{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LXFVY2STXK3KRCSSBDWR6YNQB6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d30b2adbe61eb1448aaa1368d0861beee0dd07f8c6cf108ea0202a22e25125b6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-17T16:27:25Z","title_canon_sha256":"8fc060ad90e7ef2c718227a3b568fbdbf9ed3ca3f3d48c89cab3d3a54ebd3e38"},"schema_version":"1.0","source":{"id":"2606.19250","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.19250","created_at":"2026-06-19T16:12:08Z"},{"alias_kind":"arxiv_version","alias_value":"2606.19250v1","created_at":"2026-06-19T16:12:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19250","created_at":"2026-06-19T16:12:08Z"},{"alias_kind":"pith_short_12","alias_value":"LXFVY2STXK3K","created_at":"2026-06-19T16:12:08Z"},{"alias_kind":"pith_short_16","alias_value":"LXFVY2STXK3KRCSS","created_at":"2026-06-19T16:12:08Z"},{"alias_kind":"pith_short_8","alias_value":"LXFVY2ST","created_at":"2026-06-19T16:12:08Z"}],"graph_snapshots":[{"event_id":"sha256:652f071ea6db3e5708be37a0087ea1597f41cc39eafe8c2b1fb68cf299340ff8","target":"graph","created_at":"2026-06-19T16:12:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.19250/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the well-posedness problem for the extended Schr\\\"{o}dinger-Benjamin-Ono system (eSBO) on the real line. This system couples a Schr\\\"{o}dinger field $u$ with a Benjamin-Ono type field $v$, including a term of the form $\\partial_{x}(v^2)$. This latter term, just as in the case of the Benjamin-Ono equation, causes the system to become quasilinear and unsolvable via Picard iteration. We prove that eSBO is locally well-posed in $H^{s+\\frac 12}(\\mathbb{R})\\times H^{s}(\\mathbb{R})$ for any $s\\geq 0$. In particular, this result covers the energy space at $s=\\frac 12$, yielding global well-po","authors_text":"Justin Forlano, Puti Dai","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-17T16:27:25Z","title":"Local and global well-posedness for the extended Schr\\\"{o}dinger-Benjamin-Ono system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19250","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:11aff6fff7f6aadd716f48c2061a21755f1bfa6e694007e681665dd86d4958c6","target":"record","created_at":"2026-06-19T16:12:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d30b2adbe61eb1448aaa1368d0861beee0dd07f8c6cf108ea0202a22e25125b6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-17T16:27:25Z","title_canon_sha256":"8fc060ad90e7ef2c718227a3b568fbdbf9ed3ca3f3d48c89cab3d3a54ebd3e38"},"schema_version":"1.0","source":{"id":"2606.19250","kind":"arxiv","version":1}},"canonical_sha256":"5dcb5c6a53bab6a88a5208ed1f61b00f9890f20d8aae72412468c192fd3402f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5dcb5c6a53bab6a88a5208ed1f61b00f9890f20d8aae72412468c192fd3402f4","first_computed_at":"2026-06-19T16:12:08.791052Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:08.791052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BSJVNPyBxhfY1LxV1h4+6Nyt96ZHk8tXmInn4+ge91VKa3hw/VZtIxzitBgCQTwEKK57qnpuAQVydGq333czDA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:08.791473Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.19250","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11aff6fff7f6aadd716f48c2061a21755f1bfa6e694007e681665dd86d4958c6","sha256:652f071ea6db3e5708be37a0087ea1597f41cc39eafe8c2b1fb68cf299340ff8"],"state_sha256":"a96feb8ea6f749c0dc949d3dc809f6d8501215e36d790bfbae23f2b094980d10"}