{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:VTKQGEFMBPKCMQTFJS4GZUCYSX","short_pith_number":"pith:VTKQGEFM","schema_version":"1.0","canonical_sha256":"acd50310ac0bd42642654cb86cd05895dd4018ccc09749c21e8044203bac79c1","source":{"kind":"arxiv","id":"1809.01527","version":1},"attestation_state":"computed","paper":{"title":"On scattering for the defocusing quintic nonlinear Schr\\\"odinger equation on the two-dimensional cylinder","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Xing Cheng, Zehua Zhao, Zihua Guo","submitted_at":"2018-09-05T14:07:56Z","abstract_excerpt":"In this article, we prove the scattering for the quintic defocusing nonlinear Schr\\\"odinger equation on cylinder $\\mathbb{R} \\times \\mathbb{T}$ in $H^1$. We establish an abstract linear profile decomposition in $L^2_x h^\\alpha$, $0 < \\alpha \\le 1$, motivated by the linear profile decomposition of the mass-critical Schr\\\"odinger equation in $L^2(\\mathbb{R}^d )$, $d\\ge 1$. Then by using the solution of the one-discrete-component quintic resonant nonlinear Schr\\\"odinger system, whose scattering can be proved by using the techniques in $1d$ mass critical NLS problem by B. Dodson, to approximate th"},"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":"1809.01527","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-05T14:07:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"52d255b73c8fa3af449847d66e5aeeae67c6560cc6ba3789242d7791d221f6c1","abstract_canon_sha256":"5a607867c2b5ff6a10f3ab94e03615691e9e42b4cc8253379c93d705d8fa875e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:27.327671Z","signature_b64":"jO8qw5dsAY75LpVRAJhU310Xoixb38IrDZ2cHqOn2VPM95/hhrHUe2cyvC/aynJfzeQR7/PBu/HiC+3YHyXZBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"acd50310ac0bd42642654cb86cd05895dd4018ccc09749c21e8044203bac79c1","last_reissued_at":"2026-05-18T00:06:27.327143Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:27.327143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On scattering for the defocusing quintic nonlinear Schr\\\"odinger equation on the two-dimensional cylinder","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Xing Cheng, Zehua Zhao, Zihua Guo","submitted_at":"2018-09-05T14:07:56Z","abstract_excerpt":"In this article, we prove the scattering for the quintic defocusing nonlinear Schr\\\"odinger equation on cylinder $\\mathbb{R} \\times \\mathbb{T}$ in $H^1$. We establish an abstract linear profile decomposition in $L^2_x h^\\alpha$, $0 < \\alpha \\le 1$, motivated by the linear profile decomposition of the mass-critical Schr\\\"odinger equation in $L^2(\\mathbb{R}^d )$, $d\\ge 1$. Then by using the solution of the one-discrete-component quintic resonant nonlinear Schr\\\"odinger system, whose scattering can be proved by using the techniques in $1d$ mass critical NLS problem by B. Dodson, to approximate th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01527","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":"1809.01527","created_at":"2026-05-18T00:06:27.327234+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.01527v1","created_at":"2026-05-18T00:06:27.327234+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.01527","created_at":"2026-05-18T00:06:27.327234+00:00"},{"alias_kind":"pith_short_12","alias_value":"VTKQGEFMBPKC","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"VTKQGEFMBPKCMQTF","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"VTKQGEFM","created_at":"2026-05-18T12:32:59.047623+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/VTKQGEFMBPKCMQTFJS4GZUCYSX","json":"https://pith.science/pith/VTKQGEFMBPKCMQTFJS4GZUCYSX.json","graph_json":"https://pith.science/api/pith-number/VTKQGEFMBPKCMQTFJS4GZUCYSX/graph.json","events_json":"https://pith.science/api/pith-number/VTKQGEFMBPKCMQTFJS4GZUCYSX/events.json","paper":"https://pith.science/paper/VTKQGEFM"},"agent_actions":{"view_html":"https://pith.science/pith/VTKQGEFMBPKCMQTFJS4GZUCYSX","download_json":"https://pith.science/pith/VTKQGEFMBPKCMQTFJS4GZUCYSX.json","view_paper":"https://pith.science/paper/VTKQGEFM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.01527&json=true","fetch_graph":"https://pith.science/api/pith-number/VTKQGEFMBPKCMQTFJS4GZUCYSX/graph.json","fetch_events":"https://pith.science/api/pith-number/VTKQGEFMBPKCMQTFJS4GZUCYSX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VTKQGEFMBPKCMQTFJS4GZUCYSX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VTKQGEFMBPKCMQTFJS4GZUCYSX/action/storage_attestation","attest_author":"https://pith.science/pith/VTKQGEFMBPKCMQTFJS4GZUCYSX/action/author_attestation","sign_citation":"https://pith.science/pith/VTKQGEFMBPKCMQTFJS4GZUCYSX/action/citation_signature","submit_replication":"https://pith.science/pith/VTKQGEFMBPKCMQTFJS4GZUCYSX/action/replication_record"}},"created_at":"2026-05-18T00:06:27.327234+00:00","updated_at":"2026-05-18T00:06:27.327234+00:00"}