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We show that for any initial data $(u_0,v_0)$ in $H^1(\\mathbb{R}^3)\\times H^1(\\mathbb{R}^3)$ satisfying $M(u_0,v_0)A(u_0,v_0)<M(P,Q)A(P,Q)$ and $M(u_0,v_0)E(u_0,v_0)<M(P,Q)E(P,Q)$, where $M(u,v)$ and $E(u,v)$ are the mass and energy (invariant quantities) associated to the system, the correspondi"},"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":"1603.05723","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-17T23:02:06Z","cross_cats_sorted":[],"title_canon_sha256":"69725efb0d9c60b5b3676146dc77dbef8e40a4ac736634adcb45dc2f06ce7d42","abstract_canon_sha256":"6edc0b02f2648dd516f2c40acd30d6d2ed7393e6fcadc4a47a2f4b417eb915f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:53.680112Z","signature_b64":"/dsBDe9VDCME5CxRpz8DE4oXvBcHywCQJNWpIuakOCPnINaftr8WPBRcrb8ZY0dYnj+LNoKtml0hT/ttYDtoAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e526d6c82c7204f31ffe51adac4f7a750c8a792f0d8b3dfaae415ed470988752","last_reissued_at":"2026-05-18T01:18:53.679607Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:53.679607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scattering for a 3D coupled nonlinear Schr\\\"odinger system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ademir Pastor, Luiz Gustavo Farah","submitted_at":"2016-03-17T23:02:06Z","abstract_excerpt":"We consider the three-dimensional cubic nonlinear Schr\\\"odinger system\n  \\begin{equation*} \\begin{cases} i\\partial_tu+\\Delta u+(|u|^2+\\beta |v|^2)u=0,\\\\ i\\partial_tv+\\Delta v+(|v|^2+\\beta |u|^2)v=0. \\end{cases} \\end{equation*} Let $(P,Q)$ be any ground state solution of the above Schr\\\"odinger system. We show that for any initial data $(u_0,v_0)$ in $H^1(\\mathbb{R}^3)\\times H^1(\\mathbb{R}^3)$ satisfying $M(u_0,v_0)A(u_0,v_0)<M(P,Q)A(P,Q)$ and $M(u_0,v_0)E(u_0,v_0)<M(P,Q)E(P,Q)$, where $M(u,v)$ and $E(u,v)$ are the mass and energy (invariant quantities) associated to the system, the correspondi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05723","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":"1603.05723","created_at":"2026-05-18T01:18:53.679687+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.05723v1","created_at":"2026-05-18T01:18:53.679687+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05723","created_at":"2026-05-18T01:18:53.679687+00:00"},{"alias_kind":"pith_short_12","alias_value":"4UTNNSBMOICP","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4UTNNSBMOICPGH76","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4UTNNSBM","created_at":"2026-05-18T12:29:58.707656+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/4UTNNSBMOICPGH76KGW2YT32OU","json":"https://pith.science/pith/4UTNNSBMOICPGH76KGW2YT32OU.json","graph_json":"https://pith.science/api/pith-number/4UTNNSBMOICPGH76KGW2YT32OU/graph.json","events_json":"https://pith.science/api/pith-number/4UTNNSBMOICPGH76KGW2YT32OU/events.json","paper":"https://pith.science/paper/4UTNNSBM"},"agent_actions":{"view_html":"https://pith.science/pith/4UTNNSBMOICPGH76KGW2YT32OU","download_json":"https://pith.science/pith/4UTNNSBMOICPGH76KGW2YT32OU.json","view_paper":"https://pith.science/paper/4UTNNSBM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.05723&json=true","fetch_graph":"https://pith.science/api/pith-number/4UTNNSBMOICPGH76KGW2YT32OU/graph.json","fetch_events":"https://pith.science/api/pith-number/4UTNNSBMOICPGH76KGW2YT32OU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4UTNNSBMOICPGH76KGW2YT32OU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4UTNNSBMOICPGH76KGW2YT32OU/action/storage_attestation","attest_author":"https://pith.science/pith/4UTNNSBMOICPGH76KGW2YT32OU/action/author_attestation","sign_citation":"https://pith.science/pith/4UTNNSBMOICPGH76KGW2YT32OU/action/citation_signature","submit_replication":"https://pith.science/pith/4UTNNSBMOICPGH76KGW2YT32OU/action/replication_record"}},"created_at":"2026-05-18T01:18:53.679687+00:00","updated_at":"2026-05-18T01:18:53.679687+00:00"}