{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:XCB7IT5SX4PGJX4OTPONLFMCXE","short_pith_number":"pith:XCB7IT5S","schema_version":"1.0","canonical_sha256":"b883f44fb2bf1e64df8e9bdcd59582b92bdd9f0c0f6ace1188227667b120f493","source":{"kind":"arxiv","id":"1212.6816","version":1},"attestation_state":"computed","paper":{"title":"The defocusing $\\dot{H}^{1/2}$-critical NLS in high dimensions","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jason Murphy","submitted_at":"2012-12-31T04:33:12Z","abstract_excerpt":"We consider the defocusing $\\dot{H}^{1/2}$-critical nonlinear Schr\\\"odinger equation in dimensions $d\\geq 5$. In the spirit of Kenig and Merle [Trans. Amer. Math. Soc. 362 (2010), 1937--1962], we combine a concentration-compactness approach with the Lin--Strauss Morawetz inequality to prove that if a solution $u$ is bounded in $\\dot{H}^{1/2}$ throughout its lifespan, then $u$ is global and scatters."},"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":"1212.6816","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AP","submitted_at":"2012-12-31T04:33:12Z","cross_cats_sorted":[],"title_canon_sha256":"30e21dddba38deed3d9917fcbbf13f15a07186ab42f4d7a03d0b411e93ed6376","abstract_canon_sha256":"63f93c0e2110605a805e0fe1b5ec7d2a9fbc3b73e7f06f5d37cedbe5b16c3e71"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:23.734034Z","signature_b64":"Nm5DhG6LDS8t2nElA02dbz8qPqn4PK2ot6OurMoow4drSZ6JqUgFPkX9U5QgCARm0KO3/1daeEyM/gp05KS4Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b883f44fb2bf1e64df8e9bdcd59582b92bdd9f0c0f6ace1188227667b120f493","last_reissued_at":"2026-05-18T02:29:23.733519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:23.733519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The defocusing $\\dot{H}^{1/2}$-critical NLS in high dimensions","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jason Murphy","submitted_at":"2012-12-31T04:33:12Z","abstract_excerpt":"We consider the defocusing $\\dot{H}^{1/2}$-critical nonlinear Schr\\\"odinger equation in dimensions $d\\geq 5$. In the spirit of Kenig and Merle [Trans. Amer. Math. Soc. 362 (2010), 1937--1962], we combine a concentration-compactness approach with the Lin--Strauss Morawetz inequality to prove that if a solution $u$ is bounded in $\\dot{H}^{1/2}$ throughout its lifespan, then $u$ is global and scatters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6816","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":"1212.6816","created_at":"2026-05-18T02:29:23.733582+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.6816v1","created_at":"2026-05-18T02:29:23.733582+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6816","created_at":"2026-05-18T02:29:23.733582+00:00"},{"alias_kind":"pith_short_12","alias_value":"XCB7IT5SX4PG","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_16","alias_value":"XCB7IT5SX4PGJX4O","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_8","alias_value":"XCB7IT5S","created_at":"2026-05-18T12:27:27.928770+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/XCB7IT5SX4PGJX4OTPONLFMCXE","json":"https://pith.science/pith/XCB7IT5SX4PGJX4OTPONLFMCXE.json","graph_json":"https://pith.science/api/pith-number/XCB7IT5SX4PGJX4OTPONLFMCXE/graph.json","events_json":"https://pith.science/api/pith-number/XCB7IT5SX4PGJX4OTPONLFMCXE/events.json","paper":"https://pith.science/paper/XCB7IT5S"},"agent_actions":{"view_html":"https://pith.science/pith/XCB7IT5SX4PGJX4OTPONLFMCXE","download_json":"https://pith.science/pith/XCB7IT5SX4PGJX4OTPONLFMCXE.json","view_paper":"https://pith.science/paper/XCB7IT5S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.6816&json=true","fetch_graph":"https://pith.science/api/pith-number/XCB7IT5SX4PGJX4OTPONLFMCXE/graph.json","fetch_events":"https://pith.science/api/pith-number/XCB7IT5SX4PGJX4OTPONLFMCXE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XCB7IT5SX4PGJX4OTPONLFMCXE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XCB7IT5SX4PGJX4OTPONLFMCXE/action/storage_attestation","attest_author":"https://pith.science/pith/XCB7IT5SX4PGJX4OTPONLFMCXE/action/author_attestation","sign_citation":"https://pith.science/pith/XCB7IT5SX4PGJX4OTPONLFMCXE/action/citation_signature","submit_replication":"https://pith.science/pith/XCB7IT5SX4PGJX4OTPONLFMCXE/action/replication_record"}},"created_at":"2026-05-18T02:29:23.733582+00:00","updated_at":"2026-05-18T02:29:23.733582+00:00"}