{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VRFURHM26NGBQQAFNQHEK7N7LP","short_pith_number":"pith:VRFURHM2","canonical_record":{"source":{"id":"1803.03437","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-03-09T09:44:30Z","cross_cats_sorted":[],"title_canon_sha256":"1667ecc0c33d39bb8fb61357461f9331c870b1fbc00a02cbf40e095e7f50c50c","abstract_canon_sha256":"6196a75b945a9ff90f7fc3b8f9c7382321003de83ad37b3154098dcd6004e1e2"},"schema_version":"1.0"},"canonical_sha256":"ac4b489d9af34c1840056c0e457dbf5bc31176d2fcd1b8b387580002a9b03832","source":{"kind":"arxiv","id":"1803.03437","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03437","created_at":"2026-05-18T00:21:39Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03437v1","created_at":"2026-05-18T00:21:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03437","created_at":"2026-05-18T00:21:39Z"},{"alias_kind":"pith_short_12","alias_value":"VRFURHM26NGB","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VRFURHM26NGBQQAF","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VRFURHM2","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VRFURHM26NGBQQAFNQHEK7N7LP","target":"record","payload":{"canonical_record":{"source":{"id":"1803.03437","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-03-09T09:44:30Z","cross_cats_sorted":[],"title_canon_sha256":"1667ecc0c33d39bb8fb61357461f9331c870b1fbc00a02cbf40e095e7f50c50c","abstract_canon_sha256":"6196a75b945a9ff90f7fc3b8f9c7382321003de83ad37b3154098dcd6004e1e2"},"schema_version":"1.0"},"canonical_sha256":"ac4b489d9af34c1840056c0e457dbf5bc31176d2fcd1b8b387580002a9b03832","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:39.561542Z","signature_b64":"v5GLk8EJYkhuOK7D5sfqxydiEMpRehD9rba2/j2+x5wj+iUGFhyOIygJjtBxUZKr6K8vefV1Z4yfTIpm2OoFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac4b489d9af34c1840056c0e457dbf5bc31176d2fcd1b8b387580002a9b03832","last_reissued_at":"2026-05-18T00:21:39.560837Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:39.560837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.03437","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":"2026-05-18T00:21:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rr6C0GpXyxbtbtPzh7pbINUv19phhrcnX99l3ZlNtH6oIww4b+iFRIGdjYMYycSobaAO1aurGfYYn7t0aFWXDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:49:18.462171Z"},"content_sha256":"16e099ad9d439573f00c13d9e19877fedac895b09185f632681781479e34e29e","schema_version":"1.0","event_id":"sha256:16e099ad9d439573f00c13d9e19877fedac895b09185f632681781479e34e29e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VRFURHM26NGBQQAFNQHEK7N7LP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A space-time finite element method for fractional wave problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Binjie Li, Hao Luo, Xiaoping Xie","submitted_at":"2018-03-09T09:44:30Z","abstract_excerpt":"This paper analyzes a space-time finite element method for fractional wave problems. The method uses a Petrov-Galerkin type time-stepping scheme to discretize the time fractional derivative of order $ \\gamma $ ($1<\\gamma<2$). We establish the stability of this method, and derive the optimal convergence in the $ H^1(0,T;L^2(\\Omega)) $-norm and suboptimal convergence in the discrete $ L^\\infty(0,T;H_0^1(\\Omega)) $-norm. Furthermore, we discuss the performance of this method in the case that the solution has singularity at $ t= 0 $, and show that optimal convergence rate with respect to the $ H^1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03437","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":""},"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":"2026-05-18T00:21:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mcOTOU98sMJt5v6vniDQL/Siv7Bl6xll/9TixA5BQRLf5bH/bV150nFSGveEJj1cOX6eCp8wWKpCjeZwvGukCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:49:18.462838Z"},"content_sha256":"a4b22fb4ce34d276d2109cbeb25cd772fc7ada5a68fabdc1c31039a4fd789d10","schema_version":"1.0","event_id":"sha256:a4b22fb4ce34d276d2109cbeb25cd772fc7ada5a68fabdc1c31039a4fd789d10"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VRFURHM26NGBQQAFNQHEK7N7LP/bundle.json","state_url":"https