{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:RZVBOCEFWLRJJBXGGE6GB6H3IS","short_pith_number":"pith:RZVBOCEF","schema_version":"1.0","canonical_sha256":"8e6a170885b2e29486e6313c60f8fb449811cbf4a653841fcf4a9dac8182e7be","source":{"kind":"arxiv","id":"1606.07587","version":2},"attestation_state":"computed","paper":{"title":"Discrete maximal regularity of time-stepping schemes for fractional evolution equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Bangti Jin, Buyang Li, Zhi Zhou","submitted_at":"2016-06-24T07:40:55Z","abstract_excerpt":"In this work, we establish the maximal $\\ell^p$-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order $\\alpha\\in(0,2)$, $\\alpha\\neq 1$, in time. These schemes include convolution quadratures generated by backward Euler method and second-order backward difference formula, the L1 scheme, explicit Euler method and a fractional variant of the Crank-Nicolson method. The main tools for the analysis include operator-valued Fourier multiplier theorem due to Weis [48] and its discrete analogue due to Blunck [10]. These results gen"},"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":"1606.07587","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-24T07:40:55Z","cross_cats_sorted":[],"title_canon_sha256":"1b0242ee9538c8dd5573a6533bc5d12bd3e42f24e53ecfd8dffaf62ffd5975cf","abstract_canon_sha256":"0278e5aaedd80653e532aacb2142de2d227758dad025f42b0617dc06f9b60a41"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:42.939133Z","signature_b64":"ZEch30P//hMwIaSHk0Obf/V/6xZuf77+9UhMfPzX5FVrktk+SFLME4ei3nmjav6LamAffobD9n5MI9dEXYEzCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e6a170885b2e29486e6313c60f8fb449811cbf4a653841fcf4a9dac8182e7be","last_reissued_at":"2026-05-18T00:47:42.938387Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:42.938387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Discrete maximal regularity of time-stepping schemes for fractional evolution equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Bangti Jin, Buyang Li, Zhi Zhou","submitted_at":"2016-06-24T07:40:55Z","abstract_excerpt":"In this work, we establish the maximal $\\ell^p$-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order $\\alpha\\in(0,2)$, $\\alpha\\neq 1$, in time. These schemes include convolution quadratures generated by backward Euler method and second-order backward difference formula, the L1 scheme, explicit Euler method and a fractional variant of the Crank-Nicolson method. The main tools for the analysis include operator-valued Fourier multiplier theorem due to Weis [48] and its discrete analogue due to Blunck [10]. These results gen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07587","kind":"arxiv","version":2},"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":"1606.07587","created_at":"2026-05-18T00:47:42.938500+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.07587v2","created_at":"2026-05-18T00:47:42.938500+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07587","created_at":"2026-05-18T00:47:42.938500+00:00"},{"alias_kind":"pith_short_12","alias_value":"RZVBOCEFWLRJ","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_16","alias_value":"RZVBOCEFWLRJJBXG","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_8","alias_value":"RZVBOCEF","created_at":"2026-05-18T12:30:41.710351+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/RZVBOCEFWLRJJBXGGE6GB6H3IS","json":"https://pith.science/pith/RZVBOCEFWLRJJBXGGE6GB6H3IS.json","graph_json":"https://pith.science/api/pith-number/RZVBOCEFWLRJJBXGGE6GB6H3IS/graph.json","events_json":"https://pith.science/api/pith-number/RZVBOCEFWLRJJBXGGE6GB6H3IS/events.json","paper":"https://pith.science/paper/RZVBOCEF"},"agent_actions":{"view_html":"https://pith.science/pith/RZVBOCEFWLRJJBXGGE6GB6H3IS","download_json":"https://pith.science/pith/RZVBOCEFWLRJJBXGGE6GB6H3IS.json","view_paper":"https://pith.science/paper/RZVBOCEF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.07587&json=true","fetch_graph":"https://pith.science/api/pith-number/RZVBOCEFWLRJJBXGGE6GB6H3IS/graph.json","fetch_events":"https://pith.science/api/pith-number/RZVBOCEFWLRJJBXGGE6GB6H3IS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RZVBOCEFWLRJJBXGGE6GB6H3IS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RZVBOCEFWLRJJBXGGE6GB6H3IS/action/storage_attestation","attest_author":"https://pith.science/pith/RZVBOCEFWLRJJBXGGE6GB6H3IS/action/author_attestation","sign_citation":"https://pith.science/pith/RZVBOCEFWLRJJBXGGE6GB6H3IS/action/citation_signature","submit_replication":"https://pith.science/pith/RZVBOCEFWLRJJBXGGE6GB6H3IS/action/replication_record"}},"created_at":"2026-05-18T00:47:42.938500+00:00","updated_at":"2026-05-18T00:47:42.938500+00:00"}