{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:PPTXI3USY5LSFSMOWNBWGKQG3C","short_pith_number":"pith:PPTXI3US","schema_version":"1.0","canonical_sha256":"7be7746e92c75722c98eb343632a06d8aedd2b871aea51305379655c81538cb4","source":{"kind":"arxiv","id":"1508.06814","version":1},"attestation_state":"computed","paper":{"title":"The cubic szego equation and hankel operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Patrick Gerard (LM-Orsay), Sandrine Grellier (MAPMO)","submitted_at":"2015-08-27T11:43:06Z","abstract_excerpt":"This monograph  is an expanded version of the preprint arXiv:1402.1716 or hal-00943396v1.It is devoted to the dynamics on Sobolev spaces of the cubic Szeg{\\\"o} equation on the circle ${\\mathbb S} ^1$,$$ i\\partial \\_t u=\\Pi (\\vert u\\vert ^2u)\\ .$$Here $\\Pi $ denotes the orthogonal projector from $L^2({\\mathbb S} ^1)$ onto the subspace $L^2\\_+({\\mathbb S} ^1)$ of functions with nonnegative Fourier modes.We  construct a nonlinear Fourier transformation on $H^{1/2}({\\mathbb S} ^1)\\cap L^2\\_+({\\mathbb S} ^1)$ allowing to describe explicitly the solutions of this equationwith data in $H^{1/2}({\\math"},"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":"1508.06814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-27T11:43:06Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"0b1239e4e627314947e12aebd1193258257ad7323a2618ab037a4e43f0c1d38c","abstract_canon_sha256":"9e7142b4f28b0d0d42035abea551d115fcd72c97879d2f72565ee753edd5d516"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:40.947939Z","signature_b64":"jBGkVbiwq2ALRAu+LcPOR21bz12k8FXKQaxuQEZyIYNX3Lr1rRXOrvP9qPjazyz71Yhjy/zUu9Hg8zWjoAd0Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7be7746e92c75722c98eb343632a06d8aedd2b871aea51305379655c81538cb4","last_reissued_at":"2026-05-18T01:34:40.947430Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:40.947430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The cubic szego equation and hankel operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Patrick Gerard (LM-Orsay), Sandrine Grellier (MAPMO)","submitted_at":"2015-08-27T11:43:06Z","abstract_excerpt":"This monograph  is an expanded version of the preprint arXiv:1402.1716 or hal-00943396v1.It is devoted to the dynamics on Sobolev spaces of the cubic Szeg{\\\"o} equation on the circle ${\\mathbb S} ^1$,$$ i\\partial \\_t u=\\Pi (\\vert u\\vert ^2u)\\ .$$Here $\\Pi $ denotes the orthogonal projector from $L^2({\\mathbb S} ^1)$ onto the subspace $L^2\\_+({\\mathbb S} ^1)$ of functions with nonnegative Fourier modes.We  construct a nonlinear Fourier transformation on $H^{1/2}({\\mathbb S} ^1)\\cap L^2\\_+({\\mathbb S} ^1)$ allowing to describe explicitly the solutions of this equationwith data in $H^{1/2}({\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06814","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":"1508.06814","created_at":"2026-05-18T01:34:40.947509+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.06814v1","created_at":"2026-05-18T01:34:40.947509+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06814","created_at":"2026-05-18T01:34:40.947509+00:00"},{"alias_kind":"pith_short_12","alias_value":"PPTXI3USY5LS","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"PPTXI3USY5LSFSMO","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"PPTXI3US","created_at":"2026-05-18T12:29:37.295048+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2511.03373","citing_title":"A superintegrable quantum field theory","ref_index":4,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PPTXI3USY5LSFSMOWNBWGKQG3C","json":"https://pith.science/pith/PPTXI3USY5LSFSMOWNBWGKQG3C.json","graph_json":"https://pith.science/api/pith-number/PPTXI3USY5LSFSMOWNBWGKQG3C/graph.json","events_json":"https://pith.science/api/pith-number/PPTXI3USY5LSFSMOWNBWGKQG3C/events.json","paper":"https://pith.science/paper/PPTXI3US"},"agent_actions":{"view_html":"https://pith.science/pith/PPTXI3USY5LSFSMOWNBWGKQG3C","download_json":"https://pith.science/pith/PPTXI3USY5LSFSMOWNBWGKQG3C.json","view_paper":"https://pith.science/paper/PPTXI3US","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.06814&json=true","fetch_graph":"https://pith.science/api/pith-number/PPTXI3USY5LSFSMOWNBWGKQG3C/graph.json","fetch_events":"https://pith.science/api/pith-number/PPTXI3USY5LSFSMOWNBWGKQG3C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PPTXI3USY5LSFSMOWNBWGKQG3C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PPTXI3USY5LSFSMOWNBWGKQG3C/action/storage_attestation","attest_author":"https://pith.science/pith/PPTXI3USY5LSFSMOWNBWGKQG3C/action/author_attestation","sign_citation":"https://pith.science/pith/PPTXI3USY5LSFSMOWNBWGKQG3C/action/citation_signature","submit_replication":"https://pith.science/pith/PPTXI3USY5LSFSMOWNBWGKQG3C/action/replication_record"}},"created_at":"2026-05-18T01:34:40.947509+00:00","updated_at":"2026-05-18T01:34:40.947509+00:00"}