\\in\\mathbb R, u(x,y,0)&=u_0(x,y), \\end{array} \\right\\}\\,,$$ where $0<\\alpha\\leq1$, $D_x^{\\alpha}$ denotes the operator defined through the Fourier transform by \\begin{align} (D_x^{\\alpha}f)\\widehat{\\;}(\\xi,\\eta):=|\\xi|^{\\alpha}\\widehat{f}(\\xi,\\eta)\\,, \\end{align} and $\\mathcal H$ denotes the Hilbert transform with respect to the variable $x$, is locally well "},"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":"1710.08380","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-23T16:54:02Z","cross_cats_sorted":[],"title_canon_sha256":"614a69fb3d69528d385d5c949c7d4b9f7516fc9fc4e946c385276a0a3a1ef608","abstract_canon_sha256":"184d6c25b33f691b09b55522efda10841168c9823526f414d80c6e8f807d1f6c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:34.832587Z","signature_b64":"yATEns4EWxGIxNuRJViNWDbwPUdhJOqQIOQ/kGIr9WQ3AervxCzGPvDfeZoqGIbgCq5s6AK4UD2wH8EURujrDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbda0f2c9aaa5176030c16709d8999db3b9e89631ddf395bcc91d73947214279","last_reissued_at":"2026-05-18T00:28:34.831926Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:34.831926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Cauchy problem for a family of two-dimensional fractional Benjamin-Ono equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eddye Bustamante, Jorge Mej\\'ia, Jos\\'e Jim\\'enez Urrea","submitted_at":"2017-10-23T16:54:02Z","abstract_excerpt":"In this work we prove that the initial value problem (IVP) associated to the fractional two-dimensional Benjamin-Ono equation $$\\left. \\begin{array}{rl} u_t+D_x^{\\alpha} u_x +\\mathcal Hu_{yy} +uu_x &=0,\\qquad\\qquad (x,y)\\in\\mathbb R^2,\\; t\\in\\mathbb R, u(x,y,0)&=u_0(x,y), \\end{array} \\right\\}\\,,$$ where $0<\\alpha\\leq1$, $D_x^{\\alpha}$ denotes the operator defined through the Fourier transform by \\begin{align} (D_x^{\\alpha}f)\\widehat{\\;}(\\xi,\\eta):=|\\xi|^{\\alpha}\\widehat{f}(\\xi,\\eta)\\,, \\end{align} and $\\mathcal H$ denotes the Hilbert transform with respect to the variable $x$, is locally well "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08380","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":"1710.08380","created_at":"2026-05-18T00:28:34.832023+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.08380v2","created_at":"2026-05-18T00:28:34.832023+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.08380","created_at":"2026-05-18T00:28:34.832023+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZPNA6LE2VJIX","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZPNA6LE2VJIXMAYM","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZPNA6LE2","created_at":"2026-05-18T12:31:59.375834+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/ZPNA6LE2VJIXMAYMCZYJ3CMZ3M","json":"https://pith.science/pith/ZPNA6LE2VJIXMAYMCZYJ3CMZ3M.json","graph_json":"https://pith.science/api/pith-number/ZPNA6LE2VJIXMAYMCZYJ3CMZ3M/graph.json","events_json":"https://pith.science/api/pith-number/ZPNA6LE2VJIXMAYMCZYJ3CMZ3M/events.json","paper":"https://pith.science/paper/ZPNA6LE2"},"agent_actions":{"view_html":"https://pith.science/pith/ZPNA6LE2VJIXMAYMCZYJ3CMZ3M","download_json":"https://pith.science/pith/ZPNA6LE2VJIXMAYMCZYJ3CMZ3M.json","view_paper":"https://pith.science/paper/ZPNA6LE2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.08380&json=true","fetch_graph":"https://pith.science/api/pith-number/ZPNA6LE2VJIXMAYMCZYJ3CMZ3M/graph.json","fetch_events":"https://pith.science/api/pith-number/ZPNA6LE2VJIXMAYMCZYJ3CMZ3M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZPNA6LE2VJIXMAYMCZYJ3CMZ3M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZPNA6LE2VJIXMAYMCZYJ3CMZ3M/action/storage_attestation","attest_author":"https://pith.science/pith/ZPNA6LE2VJIXMAYMCZYJ3CMZ3M/action/author_attestation","sign_citation":"https://pith.science/pith/ZPNA6LE2VJIXMAYMCZYJ3CMZ3M/action/citation_signature","submit_replication":"https://pith.science/pith/ZPNA6LE2VJIXMAYMCZYJ3CMZ3M/action/replication_record"}},"created_at":"2026-05-18T00:28:34.832023+00:00","updated_at":"2026-05-18T00:28:34.832023+00:00"}