{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:IRC22VZOJZG7O5YNDGHT3QRDXL","short_pith_number":"pith:IRC22VZO","schema_version":"1.0","canonical_sha256":"4445ad572e4e4df7770d198f3dc223bad7a5a97c2e8c9a7c09e85b73070c9d7d","source":{"kind":"arxiv","id":"1801.05165","version":3},"attestation_state":"computed","paper":{"title":"Scattering and blow-up criteria for 3D cubic focusing nonlinear inhomogeneous NLS with a potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hua Wang, Qing Guo, Xiaohua Yao","submitted_at":"2018-01-16T09:16:59Z","abstract_excerpt":"In this paper, we consider the 3d cubic focusing inhomogeneous nonlinear Schr\\\"{o}dinger equation with a potential\n  $$\n  iu_{t}+\\Delta u-Vu+|x|^{-b}|u|^{2}u=0,\\;\\;(t,x) \\in {{\\bf{R}}\\times{\\bf{R}}^{3}},\n  $$\n  where $0<b<1$. We first establish global well-posedness and scattering for the radial initial data $u_{0}$ in $H^{1}({\\bf R}^{3})$ satisfying $M(u_{0})^{1-s_{c}}E(u_{0})^{s_{c}}<\\mathcal{E}$ and $\\|u_{0}\\|_{L^{2}}^{2(1-s_{c})}\\|H^{\\frac{1}{2}}u_{0}\\|_{L^{2}}^{2s_{c}}<\\mathcal{K}$ provided that $V$ is repulsive, where $\\mathcal{E}$ and $\\mathcal{K}$ are the mass-energy and mass-kinetic o"},"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":"1801.05165","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-16T09:16:59Z","cross_cats_sorted":[],"title_canon_sha256":"2bcf05cdb7ed3e61e39d5c272dfa060fe4ca6b2bd61fab614d4082a6f18e6da0","abstract_canon_sha256":"c8bdd4d011355acc7edf20136b7899ef3d2c534bfce18676fd7b7856d0f7bf77"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:04.078696Z","signature_b64":"pT5e7XTtqPiv6atj9dgbGxahkeuECPlWJxirsemeC+u6oFtUQFkBTPYZ8Fu9OP3ymxJEJomxwFhC8VVH7ikbDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4445ad572e4e4df7770d198f3dc223bad7a5a97c2e8c9a7c09e85b73070c9d7d","last_reissued_at":"2026-05-17T23:56:04.078206Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:04.078206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scattering and blow-up criteria for 3D cubic focusing nonlinear inhomogeneous NLS with a potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hua Wang, Qing Guo, Xiaohua Yao","submitted_at":"2018-01-16T09:16:59Z","abstract_excerpt":"In this paper, we consider the 3d cubic focusing inhomogeneous nonlinear Schr\\\"{o}dinger equation with a potential\n  $$\n  iu_{t}+\\Delta u-Vu+|x|^{-b}|u|^{2}u=0,\\;\\;(t,x) \\in {{\\bf{R}}\\times{\\bf{R}}^{3}},\n  $$\n  where $0<b<1$. We first establish global well-posedness and scattering for the radial initial data $u_{0}$ in $H^{1}({\\bf R}^{3})$ satisfying $M(u_{0})^{1-s_{c}}E(u_{0})^{s_{c}}<\\mathcal{E}$ and $\\|u_{0}\\|_{L^{2}}^{2(1-s_{c})}\\|H^{\\frac{1}{2}}u_{0}\\|_{L^{2}}^{2s_{c}}<\\mathcal{K}$ provided that $V$ is repulsive, where $\\mathcal{E}$ and $\\mathcal{K}$ are the mass-energy and mass-kinetic o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05165","kind":"arxiv","version":3},"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":"1801.05165","created_at":"2026-05-17T23:56:04.078276+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.05165v3","created_at":"2026-05-17T23:56:04.078276+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.05165","created_at":"2026-05-17T23:56:04.078276+00:00"},{"alias_kind":"pith_short_12","alias_value":"IRC22VZOJZG7","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"IRC22VZOJZG7O5YN","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"IRC22VZO","created_at":"2026-05-18T12:32:31.084164+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/IRC22VZOJZG7O5YNDGHT3QRDXL","json":"https://pith.science/pith/IRC22VZOJZG7O5YNDGHT3QRDXL.json","graph_json":"https://pith.science/api/pith-number/IRC22VZOJZG7O5YNDGHT3QRDXL/graph.json","events_json":"https://pith.science/api/pith-number/IRC22VZOJZG7O5YNDGHT3QRDXL/events.json","paper":"https://pith.science/paper/IRC22VZO"},"agent_actions":{"view_html":"https://pith.science/pith/IRC22VZOJZG7O5YNDGHT3QRDXL","download_json":"https://pith.science/pith/IRC22VZOJZG7O5YNDGHT3QRDXL.json","view_paper":"https://pith.science/paper/IRC22VZO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.05165&json=true","fetch_graph":"https://pith.science/api/pith-number/IRC22VZOJZG7O5YNDGHT3QRDXL/graph.json","fetch_events":"https://pith.science/api/pith-number/IRC22VZOJZG7O5YNDGHT3QRDXL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IRC22VZOJZG7O5YNDGHT3QRDXL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IRC22VZOJZG7O5YNDGHT3QRDXL/action/storage_attestation","attest_author":"https://pith.science/pith/IRC22VZOJZG7O5YNDGHT3QRDXL/action/author_attestation","sign_citation":"https://pith.science/pith/IRC22VZOJZG7O5YNDGHT3QRDXL/action/citation_signature","submit_replication":"https://pith.science/pith/IRC22VZOJZG7O5YNDGHT3QRDXL/action/replication_record"}},"created_at":"2026-05-17T23:56:04.078276+00:00","updated_at":"2026-05-17T23:56:04.078276+00:00"}