{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:F5XR22S3DYICOWCJIDQGLFAM7H","short_pith_number":"pith:F5XR22S3","schema_version":"1.0","canonical_sha256":"2f6f1d6a5b1e1027584940e065940cf9cff35d28d9c60d9105726d8615320474","source":{"kind":"arxiv","id":"1605.01837","version":1},"attestation_state":"computed","paper":{"title":"Construction of a minimal mass blow up solution of the modified Benjamin-Ono equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Didier Pilod, Yvan Martel","submitted_at":"2016-05-06T06:43:59Z","abstract_excerpt":"We construct a minimal mass blow up solution of the modified Benjamin-Ono equation (mBO) \\[ u_{t}+(u^3-D^1 u)_{x}=0, \\] which is a standard mass critical dispersive model. Let $Q\\in H^{\\frac 12}$, $Q>0$, be the unique ground state solution of $D^1 Q +Q=Q^3$, constructed using variational arguments by Weinstein (Comm. PDE, 12 (1987), J. Diff. Eq., 69 (1987)) and Albert, Bona and Saut (Proc. Royal London Soc., 453 (1997)), and whose uniqueness was recently proved by Frank and Lenzmann (Acta Math., 210 (2013)).\n  We show the existence of a solution $S$ of (mBO) satisfying $\\|S \\|_{L^2}=\\|Q\\|_{L^2"},"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":"1605.01837","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-06T06:43:59Z","cross_cats_sorted":[],"title_canon_sha256":"69e0c2c8a01939516a0ccdcd678b5b98c6e80761cf1c333fde985d016a5fc322","abstract_canon_sha256":"ad58956e646558376c1357452eb7145e0a95b701a5de2681256dba212a949946"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:31.203466Z","signature_b64":"9dqtDHVFsww6CgMIeqgKfuFEcNHaIKagr9cgd3J6OVm5C4yJFXTXwcp0u3hW8qiAfEBWazku0tcz4PBckrXkCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f6f1d6a5b1e1027584940e065940cf9cff35d28d9c60d9105726d8615320474","last_reissued_at":"2026-05-18T01:15:31.202846Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:31.202846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Construction of a minimal mass blow up solution of the modified Benjamin-Ono equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Didier Pilod, Yvan Martel","submitted_at":"2016-05-06T06:43:59Z","abstract_excerpt":"We construct a minimal mass blow up solution of the modified Benjamin-Ono equation (mBO) \\[ u_{t}+(u^3-D^1 u)_{x}=0, \\] which is a standard mass critical dispersive model. Let $Q\\in H^{\\frac 12}$, $Q>0$, be the unique ground state solution of $D^1 Q +Q=Q^3$, constructed using variational arguments by Weinstein (Comm. PDE, 12 (1987), J. Diff. Eq., 69 (1987)) and Albert, Bona and Saut (Proc. Royal London Soc., 453 (1997)), and whose uniqueness was recently proved by Frank and Lenzmann (Acta Math., 210 (2013)).\n  We show the existence of a solution $S$ of (mBO) satisfying $\\|S \\|_{L^2}=\\|Q\\|_{L^2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01837","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":"1605.01837","created_at":"2026-05-18T01:15:31.202919+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.01837v1","created_at":"2026-05-18T01:15:31.202919+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01837","created_at":"2026-05-18T01:15:31.202919+00:00"},{"alias_kind":"pith_short_12","alias_value":"F5XR22S3DYIC","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"F5XR22S3DYICOWCJ","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"F5XR22S3","created_at":"2026-05-18T12:30:15.759754+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/F5XR22S3DYICOWCJIDQGLFAM7H","json":"https://pith.science/pith/F5XR22S3DYICOWCJIDQGLFAM7H.json","graph_json":"https://pith.science/api/pith-number/F5XR22S3DYICOWCJIDQGLFAM7H/graph.json","events_json":"https://pith.science/api/pith-number/F5XR22S3DYICOWCJIDQGLFAM7H/events.json","paper":"https://pith.science/paper/F5XR22S3"},"agent_actions":{"view_html":"https://pith.science/pith/F5XR22S3DYICOWCJIDQGLFAM7H","download_json":"https://pith.science/pith/F5XR22S3DYICOWCJIDQGLFAM7H.json","view_paper":"https://pith.science/paper/F5XR22S3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.01837&json=true","fetch_graph":"https://pith.science/api/pith-number/F5XR22S3DYICOWCJIDQGLFAM7H/graph.json","fetch_events":"https://pith.science/api/pith-number/F5XR22S3DYICOWCJIDQGLFAM7H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F5XR22S3DYICOWCJIDQGLFAM7H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F5XR22S3DYICOWCJIDQGLFAM7H/action/storage_attestation","attest_author":"https://pith.science/pith/F5XR22S3DYICOWCJIDQGLFAM7H/action/author_attestation","sign_citation":"https://pith.science/pith/F5XR22S3DYICOWCJIDQGLFAM7H/action/citation_signature","submit_replication":"https://pith.science/pith/F5XR22S3DYICOWCJIDQGLFAM7H/action/replication_record"}},"created_at":"2026-05-18T01:15:31.202919+00:00","updated_at":"2026-05-18T01:15:31.202919+00:00"}