{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:I37WTJYCCSIXOYXHK6KOJC3GMS","short_pith_number":"pith:I37WTJYC","schema_version":"1.0","canonical_sha256":"46ff69a70214917762e75794e48b666499794385e3ee4e08f1631cb39905eefd","source":{"kind":"arxiv","id":"1901.00957","version":1},"attestation_state":"computed","paper":{"title":"Dispersive estimates for time and space fractional Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Miao Li, Shiliang Zhao, Xiaoyan Su","submitted_at":"2019-01-04T00:38:36Z","abstract_excerpt":"In this paper, we consider the Cauchy problem for the fractional Schr\\\"odinger equation $i D_t^\\alpha u + (-\\Delta)^{\\frac{\\beta}{2}} u =0$ with $0<\\alpha<1$, $\\beta>0$. We establish the dispersive estimates for the solutions. In particular, we prove that the decay rates are sharp."},"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":"1901.00957","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-04T00:38:36Z","cross_cats_sorted":[],"title_canon_sha256":"7571d4f0865f0297855de0a6cd41c7ee908934b3001e669a588200a7e059d9ec","abstract_canon_sha256":"0cabebe3e71c4361d0977e92bf984c0174f2502862dc29c86c7a56d59295cc37"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:57.576703Z","signature_b64":"2nwAIKYetyVPTSb6uYs21Vu4u0zAWyfqEaB/f6U+OzjNHUsyCyWsGrHlDjQfWwhQQYWjmj0HHqyqjqLOTImYDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46ff69a70214917762e75794e48b666499794385e3ee4e08f1631cb39905eefd","last_reissued_at":"2026-05-17T23:56:57.576095Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:57.576095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dispersive estimates for time and space fractional Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Miao Li, Shiliang Zhao, Xiaoyan Su","submitted_at":"2019-01-04T00:38:36Z","abstract_excerpt":"In this paper, we consider the Cauchy problem for the fractional Schr\\\"odinger equation $i D_t^\\alpha u + (-\\Delta)^{\\frac{\\beta}{2}} u =0$ with $0<\\alpha<1$, $\\beta>0$. We establish the dispersive estimates for the solutions. In particular, we prove that the decay rates are sharp."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.00957","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":"1901.00957","created_at":"2026-05-17T23:56:57.576184+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.00957v1","created_at":"2026-05-17T23:56:57.576184+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.00957","created_at":"2026-05-17T23:56:57.576184+00:00"},{"alias_kind":"pith_short_12","alias_value":"I37WTJYCCSIX","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"I37WTJYCCSIXOYXH","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"I37WTJYC","created_at":"2026-05-18T12:33:18.533446+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/I37WTJYCCSIXOYXHK6KOJC3GMS","json":"https://pith.science/pith/I37WTJYCCSIXOYXHK6KOJC3GMS.json","graph_json":"https://pith.science/api/pith-number/I37WTJYCCSIXOYXHK6KOJC3GMS/graph.json","events_json":"https://pith.science/api/pith-number/I37WTJYCCSIXOYXHK6KOJC3GMS/events.json","paper":"https://pith.science/paper/I37WTJYC"},"agent_actions":{"view_html":"https://pith.science/pith/I37WTJYCCSIXOYXHK6KOJC3GMS","download_json":"https://pith.science/pith/I37WTJYCCSIXOYXHK6KOJC3GMS.json","view_paper":"https://pith.science/paper/I37WTJYC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.00957&json=true","fetch_graph":"https://pith.science/api/pith-number/I37WTJYCCSIXOYXHK6KOJC3GMS/graph.json","fetch_events":"https://pith.science/api/pith-number/I37WTJYCCSIXOYXHK6KOJC3GMS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I37WTJYCCSIXOYXHK6KOJC3GMS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I37WTJYCCSIXOYXHK6KOJC3GMS/action/storage_attestation","attest_author":"https://pith.science/pith/I37WTJYCCSIXOYXHK6KOJC3GMS/action/author_attestation","sign_citation":"https://pith.science/pith/I37WTJYCCSIXOYXHK6KOJC3GMS/action/citation_signature","submit_replication":"https://pith.science/pith/I37WTJYCCSIXOYXHK6KOJC3GMS/action/replication_record"}},"created_at":"2026-05-17T23:56:57.576184+00:00","updated_at":"2026-05-17T23:56:57.576184+00:00"}