{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:N7CHM23OGC5T6EPGXZLM5MFA6O","short_pith_number":"pith:N7CHM23O","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"},"canonical_sha256":"6fc4766b6e30bb3f11e6be56ceb0a0f394eee87c90437f4ee6b8eff430e41872","source":{"kind":"arxiv","id":"2112.13609","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.13609","created_at":"2026-07-05T06:24:08Z"},{"alias_kind":"arxiv_version","alias_value":"2112.13609v1","created_at":"2026-07-05T06:24:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.13609","created_at":"2026-07-05T06:24:08Z"},{"alias_kind":"pith_short_12","alias_value":"N7CHM23OGC5T","created_at":"2026-07-05T06:24:08Z"},{"alias_kind":"pith_short_16","alias_value":"N7CHM23OGC5T6EPG","created_at":"2026-07-05T06:24:08Z"},{"alias_kind":"pith_short_8","alias_value":"N7CHM23O","created_at":"2026-07-05T06:24:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:N7CHM23OGC5T6EPGXZLM5MFA6O","target":"record","payload":{"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"},"canonical_sha256":"6fc4766b6e30bb3f11e6be56ceb0a0f394eee87c90437f4ee6b8eff430e41872","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"},"source_kind":"arxiv","source_id":"2112.13609","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":"2026-07-05T06:24:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B5QJasUgQU9qEv83I3VICShxFA2oLhxZFIv+kwcYVz0ewThd0PAQOd3Rn9nV2qrZYPVDBJ1tPYwej71pxHDRDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T20:29:41.178457Z"},"content_sha256":"00addad6a3e2d1ec3ceff8891a3b094463ab7af53543c299e8568daf43d60250","schema_version":"1.0","event_id":"sha256:00addad6a3e2d1ec3ceff8891a3b094463ab7af53543c299e8568daf43d60250"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:N7CHM23OGC5T6EPGXZLM5MFA6O","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:24:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5XwzFuu3XLzwwj2qh1aSlw3KDzJ92BnfKcuyoxst6wlf8bb+5VLz922T90nFLCjpJY69s8UPyaYIlhLu4rv5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T20:29:41.178795Z"},"content_sha256":"c3490a437d9b48ccc07983176ecff8378f1d10d8a9090225171fd639818533c5","schema_version":"1.0","event_id":"sha256:c3490a437d9b48ccc07983176ecff8378f1d10d8a9090225171fd639818533c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N7CHM23OGC5T6EPGXZLM5MFA6O/bundle.json","state_url":"https://pith.science/pith/N7CHM23OGC5T6EPGXZLM5MFA6O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N7CHM23OGC5T6EPGXZLM5MFA6O/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":"2026-08-06T20:29:41Z","links":{"resolver":"https://pith.science/pith/N7CHM23OGC5T6EPGXZLM5MFA6O","bundle":"https://pith.science/pith/N7CHM23OGC5T6EPGXZLM5MFA6O/bundle.json","state":"https://pith.science/pith/N7CHM23OGC5T6EPGXZLM5MFA6O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N7CHM23OGC5T6EPGXZLM5MFA6O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:N7CHM23OGC5T6EPGXZLM5MFA6O","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":"797be841bafb0b22365eb495f5b4fec2d1dd1cebc5bce9f9095cd4e5e24bb687","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-12-27T11:05:45Z","title_canon_sha256":"030be531ded08f535a817c803201ec0b3d9b7dbb4b766c2b0d5f10373f5e8f05"},"schema_version":"1.0","source":{"id":"2112.13609","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.13609","created_at":"2026-07-05T06:24:08Z"},{"alias_kind":"arxiv_version","alias_value":"2112.13609v1","created_at":"2026-07-05T06:24:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.13609","created_at":"2026-07-05T06:24:08Z"},{"alias_kind":"pith_short_12","alias_value":"N7CHM23OGC5T","created_at":"2026-07-05T06:24:08Z"},{"alias_kind":"pith_short_16","alias_value":"N7CHM23OGC5T6EPG","created_at":"2026-07-05T06:24:08Z"},{"alias_kind":"pith_short_8","alias_value":"N7CHM23O","created_at":"2026-07-05T06:24:08Z"}],"graph_snapshots":[{"event_id":"sha256:c3490a437d9b48ccc07983176ecff8378f1d10d8a9090225171fd639818533c5","target":"graph","created_at":"2026-07-05T06:24:08Z","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/2112.13609/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Jiankang Shi, Jianxiong Cao, Minghua Chen, Yubin Yan","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-12-27T11:05:45Z","title":"Correction of high-order $L_k$ approximation for subdiffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.13609","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":"sha256:00addad6a3e2d1ec3ceff8891a3b094463ab7af53543c299e8568daf43d60250","target":"record","created_at":"2026-07-05T06:24:08Z","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":"797be841bafb0b22365eb495f5b4fec2d1dd1cebc5bce9f9095cd4e5e24bb687","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-12-27T11:05:45Z","title_canon_sha256":"030be531ded08f535a817c803201ec0b3d9b7dbb4b766c2b0d5f10373f5e8f05"},"schema_version":"1.0","source":{"id":"2112.13609","kind":"arxiv","version":1}},"canonical_sha256":"6fc4766b6e30bb3f11e6be56ceb0a0f394eee87c90437f4ee6b8eff430e41872","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fc4766b6e30bb3f11e6be56ceb0a0f394eee87c90437f4ee6b8eff430e41872","first_computed_at":"2026-07-05T06:24:08.708321Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:24:08.708321Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OEOJLkeBQ3Y8CsCQu6sQvJA5dqVgsJfzOKD8BbyIlrW08h13TgyM6WLuMlIP5gV6OdCpzZbM+lnhN0YkARVGAw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:24:08.708808Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.13609","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00addad6a3e2d1ec3ceff8891a3b094463ab7af53543c299e8568daf43d60250","sha256:c3490a437d9b48ccc07983176ecff8378f1d10d8a9090225171fd639818533c5"],"state_sha256":"c751ed3e6bbd868c8c809fbd072422b6969eaa5ad94e53490ef2a8a897b5828e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t0/6k2IaWO+MYG2wX/NcWK6dOPlKflEm1AzI9Lqp+r8SNqrBP/d0RrWc+6gKCY2QGBWkKEsz2BJxrvBqoLWuAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T20:29:41.182202Z","bundle_sha256":"1fc73ef9067915af582610b4bfaa724692e1698574ddfc168debabcedd7eaec3"}}