://pith.science/pith/VRFURHM26NGBQQAFNQHEK7N7LP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VRFURHM26NGBQQAFNQHEK7N7LP/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":"2026-05-31T11:49:18Z","links":{"resolver":"https://pith.science/pith/VRFURHM26NGBQQAFNQHEK7N7LP","bundle":"https://pith.science/pith/VRFURHM26NGBQQAFNQHEK7N7LP/bundle.json","state":"https://pith.science/pith/VRFURHM26NGBQQAFNQHEK7N7LP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VRFURHM26NGBQQAFNQHEK7N7LP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VRFURHM26NGBQQAFNQHEK7N7LP","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":"6196a75b945a9ff90f7fc3b8f9c7382321003de83ad37b3154098dcd6004e1e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-03-09T09:44:30Z","title_canon_sha256":"1667ecc0c33d39bb8fb61357461f9331c870b1fbc00a02cbf40e095e7f50c50c"},"schema_version":"1.0","source":{"id":"1803.03437","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03437","created_at":"2026-05-18T00:21:39Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03437v1","created_at":"2026-05-18T00:21:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03437","created_at":"2026-05-18T00:21:39Z"},{"alias_kind":"pith_short_12","alias_value":"VRFURHM26NGB","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VRFURHM26NGBQQAF","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VRFURHM2","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:a4b22fb4ce34d276d2109cbeb25cd772fc7ada5a68fabdc1c31039a4fd789d10","target":"graph","created_at":"2026-05-18T00:21:39Z","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"},"paper":{"abstract_excerpt":"This paper analyzes a space-time finite element method for fractional wave problems. The method uses a Petrov-Galerkin type time-stepping scheme to discretize the time fractional derivative of order $ \\gamma $ ($1<\\gamma<2$). We establish the stability of this method, and derive the optimal convergence in the $ H^1(0,T;L^2(\\Omega)) $-norm and suboptimal convergence in the discrete $ L^\\infty(0,T;H_0^1(\\Omega)) $-norm. Furthermore, we discuss the performance of this method in the case that the solution has singularity at $ t= 0 $, and show that optimal convergence rate with respect to the $ H^1","authors_text":"Binjie Li, Hao Luo, Xiaoping Xie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-03-09T09:44:30Z","title":"A space-time finite element method for fractional wave problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03437","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":"sha256:16e099ad9d439573f00c13d9e19877fedac895b09185f632681781479e34e29e","target":"record","created_at":"2026-05-18T00:21:39Z","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":"6196a75b945a9ff90f7fc3b8f9c7382321003de83ad37b3154098dcd6004e1e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-03-09T09:44:30Z","title_canon_sha256":"1667ecc0c33d39bb8fb61357461f9331c870b1fbc00a02cbf40e095e7f50c50c"},"schema_version":"1.0","source":{"id":"1803.03437","kind":"arxiv","version":1}},"canonical_sha256":"ac4b489d9af34c1840056c0e457dbf5bc31176d2fcd1b8b387580002a9b03832","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac4b489d9af34c1840056c0e457dbf5bc31176d2fcd1b8b387580002a9b03832","first_computed_at":"2026-05-18T00:21:39.560837Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:39.560837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v5GLk8EJYkhuOK7D5sfqxydiEMpRehD9rba2/j2+x5wj+iUGFhyOIygJjtBxUZKr6K8vefV1Z4yfTIpm2OoFCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:39.561542Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03437","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16e099ad9d439573f00c13d9e19877fedac895b09185f632681781479e34e29e","sha256:a4b22fb4ce34d276d2109cbeb25cd772fc7ada5a68fabdc1c31039a4fd789d10"],"state_sha256":"e7ce207592a6082233725be9c9dcb5c375a2d9b78ae48596a77d48a470c97f02"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/g4QTKELWhlAzxKu/BRy4MD9KE+1+Or5jT343cV2Kc/gkJUV8izelkvRssQIu1l1CjZ+lsXpcD/hMSCGckO+BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T11:49:18.466240Z","bundle_sha256":"c01b6522423ab72e6cef793a0ae921157c2d535bb2a7079ce6a1b8389a6437cb"}}