{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:EOOLLOCT7B5VYGCQ7O4VD7WQLR","short_pith_number":"pith:EOOLLOCT","schema_version":"1.0","canonical_sha256":"239cb5b853f87b5c1850fbb951fed05c4297ecfc44aa098b3bc437b60beb28ee","source":{"kind":"arxiv","id":"2606.01778","version":1},"attestation_state":"computed","paper":{"title":"Long Time Well-posedness for the Benjamin-Ono Equation with Quasi-Periodic Initial Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yubo Wang","submitted_at":"2026-06-01T06:59:21Z","abstract_excerpt":"This paper investigates the long time well-posedness of the Benjamin-Ono (BO) equation with quasi-periodic initial data in analytic space. We demonstrate that the Lax operator of the BO equation exhibits a trivial spectrum, and elucidate the fundamental mathematical obstacles to establishing global well-posedness.\n  Furthermore, by employing Tao's gauge transformation in conjunction with the Birkhoff Normal Form method, we extend the lifespan of the solutions to $O(\\epsilon^{-3})$."},"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":"2606.01778","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-01T06:59:21Z","cross_cats_sorted":[],"title_canon_sha256":"64cd61a935b492d8773bf8f04851424436bb11b570443b89813e80ba9b897f47","abstract_canon_sha256":"bf9ead65b3118cd2b6f8238c77ca7317753b119359f5eacc6519bb31d1d7f7ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:56.466469Z","signature_b64":"LI/YIDyuJOGcLJDYhd+EbMioPgILWZg4AlkTBGiJYkmCJcnPrWNduEJX4m+d6B9t8L39n3+8zoWlTaK7oKdLAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"239cb5b853f87b5c1850fbb951fed05c4297ecfc44aa098b3bc437b60beb28ee","last_reissued_at":"2026-06-02T02:04:56.466091Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:56.466091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Long Time Well-posedness for the Benjamin-Ono Equation with Quasi-Periodic Initial Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yubo Wang","submitted_at":"2026-06-01T06:59:21Z","abstract_excerpt":"This paper investigates the long time well-posedness of the Benjamin-Ono (BO) equation with quasi-periodic initial data in analytic space. We demonstrate that the Lax operator of the BO equation exhibits a trivial spectrum, and elucidate the fundamental mathematical obstacles to establishing global well-posedness.\n  Furthermore, by employing Tao's gauge transformation in conjunction with the Birkhoff Normal Form method, we extend the lifespan of the solutions to $O(\\epsilon^{-3})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01778","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.01778/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.01778","created_at":"2026-06-02T02:04:56.466154+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.01778v1","created_at":"2026-06-02T02:04:56.466154+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01778","created_at":"2026-06-02T02:04:56.466154+00:00"},{"alias_kind":"pith_short_12","alias_value":"EOOLLOCT7B5V","created_at":"2026-06-02T02:04:56.466154+00:00"},{"alias_kind":"pith_short_16","alias_value":"EOOLLOCT7B5VYGCQ","created_at":"2026-06-02T02:04:56.466154+00:00"},{"alias_kind":"pith_short_8","alias_value":"EOOLLOCT","created_at":"2026-06-02T02:04:56.466154+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/EOOLLOCT7B5VYGCQ7O4VD7WQLR","json":"https://pith.science/pith/EOOLLOCT7B5VYGCQ7O4VD7WQLR.json","graph_json":"https://pith.science/api/pith-number/EOOLLOCT7B5VYGCQ7O4VD7WQLR/graph.json","events_json":"https://pith.science/api/pith-number/EOOLLOCT7B5VYGCQ7O4VD7WQLR/events.json","paper":"https://pith.science/paper/EOOLLOCT"},"agent_actions":{"view_html":"https://pith.science/pith/EOOLLOCT7B5VYGCQ7O4VD7WQLR","download_json":"https://pith.science/pith/EOOLLOCT7B5VYGCQ7O4VD7WQLR.json","view_paper":"https://pith.science/paper/EOOLLOCT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.01778&json=true","fetch_graph":"https://pith.science/api/pith-number/EOOLLOCT7B5VYGCQ7O4VD7WQLR/graph.json","fetch_events":"https://pith.science/api/pith-number/EOOLLOCT7B5VYGCQ7O4VD7WQLR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EOOLLOCT7B5VYGCQ7O4VD7WQLR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EOOLLOCT7B5VYGCQ7O4VD7WQLR/action/storage_attestation","attest_author":"https://pith.science/pith/EOOLLOCT7B5VYGCQ7O4VD7WQLR/action/author_attestation","sign_citation":"https://pith.science/pith/EOOLLOCT7B5VYGCQ7O4VD7WQLR/action/citation_signature","submit_replication":"https://pith.science/pith/EOOLLOCT7B5VYGCQ7O4VD7WQLR/action/replication_record"}},"created_at":"2026-06-02T02:04:56.466154+00:00","updated_at":"2026-06-02T02:04:56.466154+00:00"}