{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:V6BYVLBRA5QHE5IHDXTOLLQFTE","short_pith_number":"pith:V6BYVLBR","schema_version":"1.0","canonical_sha256":"af838aac3107607275071de6e5ae05991d1d33e4ef0fcce1506c66a0c11bc904","source":{"kind":"arxiv","id":"2304.06855","version":3},"attestation_state":"computed","paper":{"title":"A static memory sparse spectral method for time-fractional PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Jos\\'e A. Carrillo, Timon S. Gutleb","submitted_at":"2023-04-13T22:50:58Z","abstract_excerpt":"We introduce a method which provides accurate numerical solutions to fractional-in-time partial differential equations posed on $[0,T] \\times \\Omega$ with $\\Omega \\subset \\mathbb{R}^d$ without the excessive memory requirements associated with the nonlocal fractional derivative operator. Our approach combines recent advances in the development and utilization of multivariate sparse spectral methods as well as fast methods for the computation of Gauss quadrature nodes with recursive non-classical methods for the Caputo fractional derivative of general fractional order $\\alpha > 0$. An attractive"},"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":"2304.06855","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-04-13T22:50:58Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"618515275764bb18850806004192cf10ab2a23679b8d4ea14a93acfc6c596d68","abstract_canon_sha256":"ffc17cbede17c035d381acc40bb374a41877dca7c1aa11c8037a7ab1bf3e9455"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:59:31.317988Z","signature_b64":"EyFM0FiFDjX1ErWYgFMahidpG/KlQp/q6gXS6w/Apm3RIzoUl2cTEeiwTNM99QjabffnftxO6ACPUdmw/7e2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af838aac3107607275071de6e5ae05991d1d33e4ef0fcce1506c66a0c11bc904","last_reissued_at":"2026-07-05T06:59:31.317517Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:59:31.317517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A static memory sparse spectral method for time-fractional PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Jos\\'e A. Carrillo, Timon S. Gutleb","submitted_at":"2023-04-13T22:50:58Z","abstract_excerpt":"We introduce a method which provides accurate numerical solutions to fractional-in-time partial differential equations posed on $[0,T] \\times \\Omega$ with $\\Omega \\subset \\mathbb{R}^d$ without the excessive memory requirements associated with the nonlocal fractional derivative operator. Our approach combines recent advances in the development and utilization of multivariate sparse spectral methods as well as fast methods for the computation of Gauss quadrature nodes with recursive non-classical methods for the Caputo fractional derivative of general fractional order $\\alpha > 0$. An attractive"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.06855","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.06855/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2304.06855","created_at":"2026-07-05T06:59:31.317573+00:00"},{"alias_kind":"arxiv_version","alias_value":"2304.06855v3","created_at":"2026-07-05T06:59:31.317573+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.06855","created_at":"2026-07-05T06:59:31.317573+00:00"},{"alias_kind":"pith_short_12","alias_value":"V6BYVLBRA5QH","created_at":"2026-07-05T06:59:31.317573+00:00"},{"alias_kind":"pith_short_16","alias_value":"V6BYVLBRA5QHE5IH","created_at":"2026-07-05T06:59:31.317573+00:00"},{"alias_kind":"pith_short_8","alias_value":"V6BYVLBR","created_at":"2026-07-05T06:59:31.317573+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/V6BYVLBRA5QHE5IHDXTOLLQFTE","json":"https://pith.science/pith/V6BYVLBRA5QHE5IHDXTOLLQFTE.json","graph_json":"https://pith.science/api/pith-number/V6BYVLBRA5QHE5IHDXTOLLQFTE/graph.json","events_json":"https://pith.science/api/pith-number/V6BYVLBRA5QHE5IHDXTOLLQFTE/events.json","paper":"https://pith.science/paper/V6BYVLBR"},"agent_actions":{"view_html":"https://pith.science/pith/V6BYVLBRA5QHE5IHDXTOLLQFTE","download_json":"https://pith.science/pith/V6BYVLBRA5QHE5IHDXTOLLQFTE.json","view_paper":"https://pith.science/paper/V6BYVLBR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2304.06855&json=true","fetch_graph":"https://pith.science/api/pith-number/V6BYVLBRA5QHE5IHDXTOLLQFTE/graph.json","fetch_events":"https://pith.science/api/pith-number/V6BYVLBRA5QHE5IHDXTOLLQFTE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V6BYVLBRA5QHE5IHDXTOLLQFTE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V6BYVLBRA5QHE5IHDXTOLLQFTE/action/storage_attestation","attest_author":"https://pith.science/pith/V6BYVLBRA5QHE5IHDXTOLLQFTE/action/author_attestation","sign_citation":"https://pith.science/pith/V6BYVLBRA5QHE5IHDXTOLLQFTE/action/citation_signature","submit_replication":"https://pith.science/pith/V6BYVLBRA5QHE5IHDXTOLLQFTE/action/replication_record"}},"created_at":"2026-07-05T06:59:31.317573+00:00","updated_at":"2026-07-05T06:59:31.317573+00:00"}