{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:EHGC7QYWOQGX42OVDOJ7WMSLF4","short_pith_number":"pith:EHGC7QYW","canonical_record":{"source":{"id":"2104.09032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-04-19T03:32:45Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"01934c11511cc6ac04658ceb4870271d536febc4fa5ad15d300296c722ac0add","abstract_canon_sha256":"cde288a36b047fb5698b62e72733fdd2415c5a2e0826a7625a39f568a87b48b8"},"schema_version":"1.0"},"canonical_sha256":"21cc2fc316740d7e69d51b93fb324b2f149467c7f5850715ab43d6c3d9a54d1d","source":{"kind":"arxiv","id":"2104.09032","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.09032","created_at":"2026-07-05T02:32:58Z"},{"alias_kind":"arxiv_version","alias_value":"2104.09032v1","created_at":"2026-07-05T02:32:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.09032","created_at":"2026-07-05T02:32:58Z"},{"alias_kind":"pith_short_12","alias_value":"EHGC7QYWOQGX","created_at":"2026-07-05T02:32:58Z"},{"alias_kind":"pith_short_16","alias_value":"EHGC7QYWOQGX42OV","created_at":"2026-07-05T02:32:58Z"},{"alias_kind":"pith_short_8","alias_value":"EHGC7QYW","created_at":"2026-07-05T02:32:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:EHGC7QYWOQGX42OVDOJ7WMSLF4","target":"record","payload":{"canonical_record":{"source":{"id":"2104.09032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-04-19T03:32:45Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"01934c11511cc6ac04658ceb4870271d536febc4fa5ad15d300296c722ac0add","abstract_canon_sha256":"cde288a36b047fb5698b62e72733fdd2415c5a2e0826a7625a39f568a87b48b8"},"schema_version":"1.0"},"canonical_sha256":"21cc2fc316740d7e69d51b93fb324b2f149467c7f5850715ab43d6c3d9a54d1d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:32:58.168755Z","signature_b64":"OCV7VSxgeXi+MGndAyftO0uAOl7aK7B0rkkUh294SZMU0mOlfiNdor1qJujqWkl/POtonYVgfqwi4ReHOBeuCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21cc2fc316740d7e69d51b93fb324b2f149467c7f5850715ab43d6c3d9a54d1d","last_reissued_at":"2026-07-05T02:32:58.168343Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:32:58.168343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2104.09032","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:32:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QR278VblvEi5khpG6h+UW+xzVrXBg98EX90K1pxbejM3VmopnMCcT9ABFHajCQHbtlmkRY866z948bP5raDwCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T08:03:02.407607Z"},"content_sha256":"1da4b6618b993229c14fb8df81d565e573cc376d13e13283b9210d7c2b0c5595","schema_version":"1.0","event_id":"sha256:1da4b6618b993229c14fb8df81d565e573cc376d13e13283b9210d7c2b0c5595"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:EHGC7QYWOQGX42OVDOJ7WMSLF4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"BDF$6$ SAV schemes for time-fractional Allen-Cahn dissipative systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Fan Yu, Minghua Chen","submitted_at":"2021-04-19T03:32:45Z","abstract_excerpt":"Recently, the error analysis of BDF$k$ $(1\\leqslant k\\leqslant5)$ SAV (scalar auxiliary variable) schemes are given in \\cite{Huangg:20} for the classical Allen-Cahn equation. However, it remains unavailable for BDF$6$ SAV schemes. In this paper, we construct and analyze BDF$6$ SAV schemes for the time-fractional dissipative systems. We carry out a rigorous error analysis for the time-fractional Allen-Cahn equation, which also fills up a gap for the classical case. Finally, numerical experiment is shown to illustrate the effectiveness of the presented methods. As far as we know, this is the fir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.09032","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/2104.09032/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:32:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qwEJHhRdsN3Aw91IvR5VPrLRXj2drYqjH09bZ9eESEw2MvMaFbKpgYZGh9Xg8T63wpgv6gCE3dLPMukYOqn+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T08:03:02.408101Z"},"content_sha256":"276c78040114e00ff747f53e72447d73cb168bd65711ddf1bf5221a76a23b986","schema_version":"1.0","event_id":"sha256:276c78040114e00ff747f53e72447d73cb168bd65711ddf1bf5221a76a23b986"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EHGC7QYWOQGX42OVDOJ7WMSLF4/bundle.json","state_url":"https://pith.science/