{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:MVAITYS6ZAT4KEYXYTVQVNXN3R","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6085c2ad2b6e887b6fc31cdf04a60e4f3f2826612a6450dbe21447e8dc5b63b8","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-05-05T09:30:43Z","title_canon_sha256":"5efdef54910a4e09b0c51e9807ffbf2f9073a3cc6c2e33a50c0b30af3d03af91"},"schema_version":"1.0","source":{"id":"2305.03384","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.03384","created_at":"2026-07-05T06:24:12Z"},{"alias_kind":"arxiv_version","alias_value":"2305.03384v1","created_at":"2026-07-05T06:24:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.03384","created_at":"2026-07-05T06:24:12Z"},{"alias_kind":"pith_short_12","alias_value":"MVAITYS6ZAT4","created_at":"2026-07-05T06:24:12Z"},{"alias_kind":"pith_short_16","alias_value":"MVAITYS6ZAT4KEYX","created_at":"2026-07-05T06:24:12Z"},{"alias_kind":"pith_short_8","alias_value":"MVAITYS6","created_at":"2026-07-05T06:24:12Z"}],"graph_snapshots":[{"event_id":"sha256:ae53dc63fad024076e118425dacdb8561db70508d017f3ef2b82ecab01378cf5","target":"graph","created_at":"2026-07-05T06:24:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2305.03384/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Anomalous diffusion is often modelled in terms of the subdiffusion equation, which can involve a weakly singular source term. For this case, many predominant time stepping methods, including the correction of high-order BDF schemes [{\\sc Jin, Li, and Zhou}, SIAM J. Sci. Comput., 39 (2017), A3129--A3152], may suffer from a severe order reduction.\n  To fill in this gap, we propose a smoothing method for time stepping schemes, where the singular term is regularized by using a $m$-fold integral-differential calculus and the equation is discretized by the $k$-step BDF convolution quadrature, called","authors_text":"Jiankang Shi, Minghua Chen","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-05-05T09:30:43Z","title":"High-order BDF convolution quadrature for subdiffusion models with a singular source term"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.03384","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d48cded43292aea713f1ef76d9aece83da5a73f2ba8bf02ee7d4052f2f02036e","target":"record","created_at":"2026-07-05T06:24:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6085c2ad2b6e887b6fc31cdf04a60e4f3f2826612a6450dbe21447e8dc5b63b8","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-05-05T09:30:43Z","title_canon_sha256":"5efdef54910a4e09b0c51e9807ffbf2f9073a3cc6c2e33a50c0b30af3d03af91"},"schema_version":"1.0","source":{"id":"2305.03384","kind":"arxiv","version":1}},"canonical_sha256":"654089e25ec827c51317c4eb0ab6eddc454b208f4eda2627869f219352fd528e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"654089e25ec827c51317c4eb0ab6eddc454b208f4eda2627869f219352fd528e","first_computed_at":"2026-07-05T06:24:12.473247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:24:12.473247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iEDj9p34w0K41PcL5Ddui/YsMFxQgFRjoap0KRC/AK1eGGCDE3iTAyi9O795UwVT5UVFKS8uxNB0GZGSXXFPCw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:24:12.473586Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.03384","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d48cded43292aea713f1ef76d9aece83da5a73f2ba8bf02ee7d4052f2f02036e","sha256:ae53dc63fad024076e118425dacdb8561db70508d017f3ef2b82ecab01378cf5"],"state_sha256":"68a3272a03b10ee6842bd1187f6687c6be0399eb995784ca9195f93572941b0c"}