{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HKPOM7MJYT7MDBMBLU46UUZ7A3","short_pith_number":"pith:HKPOM7MJ","canonical_record":{"source":{"id":"1310.0066","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-09-30T21:31:43Z","cross_cats_sorted":[],"title_canon_sha256":"a17b73bba7906f9d6bb665beec0350147e5c53c58ab1a609677cb1b5e13e97f8","abstract_canon_sha256":"49bfeeecfc4db36ce4cf9e7482d593b67d75dabed1b5133cce09e3d9cd4b910b"},"schema_version":"1.0"},"canonical_sha256":"3a9ee67d89c4fec185815d39ea533f06de326314c87a580c2b5f1135914f2eb5","source":{"kind":"arxiv","id":"1310.0066","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0066","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0066v1","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0066","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"HKPOM7MJYT7M","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HKPOM7MJYT7MDBMB","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HKPOM7MJ","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HKPOM7MJYT7MDBMBLU46UUZ7A3","target":"record","payload":{"canonical_record":{"source":{"id":"1310.0066","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-09-30T21:31:43Z","cross_cats_sorted":[],"title_canon_sha256":"a17b73bba7906f9d6bb665beec0350147e5c53c58ab1a609677cb1b5e13e97f8","abstract_canon_sha256":"49bfeeecfc4db36ce4cf9e7482d593b67d75dabed1b5133cce09e3d9cd4b910b"},"schema_version":"1.0"},"canonical_sha256":"3a9ee67d89c4fec185815d39ea533f06de326314c87a580c2b5f1135914f2eb5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:45.749897Z","signature_b64":"sE1SQbON8KTQ1ukyrVti97KgTTpWk++J7a+XGomesVhSxA33Gsb0V5RFHRpo5Nr78A+oZMOhBBxS5TZDKAE2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a9ee67d89c4fec185815d39ea533f06de326314c87a580c2b5f1135914f2eb5","last_reissued_at":"2026-05-18T03:11:45.749235Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:45.749235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.0066","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":"2026-05-18T03:11:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5GRgleMK080GpDRGRs79LJPtjPoj5h2hLgTjp/rOrYqDzQctUS/0/HaTLTHLeOtMqSvoMCn/tKE54vX3/XP2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:11:24.725630Z"},"content_sha256":"8b84a697f9ee683010e5e5ce74b99000ebdf58d38d06e0e32795aa5b7630430e","schema_version":"1.0","event_id":"sha256:8b84a697f9ee683010e5e5ce74b99000ebdf58d38d06e0e32795aa5b7630430e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HKPOM7MJYT7MDBMBLU46UUZ7A3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Error Analysis of Finite Element Methods for Space-Fractional Parabolic Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Bangti Jin, Joseph Pasciak, Raytcho Lazarov, Zhi Zhou","submitted_at":"2013-09-30T21:31:43Z","abstract_excerpt":"We consider an initial/boundary value problem for one-dimensional fractional-order parabolic equations with a space fractional derivative of Riemann-Liouville type and order $\\alpha\\in (1,2)$. We study a spatial semidiscrete scheme with the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and Crank-Nicolson method. Error estimates in the $L^2\\II$- and $H^{\\alpha/2}\\II$-norm are derived for the semidiscrete scheme, and in the $L^2\\II$-norm for the fully discrete schemes. These estimates are for bo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0066","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":"2026-05-18T03:11:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Yxz0uzN1ar/exdO8X2+QgzaUCaeRECVH1f1TstGPFrmOdnKgsOmakEzXJUCBS4umVotljrzs21BG3RUIO8OAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:11:24.725993Z"},"content_sha256":"2b9da134e168f24e010482eaf034247a5580c23b6cd4aaa81d1be717aff131ed","schema_version":"1.0","event_id":"sha256:2b9da134e168f24e010482eaf034247a5580c23b6cd4aaa81d1be717aff131ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HKPOM7MJYT7MDBMBLU46UUZ7A3/bundle.json","state_url":"https://pith.science