{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:3NQIT5CSYRDGF3VI6NUCRH75B5","short_pith_number":"pith:3NQIT5CS","schema_version":"1.0","canonical_sha256":"db6089f452c44662eea8f368289ffd0f459efd13097e73aa0bb6031e08360faf","source":{"kind":"arxiv","id":"1903.05880","version":1},"attestation_state":"computed","paper":{"title":"Scattering for the quadratic nonlinear Schr\\\"{o}dinger system in $\\mathbb{R}^5$ without mass-resonance condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kuranosuke Nishimura, Masaru Hamano, Takahisa Inui","submitted_at":"2019-03-14T09:50:37Z","abstract_excerpt":"We consider the quadratic nonlinear Schr\\\"{o}dinger system (NLS system) \\begin{align*}\\begin{cases} i\\partial_t u + \\Delta u = v \\overline{u}, \\\\ i\\partial_t v+\\kappa \\Delta v = u^2, \\end{cases} \\text{ on } I \\times \\mathbb{R}^5, \\end{align*} where $\\kappa>0$. The scattering below the standing wave solutions for NLS system was obtained by the first author when $\\kappa = 1/2$. The condition of $\\kappa=1/2$ is called mass-resonance. In this paper, we prove scattering below the standing wave solutions when $\\kappa \\neq 1/2$ under the radially symmetric assumption. Our proof is based on the concen"},"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":"1903.05880","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-14T09:50:37Z","cross_cats_sorted":[],"title_canon_sha256":"2d219190a873ee4ee413cd3ae2572fd5ab68ae646a673e5091d75bb1a78dab8a","abstract_canon_sha256":"1561b1512cf4cc146602098d88d71ba2621daebb89b390ffcd824af60b197acb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:15.226952Z","signature_b64":"rDgyfKsWtmzXqlIHiyAE3qMyoFCmTOxi0Hnn7snaWecgCDd+AfSa0sFxPcJlHKRriHFNsa7iGV5xR9B9hbQTBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db6089f452c44662eea8f368289ffd0f459efd13097e73aa0bb6031e08360faf","last_reissued_at":"2026-05-17T23:51:15.226457Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:15.226457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scattering for the quadratic nonlinear Schr\\\"{o}dinger system in $\\mathbb{R}^5$ without mass-resonance condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kuranosuke Nishimura, Masaru Hamano, Takahisa Inui","submitted_at":"2019-03-14T09:50:37Z","abstract_excerpt":"We consider the quadratic nonlinear Schr\\\"{o}dinger system (NLS system) \\begin{align*}\\begin{cases} i\\partial_t u + \\Delta u = v \\overline{u}, \\\\ i\\partial_t v+\\kappa \\Delta v = u^2, \\end{cases} \\text{ on } I \\times \\mathbb{R}^5, \\end{align*} where $\\kappa>0$. The scattering below the standing wave solutions for NLS system was obtained by the first author when $\\kappa = 1/2$. The condition of $\\kappa=1/2$ is called mass-resonance. In this paper, we prove scattering below the standing wave solutions when $\\kappa \\neq 1/2$ under the radially symmetric assumption. Our proof is based on the concen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05880","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":"1903.05880","created_at":"2026-05-17T23:51:15.226530+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.05880v1","created_at":"2026-05-17T23:51:15.226530+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.05880","created_at":"2026-05-17T23:51:15.226530+00:00"},{"alias_kind":"pith_short_12","alias_value":"3NQIT5CSYRDG","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"3NQIT5CSYRDGF3VI","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"3NQIT5CS","created_at":"2026-05-18T12:33:07.085635+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/3NQIT5CSYRDGF3VI6NUCRH75B5","json":"https://pith.science/pith/3NQIT5CSYRDGF3VI6NUCRH75B5.json","graph_json":"https://pith.science/api/pith-number/3NQIT5CSYRDGF3VI6NUCRH75B5/graph.json","events_json":"https://pith.science/api/pith-number/3NQIT5CSYRDGF3VI6NUCRH75B5/events.json","paper":"https://pith.science/paper/3NQIT5CS"},"agent_actions":{"view_html":"https://pith.science/pith/3NQIT5CSYRDGF3VI6NUCRH75B5","download_json":"https://pith.science/pith/3NQIT5CSYRDGF3VI6NUCRH75B5.json","view_paper":"https://pith.science/paper/3NQIT5CS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.05880&json=true","fetch_graph":"https://pith.science/api/pith-number/3NQIT5CSYRDGF3VI6NUCRH75B5/graph.json","fetch_events":"https://pith.science/api/pith-number/3NQIT5CSYRDGF3VI6NUCRH75B5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3NQIT5CSYRDGF3VI6NUCRH75B5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3NQIT5CSYRDGF3VI6NUCRH75B5/action/storage_attestation","attest_author":"https://pith.science/pith/3NQIT5CSYRDGF3VI6NUCRH75B5/action/author_attestation","sign_citation":"https://pith.science/pith/3NQIT5CSYRDGF3VI6NUCRH75B5/action/citation_signature","submit_replication":"https://pith.science/pith/3NQIT5CSYRDGF3VI6NUCRH75B5/action/replication_record"}},"created_at":"2026-05-17T23:51:15.226530+00:00","updated_at":"2026-05-17T23:51:15.226530+00:00"}