{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:C66MTXBDXID6SM2CM7XJ3ND4QG","short_pith_number":"pith:C66MTXBD","schema_version":"1.0","canonical_sha256":"17bcc9dc23ba07e9334267ee9db47c81be254d056b7a57a2285e96fa2085a21f","source":{"kind":"arxiv","id":"1611.08899","version":1},"attestation_state":"computed","paper":{"title":"The time fractional Schr\\\"odinger equation on Hilbert space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Humberto Prado, Juan Trujillo, Przemys{\\l}aw G\\'orka","submitted_at":"2016-11-27T19:49:36Z","abstract_excerpt":"We study the linear fractional Schr\\\"odinger equation on a Hilbert space, with a fractional time derivative of order $0<\\alpha<1,$ and a self-adjoint generator $A.$ Using the spectral theorem we prove existence and uniqueness of strong solutions, and we show that the solutions are governed by an operator solution family $\\{U_{\\alpha}(t)\\}_{t\\geq 0}$. Moreover, we prove that the solution family $U_{\\alpha}(t)$ converges strongly to the family of unitary operators $e^{-itA},$ as $\\alpha$ approaches to $1$."},"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":"1611.08899","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-27T19:49:36Z","cross_cats_sorted":[],"title_canon_sha256":"08526889dbb6d5cfb539b4cb57bad4c75a1b22e6de3034c9e8d2da8b47e21d00","abstract_canon_sha256":"dc9fd93de8cd52fc6a6bbfece33c69081b62f0fcbdba1cb43cfd200e1d975e8f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:29.895822Z","signature_b64":"KJBIPVsuHU5V/kTp8sMR086o2yPuo1OX5c1NdvEzWM3/cvO/J1wZXgKXfjxrMRdBj3xmeLsVlldbcqJQqlZsCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17bcc9dc23ba07e9334267ee9db47c81be254d056b7a57a2285e96fa2085a21f","last_reissued_at":"2026-05-18T00:56:29.895005Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:29.895005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The time fractional Schr\\\"odinger equation on Hilbert space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Humberto Prado, Juan Trujillo, Przemys{\\l}aw G\\'orka","submitted_at":"2016-11-27T19:49:36Z","abstract_excerpt":"We study the linear fractional Schr\\\"odinger equation on a Hilbert space, with a fractional time derivative of order $0<\\alpha<1,$ and a self-adjoint generator $A.$ Using the spectral theorem we prove existence and uniqueness of strong solutions, and we show that the solutions are governed by an operator solution family $\\{U_{\\alpha}(t)\\}_{t\\geq 0}$. Moreover, we prove that the solution family $U_{\\alpha}(t)$ converges strongly to the family of unitary operators $e^{-itA},$ as $\\alpha$ approaches to $1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08899","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":"1611.08899","created_at":"2026-05-18T00:56:29.895126+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.08899v1","created_at":"2026-05-18T00:56:29.895126+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08899","created_at":"2026-05-18T00:56:29.895126+00:00"},{"alias_kind":"pith_short_12","alias_value":"C66MTXBDXID6","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"C66MTXBDXID6SM2C","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"C66MTXBD","created_at":"2026-05-18T12:30:09.641336+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/C66MTXBDXID6SM2CM7XJ3ND4QG","json":"https://pith.science/pith/C66MTXBDXID6SM2CM7XJ3ND4QG.json","graph_json":"https://pith.science/api/pith-number/C66MTXBDXID6SM2CM7XJ3ND4QG/graph.json","events_json":"https://pith.science/api/pith-number/C66MTXBDXID6SM2CM7XJ3ND4QG/events.json","paper":"https://pith.science/paper/C66MTXBD"},"agent_actions":{"view_html":"https://pith.science/pith/C66MTXBDXID6SM2CM7XJ3ND4QG","download_json":"https://pith.science/pith/C66MTXBDXID6SM2CM7XJ3ND4QG.json","view_paper":"https://pith.science/paper/C66MTXBD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.08899&json=true","fetch_graph":"https://pith.science/api/pith-number/C66MTXBDXID6SM2CM7XJ3ND4QG/graph.json","fetch_events":"https://pith.science/api/pith-number/C66MTXBDXID6SM2CM7XJ3ND4QG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C66MTXBDXID6SM2CM7XJ3ND4QG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C66MTXBDXID6SM2CM7XJ3ND4QG/action/storage_attestation","attest_author":"https://pith.science/pith/C66MTXBDXID6SM2CM7XJ3ND4QG/action/author_attestation","sign_citation":"https://pith.science/pith/C66MTXBDXID6SM2CM7XJ3ND4QG/action/citation_signature","submit_replication":"https://pith.science/pith/C66MTXBDXID6SM2CM7XJ3ND4QG/action/replication_record"}},"created_at":"2026-05-18T00:56:29.895126+00:00","updated_at":"2026-05-18T00:56:29.895126+00:00"}