{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:H4CRM3E3MFOMBHPODWFYZQZBL6","short_pith_number":"pith:H4CRM3E3","canonical_record":{"source":{"id":"1907.00440","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-30T19:52:05Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"7805e1bdb29dc2c383aaa6eeb8a316230eb300144938621cf9bcf0ae2b3acb3d","abstract_canon_sha256":"0145476655d6805228e02e6bd7d67457e017e04026a205f41afdda69196945f7"},"schema_version":"1.0"},"canonical_sha256":"3f05166c9b615cc09dee1d8b8cc3215f868fb9b169b28fb4bea0ccdde47afe7d","source":{"kind":"arxiv","id":"1907.00440","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.00440","created_at":"2026-05-17T23:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"1907.00440v1","created_at":"2026-05-17T23:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.00440","created_at":"2026-05-17T23:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"H4CRM3E3MFOM","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"H4CRM3E3MFOMBHPO","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"H4CRM3E3","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:H4CRM3E3MFOMBHPODWFYZQZBL6","target":"record","payload":{"canonical_record":{"source":{"id":"1907.00440","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-30T19:52:05Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"7805e1bdb29dc2c383aaa6eeb8a316230eb300144938621cf9bcf0ae2b3acb3d","abstract_canon_sha256":"0145476655d6805228e02e6bd7d67457e017e04026a205f41afdda69196945f7"},"schema_version":"1.0"},"canonical_sha256":"3f05166c9b615cc09dee1d8b8cc3215f868fb9b169b28fb4bea0ccdde47afe7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:51.716889Z","signature_b64":"h2a1vt+ltqpHvtIh19MP3OVCfgOwNxyqvegwoIiW0WTBjWzWMzmpw7FjTAuNW/57axfZo3gwCp0Tb5vQD+SECA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f05166c9b615cc09dee1d8b8cc3215f868fb9b169b28fb4bea0ccdde47afe7d","last_reissued_at":"2026-05-17T23:41:51.716145Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:51.716145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.00440","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":"2026-05-17T23:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VX6k6AGzk4T4ZH7uWoRQMd2ziJUmP+zTDrO5SicCi5yPm1QxDgVD7hMrJempznDmdz5glPlQoeR0F0TI2bdXCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T01:22:48.871104Z"},"content_sha256":"87ebbda095efe62a9db6c76d85b8f6d23aec6518f4727b76116995acd36ee814","schema_version":"1.0","event_id":"sha256:87ebbda095efe62a9db6c76d85b8f6d23aec6518f4727b76116995acd36ee814"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:H4CRM3E3MFOMBHPODWFYZQZBL6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Prager-Synge theorem in reconstruction based a posteriori error estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Daniele Boffi, Fleurianne Bertrand","submitted_at":"2019-06-30T19:52:05Z","abstract_excerpt":"In this paper we review the hypercircle method of Prager and Synge. This theory inspired several studies and induced an active research in the area of a posteriori error analysis. In particular, we review the Braess--Sch\\\"oberl error estimator in the context of the Poisson problem. We discuss adaptive finite element schemes based on two variants of the estimator and we prove the convergence and optimality of the resulting algorithms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00440","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":"2026-05-17T23:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q/6e/LJF808q/lUNtfH6qiI277F89ZR2thrxkw2CNuWJIrkLk/aq54hTTTzs/sGAl75YD7FhuMZss8IF4wCRCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T01:22:48.871476Z"},"content_sha256":"1fdd825c967a57e3357be2b90dcad6527320aa614b1b61bc979b882a18f975fa","schema_version":"1.0","event_id":"sha256:1fdd825c967a57e3357be2b90dcad6527320aa614b1b61bc979b882a18f975fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H4CRM3E3MFOMBHPODWFYZQZBL6/bundle.json","state_url":"https://pith.science/pith/H4CRM3E3MFOMBHPODWFYZQZBL6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H4CRM3E3MFOMBHPODWFYZQZBL6/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":"2026-06-22T01:22:48Z","links":{"resolver":"https://pith.science/pith/H4CRM3E3MFOMBHPODWFYZQZBL6","bundle":"https://pith.science/pith/H4CRM3E3MFOMBHPODWFYZQZBL6/bundle.json","state":"https://pith.science/pith/H4CRM3E3MFOMBHPODWFYZQZBL6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H4CRM3E3MFOMBHPODWFYZQZBL6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:H4CRM3E3MFOMBHPODWFYZQZBL6","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":"0145476655d6805228e02e6bd7d67457e017e04026a205f41afdda69196945f7","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-30T19:52:05Z","title_canon_sha256":"7805e1bdb29dc2c383aaa6eeb8a316230eb300144938621cf9bcf0ae2b3acb3d"},"schema_version":"1.0","source":{"id":"1907.00440","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.00440","created_at":"2026-05-17T23:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"1907.00440v1","created_at":"2026-05-17T23:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.00440","created_at":"2026-05-17T23:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"H4CRM3E3MFOM","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"H4CRM3E3MFOMBHPO","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"H4CRM3E3","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:1fdd825c967a57e3357be2b90dcad6527320aa614b1b61bc979b882a18f975fa","target":"graph","created_at":"2026-05-17T23:41:51Z","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":"In this paper we review the hypercircle method of Prager and Synge. This theory inspired several studies and induced an active research in the area of a posteriori error analysis. In particular, we review the Braess--Sch\\\"oberl error estimator in the context of the Poisson problem. We discuss adaptive finite element schemes based on two variants of the estimator and we prove the convergence and optimality of the resulting algorithms.","authors_text":"Daniele Boffi, Fleurianne Bertrand","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-30T19:52:05Z","title":"The Prager-Synge theorem in reconstruction based a posteriori error estimation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00440","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":"sha256:87ebbda095efe62a9db6c76d85b8f6d23aec6518f4727b76116995acd36ee814","target":"record","created_at":"2026-05-17T23:41:51Z","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":"0145476655d6805228e02e6bd7d67457e017e04026a205f41afdda69196945f7","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-30T19:52:05Z","title_canon_sha256":"7805e1bdb29dc2c383aaa6eeb8a316230eb300144938621cf9bcf0ae2b3acb3d"},"schema_version":"1.0","source":{"id":"1907.00440","kind":"arxiv","version":1}},"canonical_sha256":"3f05166c9b615cc09dee1d8b8cc3215f868fb9b169b28fb4bea0ccdde47afe7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f05166c9b615cc09dee1d8b8cc3215f868fb9b169b28fb4bea0ccdde47afe7d","first_computed_at":"2026-05-17T23:41:51.716145Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:51.716145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h2a1vt+ltqpHvtIh19MP3OVCfgOwNxyqvegwoIiW0WTBjWzWMzmpw7FjTAuNW/57axfZo3gwCp0Tb5vQD+SECA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:51.716889Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.00440","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87ebbda095efe62a9db6c76d85b8f6d23aec6518f4727b76116995acd36ee814","sha256:1fdd825c967a57e3357be2b90dcad6527320aa614b1b61bc979b882a18f975fa"],"state_sha256":"615ba9c4941c95a81949d03c45515f863ed583b716cad65833e46cba8c9f9a82"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"COOfmOgULseQPwN6XLPwUmytTyQp7rpnSMgqqEYw1m2y5QL0zCudh7p4I5YAmWW36zv8cFqb12U7121sbThMCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T01:22:48.873386Z","bundle_sha256":"bbd3ddd0663322cf76bc168880723e58cd3a2457c3ac003153915e79216dcafc"}}