/pith/HKPOM7MJYT7MDBMBLU46UUZ7A3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HKPOM7MJYT7MDBMBLU46UUZ7A3/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":"2026-05-30T07:11:24Z","links":{"resolver":"https://pith.science/pith/HKPOM7MJYT7MDBMBLU46UUZ7A3","bundle":"https://pith.science/pith/HKPOM7MJYT7MDBMBLU46UUZ7A3/bundle.json","state":"https://pith.science/pith/HKPOM7MJYT7MDBMBLU46UUZ7A3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HKPOM7MJYT7MDBMBLU46UUZ7A3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HKPOM7MJYT7MDBMBLU46UUZ7A3","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":"49bfeeecfc4db36ce4cf9e7482d593b67d75dabed1b5133cce09e3d9cd4b910b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-09-30T21:31:43Z","title_canon_sha256":"a17b73bba7906f9d6bb665beec0350147e5c53c58ab1a609677cb1b5e13e97f8"},"schema_version":"1.0","source":{"id":"1310.0066","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0066","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0066v1","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0066","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"HKPOM7MJYT7M","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HKPOM7MJYT7MDBMB","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HKPOM7MJ","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:2b9da134e168f24e010482eaf034247a5580c23b6cd4aaa81d1be717aff131ed","target":"graph","created_at":"2026-05-18T03:11:45Z","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":"We consider an initial/boundary value problem for one-dimensional fractional-order parabolic equations with a space fractional derivative of Riemann-Liouville type and order $\\alpha\\in (1,2)$. We study a spatial semidiscrete scheme with the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and Crank-Nicolson method. Error estimates in the $L^2\\II$- and $H^{\\alpha/2}\\II$-norm are derived for the semidiscrete scheme, and in the $L^2\\II$-norm for the fully discrete schemes. These estimates are for bo","authors_text":"Bangti Jin, Joseph Pasciak, Raytcho Lazarov, Zhi Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-09-30T21:31:43Z","title":"Error Analysis of Finite Element Methods for Space-Fractional Parabolic Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0066","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":"sha256:8b84a697f9ee683010e5e5ce74b99000ebdf58d38d06e0e32795aa5b7630430e","target":"record","created_at":"2026-05-18T03:11:45Z","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":"49bfeeecfc4db36ce4cf9e7482d593b67d75dabed1b5133cce09e3d9cd4b910b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-09-30T21:31:43Z","title_canon_sha256":"a17b73bba7906f9d6bb665beec0350147e5c53c58ab1a609677cb1b5e13e97f8"},"schema_version":"1.0","source":{"id":"1310.0066","kind":"arxiv","version":1}},"canonical_sha256":"3a9ee67d89c4fec185815d39ea533f06de326314c87a580c2b5f1135914f2eb5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a9ee67d89c4fec185815d39ea533f06de326314c87a580c2b5f1135914f2eb5","first_computed_at":"2026-05-18T03:11:45.749235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:45.749235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sE1SQbON8KTQ1ukyrVti97KgTTpWk++J7a+XGomesVhSxA33Gsb0V5RFHRpo5Nr78A+oZMOhBBxS5TZDKAE2Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:45.749897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.0066","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b84a697f9ee683010e5e5ce74b99000ebdf58d38d06e0e32795aa5b7630430e","sha256:2b9da134e168f24e010482eaf034247a5580c23b6cd4aaa81d1be717aff131ed"],"state_sha256":"503d4b2075ec11bd71db990cc3f6bbabb8b19827caa4e38caeb80591af34db82"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vdVkmy7oTIWPTaC+uXGuZix13IZATi/7RtFJ7uc17kN0CjFg1yAeku8xMROQ5SJxi4iRKoDVg2XHOd1+wbIuBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:11:24.728151Z","bundle_sha256":"710bc5168a694d3c1d79f02bf908d123e366a8ccbf01c89e06f055123eb45b73"}}