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We use the decaying property of angularly regular functions, which are defined as functions in Sobolev space $H_\\theta^{1, 1} \\subset H^1$ with angular regularity such that $\\|\\partial_\\theta f\\|_{H^1} < \\infty$, and also use the recently developed"},"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":"1904.11073","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-24T21:17:42Z","cross_cats_sorted":[],"title_canon_sha256":"3d8c67dc9592a17d85d407facd5f23a456989002a8d8995997007ef89c1eecdd","abstract_canon_sha256":"9d9e686403064a13e7da8923aab1c0e7772b135274cf09dfe548227029e2894e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:02.233215Z","signature_b64":"d1EPR1RCP+KISn0juDNZ6KXKU17Ybs7cNH35s75ODuby+sqa67ShwSCNbBT4bP5O3WAh6MkTcSOjfx/nNZBpDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f53e5ef4a15bc95fdda2eefe104d7278b76de2ecea3ce7388c2fb4dfcc6f934","last_reissued_at":"2026-05-17T23:44:02.232540Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:02.232540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Small data scattering of the inhomogeneous cubic-quintic NLS in 2 dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kiyeon Lee, Yonggeun Cho","submitted_at":"2019-04-24T21:17:42Z","abstract_excerpt":"The aim of this paper is to show the small data scattering for 2D ICQNLS:\n  $$iu_t=-\\Delta u + K_1(x)|u|^2u+K_2(x)|u|^4u.$$ Under the assumption that $\\left| \\partial^j K_l \\right| \\lesssim |x|^{b_l -j}$ for $j=0, 1, 2, l=1, 2$ and $0 \\le b_l \\le l - \\frac23$, we prove the small data scattering in an angularly regular Sobolev space $H_\\theta^{1,1}$. We use the decaying property of angularly regular functions, which are defined as functions in Sobolev space $H_\\theta^{1, 1} \\subset H^1$ with angular regularity such that $\\|\\partial_\\theta f\\|_{H^1} < \\infty$, and also use the recently developed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11073","kind":"arxiv","version":2},"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":"1904.11073","created_at":"2026-05-17T23:44:02.232645+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.11073v2","created_at":"2026-05-17T23:44:02.232645+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.11073","created_at":"2026-05-17T23:44:02.232645+00:00"},{"alias_kind":"pith_short_12","alias_value":"D5J6L32KCW6J","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"D5J6L32KCW6JL7O2","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"D5J6L32K","created_at":"2026-05-18T12:33:15.570797+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/D5J6L32KCW6JL7O2F3X6CBGXE6","json":"https://pith.science/pith/D5J6L32KCW6JL7O2F3X6CBGXE6.json","graph_json":"https://pith.science/api/pith-number/D5J6L32KCW6JL7O2F3X6CBGXE6/graph.json","events_json":"https://pith.science/api/pith-number/D5J6L32KCW6JL7O2F3X6CBGXE6/events.json","paper":"https://pith.science/paper/D5J6L32K"},"agent_actions":{"view_html":"https://pith.science/pith/D5J6L32KCW6JL7O2F3X6CBGXE6","download_json":"https://pith.science/pith/D5J6L32KCW6JL7O2F3X6CBGXE6.json","view_paper":"https://pith.science/paper/D5J6L32K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.11073&json=true","fetch_graph":"https://pith.science/api/pith-number/D5J6L32KCW6JL7O2F3X6CBGXE6/graph.json","fetch_events":"https://pith.science/api/pith-number/D5J6L32KCW6JL7O2F3X6CBGXE6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D5J6L32KCW6JL7O2F3X6CBGXE6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D5J6L32KCW6JL7O2F3X6CBGXE6/action/storage_attestation","attest_author":"https://pith.science/pith/D5J6L32KCW6JL7O2F3X6CBGXE6/action/author_attestation","sign_citation":"https://pith.science/pith/D5J6L32KCW6JL7O2F3X6CBGXE6/action/citation_signature","submit_replication":"https://pith.science/pith/D5J6L32KCW6JL7O2F3X6CBGXE6/action/replication_record"}},"created_at":"2026-05-17T23:44:02.232645+00:00","updated_at":"2026-05-17T23:44:02.232645+00:00"}