pith/EHGC7QYWOQGX42OVDOJ7WMSLF4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EHGC7QYWOQGX42OVDOJ7WMSLF4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-05T08:03:02Z","links":{"resolver":"https://pith.science/pith/EHGC7QYWOQGX42OVDOJ7WMSLF4","bundle":"https://pith.science/pith/EHGC7QYWOQGX42OVDOJ7WMSLF4/bundle.json","state":"https://pith.science/pith/EHGC7QYWOQGX42OVDOJ7WMSLF4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EHGC7QYWOQGX42OVDOJ7WMSLF4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:EHGC7QYWOQGX42OVDOJ7WMSLF4","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":"cde288a36b047fb5698b62e72733fdd2415c5a2e0826a7625a39f568a87b48b8","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-04-19T03:32:45Z","title_canon_sha256":"01934c11511cc6ac04658ceb4870271d536febc4fa5ad15d300296c722ac0add"},"schema_version":"1.0","source":{"id":"2104.09032","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.09032","created_at":"2026-07-05T02:32:58Z"},{"alias_kind":"arxiv_version","alias_value":"2104.09032v1","created_at":"2026-07-05T02:32:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.09032","created_at":"2026-07-05T02:32:58Z"},{"alias_kind":"pith_short_12","alias_value":"EHGC7QYWOQGX","created_at":"2026-07-05T02:32:58Z"},{"alias_kind":"pith_short_16","alias_value":"EHGC7QYWOQGX42OV","created_at":"2026-07-05T02:32:58Z"},{"alias_kind":"pith_short_8","alias_value":"EHGC7QYW","created_at":"2026-07-05T02:32:58Z"}],"graph_snapshots":[{"event_id":"sha256:276c78040114e00ff747f53e72447d73cb168bd65711ddf1bf5221a76a23b986","target":"graph","created_at":"2026-07-05T02:32:58Z","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/2104.09032/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recently, the error analysis of BDF$k$ $(1\\leqslant k\\leqslant5)$ SAV (scalar auxiliary variable) schemes are given in \\cite{Huangg:20} for the classical Allen-Cahn equation. However, it remains unavailable for BDF$6$ SAV schemes. In this paper, we construct and analyze BDF$6$ SAV schemes for the time-fractional dissipative systems. We carry out a rigorous error analysis for the time-fractional Allen-Cahn equation, which also fills up a gap for the classical case. Finally, numerical experiment is shown to illustrate the effectiveness of the presented methods. As far as we know, this is the fir","authors_text":"Fan Yu, Minghua Chen","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-04-19T03:32:45Z","title":"BDF$6$ SAV schemes for time-fractional Allen-Cahn dissipative systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.09032","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":"sha256:1da4b6618b993229c14fb8df81d565e573cc376d13e13283b9210d7c2b0c5595","target":"record","created_at":"2026-07-05T02:32:58Z","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":"cde288a36b047fb5698b62e72733fdd2415c5a2e0826a7625a39f568a87b48b8","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-04-19T03:32:45Z","title_canon_sha256":"01934c11511cc6ac04658ceb4870271d536febc4fa5ad15d300296c722ac0add"},"schema_version":"1.0","source":{"id":"2104.09032","kind":"arxiv","version":1}},"canonical_sha256":"21cc2fc316740d7e69d51b93fb324b2f149467c7f5850715ab43d6c3d9a54d1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21cc2fc316740d7e69d51b93fb324b2f149467c7f5850715ab43d6c3d9a54d1d","first_computed_at":"2026-07-05T02:32:58.168343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:32:58.168343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OCV7VSxgeXi+MGndAyftO0uAOl7aK7B0rkkUh294SZMU0mOlfiNdor1qJujqWkl/POtonYVgfqwi4ReHOBeuCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:32:58.168755Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.09032","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1da4b6618b993229c14fb8df81d565e573cc376d13e13283b9210d7c2b0c5595","sha256:276c78040114e00ff747f53e72447d73cb168bd65711ddf1bf5221a76a23b986"],"state_sha256":"9c51e196b6a7b336ff4584c723b91ce97c3e358ef6dcf44e4acac1196c15a97b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7vgEz8hOLvhHMAAP8W+ggC0L+a8dqP+pKIZAgea3yWuigRVXA9dHcf+NQ1awqOyL6itw8ywKdGgdty27QwVpDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T08:03:02.416681Z","bundle_sha256":"96c3c00b59109499058d3c1ee10e7820b83eec376e9145608398c989a6f742a4"}}