{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:N7CHM23OGC5T6EPGXZLM5MFA6O","short_pith_number":"pith:N7CHM23O","schema_version":"1.0","canonical_sha256":"6fc4766b6e30bb3f11e6be56ceb0a0f394eee87c90437f4ee6b8eff430e41872","source":{"kind":"arxiv","id":"2112.13609","version":1},"attestation_state":"computed","paper":{"title":"Correction of high-order $L_k$ approximation for subdiffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Jiankang Shi, Jianxiong Cao, Minghua Chen, Yubin Yan","submitted_at":"2021-12-27T11:05:45Z","abstract_excerpt":"The subdiffusion equations with a Caputo fractional derivative of order $\\alpha \\in (0,1)$ arise in a wide variety of practical problems, which is describing the transport processes, in the force-free limit, slower than Brownian diffusion. In this work, we derive the correction schemes of the Lagrange interpolation with degree $k$ ($k\\leq 6$) convolution quadrature, called $L_k$ approximation, for the subdiffusion, which are easy to implement on variable grids. The key step of designing correction algorithm is to calculate the explicit form of the coefficients of $L_k$ approximation by the pol"},"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":"2112.13609","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-12-27T11:05:45Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"030be531ded08f535a817c803201ec0b3d9b7dbb4b766c2b0d5f10373f5e8f05","abstract_canon_sha256":"797be841bafb0b22365eb495f5b4fec2d1dd1cebc5bce9f9095cd4e5e24bb687"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:24:08.708808Z","signature_b64":"OEOJLkeBQ3Y8CsCQu6sQvJA5dqVgsJfzOKD8BbyIlrW08h13TgyM6WLuMlIP5gV6OdCpzZbM+lnhN0YkARVGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fc4766b6e30bb3f11e6be56ceb0a0f394eee87c90437f4ee6b8eff430e41872","last_reissued_at":"2026-07-05T06:24:08.708321Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:24:08.708321Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Correction of high-order $L_k$ approximation for subdiffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Jiankang Shi, Jianxiong Cao, Minghua Chen, Yubin Yan","submitted_at":"2021-12-27T11:05:45Z","abstract_excerpt":"The subdiffusion equations with a Caputo fractional derivative of order $\\alpha \\in (0,1)$ arise in a wide variety of practical problems, which is describing the transport processes, in the force-free limit, slower than Brownian diffusion. In this work, we derive the correction schemes of the Lagrange interpolation with degree $k$ ($k\\leq 6$) convolution quadrature, called $L_k$ approximation, for the subdiffusion, which are easy to implement on variable grids. The key step of designing correction algorithm is to calculate the explicit form of the coefficients of $L_k$ approximation by the pol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.13609","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.13609/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":"2112.13609","created_at":"2026-07-05T06:24:08.708382+00:00"},{"alias_kind":"arxiv_version","alias_value":"2112.13609v1","created_at":"2026-07-05T06:24:08.708382+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.13609","created_at":"2026-07-05T06:24:08.708382+00:00"},{"alias_kind":"pith_short_12","alias_value":"N7CHM23OGC5T","created_at":"2026-07-05T06:24:08.708382+00:00"},{"alias_kind":"pith_short_16","alias_value":"N7CHM23OGC5T6EPG","created_at":"2026-07-05T06:24:08.708382+00:00"},{"alias_kind":"pith_short_8","alias_value":"N7CHM23O","created_at":"2026-07-05T06:24:08.708382+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/N7CHM23OGC5T6EPGXZLM5MFA6O","json":"https://pith.science/pith/N7CHM23OGC5T6EPGXZLM5MFA6O.json","graph_json":"https://pith.science/api/pith-number/N7CHM23OGC5T6EPGXZLM5MFA6O/graph.json","events_json":"https://pith.science/api/pith-number/N7CHM23OGC5T6EPGXZLM5MFA6O/events.json","paper":"https://pith.science/paper/N7CHM23O"},"agent_actions":{"view_html":"https://pith.science/pith/N7CHM23OGC5T6EPGXZLM5MFA6O","download_json":"https://pith.science/pith/N7CHM23OGC5T6EPGXZLM5MFA6O.json","view_paper":"https://pith.science/paper/N7CHM23O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2112.13609&json=true","fetch_graph":"https://pith.science/api/pith-number/N7CHM23OGC5T6EPGXZLM5MFA6O/graph.json","fetch_events":"https://pith.science/api/pith-number/N7CHM23OGC5T6EPGXZLM5MFA6O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N7CHM23OGC5T6EPGXZLM5MFA6O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N7CHM23OGC5T6EPGXZLM5MFA6O/action/storage_attestation","attest_author":"https://pith.science/pith/N7CHM23OGC5T6EPGXZLM5MFA6O/action/author_attestation","sign_citation":"https://pith.science/pith/N7CHM23OGC5T6EPGXZLM5MFA6O/action/citation_signature","submit_replication":"https://pith.science/pith/N7CHM23OGC5T6EPGXZLM5MFA6O/action/replication_record"}},"created_at":"2026-07-05T06:24:08.708382+00:00","updated_at":"2026-07-05T06:24:08.708382+00:00"}