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This is a mass-critical NLS-type equation with a Lax pair structure. The Cauchy problem is global well-posed in the class of Hardy-Sobolev spaces $H^s_+(\\mathbb{T})=L^2_+(\\mathbb{T}) \\cap H^s(\\mathbb{T})$ for small $L^2$-mass $\\| u_0 \\|_{L^2}^2 < 1$ as recently proven"},"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":"2605.28789","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-27T17:48:11Z","cross_cats_sorted":[],"title_canon_sha256":"145b76bb4d029a3aab909d259611e90de6cffb9fc76049aecf9cdf0cc6c27b3d","abstract_canon_sha256":"611a39ffa37671a52284d73796325a7136d8fb3adea88e644a78d6cc70781f10"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T02:05:03.651488Z","signature_b64":"kjrZFbup9qr6EolZ/hizZxsjt30mUkRnmDPkHY3Uxujm6WMVyxGC+w6la7VSLNSElNxQzDW94lDpyZeUujNJCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86919dc0e09e6ff238353c1ecb35b0121ada40a924455e2ef06a2812646ef2c4","last_reissued_at":"2026-05-28T02:05:03.651069Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T02:05:03.651069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite-time blow-up solutions for the Calogero--Sutherland derivative NLS","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enno Lenzmann, Xi Chen","submitted_at":"2026-05-27T17:48:11Z","abstract_excerpt":"We construct an explicit family of smooth finite-time blow-up solutions for the focusing Calogero--Sutherland derivative NLS given by $$ i \\partial_t u = -\\partial_x^2 u - 2 D \\Pi(|u|^2) u \\quad \\mbox{with} \\quad (t,x) \\in \\mathbb{R} \\times \\mathbb{T} , $$ where $D=-i \\partial_x$ and $\\Pi$ denotes the Cauchy--Szeg\\H{o} projector. This is a mass-critical NLS-type equation with a Lax pair structure. The Cauchy problem is global well-posed in the class of Hardy-Sobolev spaces $H^s_+(\\mathbb{T})=L^2_+(\\mathbb{T}) \\cap H^s(\\mathbb{T})$ for small $L^2$-mass $\\| u_0 \\|_{L^2}^2 < 1$ as recently proven"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28789","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/2605.28789/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":"2605.28789","created_at":"2026-05-28T02:05:03.651133+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.28789v1","created_at":"2026-05-28T02:05:03.651133+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.28789","created_at":"2026-05-28T02:05:03.651133+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q2IZ3QHATZX7","created_at":"2026-05-28T02:05:03.651133+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q2IZ3QHATZX7EOBV","created_at":"2026-05-28T02:05:03.651133+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q2IZ3QHA","created_at":"2026-05-28T02:05:03.651133+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/Q2IZ3QHATZX7EOBVHQPMWNNQCI","json":"https://pith.science/pith/Q2IZ3QHATZX7EOBVHQPMWNNQCI.json","graph_json":"https://pith.science/api/pith-number/Q2IZ3QHATZX7EOBVHQPMWNNQCI/graph.json","events_json":"https://pith.science/api/pith-number/Q2IZ3QHATZX7EOBVHQPMWNNQCI/events.json","paper":"https://pith.science/paper/Q2IZ3QHA"},"agent_actions":{"view_html":"https://pith.science/pith/Q2IZ3QHATZX7EOBVHQPMWNNQCI","download_json":"https://pith.science/pith/Q2IZ3QHATZX7EOBVHQPMWNNQCI.json","view_paper":"https://pith.science/paper/Q2IZ3QHA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.28789&json=true","fetch_graph":"https://pith.science/api/pith-number/Q2IZ3QHATZX7EOBVHQPMWNNQCI/graph.json","fetch_events":"https://pith.science/api/pith-number/Q2IZ3QHATZX7EOBVHQPMWNNQCI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q2IZ3QHATZX7EOBVHQPMWNNQCI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q2IZ3QHATZX7EOBVHQPMWNNQCI/action/storage_attestation","attest_author":"https://pith.science/pith/Q2IZ3QHATZX7EOBVHQPMWNNQCI/action/author_attestation","sign_citation":"https://pith.science/pith/Q2IZ3QHATZX7EOBVHQPMWNNQCI/action/citation_signature","submit_replication":"https://pith.science/pith/Q2IZ3QHATZX7EOBVHQPMWNNQCI/action/replication_record"}},"created_at":"2026-05-28T02:05:03.651133+00:00","updated_at":"2026-05-28T02:05:03.651133+00:00"}