{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OATJAAQVJDY7NZD2P2FHLIBATM","short_pith_number":"pith:OATJAAQV","canonical_record":{"source":{"id":"1406.4371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-17T14:09:26Z","cross_cats_sorted":[],"title_canon_sha256":"edd63be59259e6601bbec1b5e5002343472ff17b6c84f4a2a245e1bc93e88808","abstract_canon_sha256":"5ffd6b7634530157ff3ed9a03aa79d4225206e25bd60c77dec0a5332fe4943d0"},"schema_version":"1.0"},"canonical_sha256":"702690021548f1f6e47a7e8a75a0209b13cf31e901bca34d24f631f2f98ff14c","source":{"kind":"arxiv","id":"1406.4371","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4371","created_at":"2026-05-18T02:49:37Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4371v1","created_at":"2026-05-18T02:49:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4371","created_at":"2026-05-18T02:49:37Z"},{"alias_kind":"pith_short_12","alias_value":"OATJAAQVJDY7","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OATJAAQVJDY7NZD2","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OATJAAQV","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OATJAAQVJDY7NZD2P2FHLIBATM","target":"record","payload":{"canonical_record":{"source":{"id":"1406.4371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-17T14:09:26Z","cross_cats_sorted":[],"title_canon_sha256":"edd63be59259e6601bbec1b5e5002343472ff17b6c84f4a2a245e1bc93e88808","abstract_canon_sha256":"5ffd6b7634530157ff3ed9a03aa79d4225206e25bd60c77dec0a5332fe4943d0"},"schema_version":"1.0"},"canonical_sha256":"702690021548f1f6e47a7e8a75a0209b13cf31e901bca34d24f631f2f98ff14c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:37.713676Z","signature_b64":"sxmi0iY/M6XcY0sZf/7UTgvIrsIeknYmjKV0CFer5hhLvMIuFLo8ZFtlXQo8/7292PTClhSo1cyk+9sbkEtrBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"702690021548f1f6e47a7e8a75a0209b13cf31e901bca34d24f631f2f98ff14c","last_reissued_at":"2026-05-18T02:49:37.713185Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:37.713185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.4371","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":"2026-05-18T02:49:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R+y/ME1L1lj1KC0aHi3VcI/GKCmao2pCdCUWAPJagglOYtc/3kFF+Y5+ra5GNcQgkJLD3p5CYu/uoVkIDuEOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:50:22.501664Z"},"content_sha256":"f9416ae5e4688f2e77981d9d3e54ed07a64e3ad044d8b9918d6eaa6ff3f5cf69","schema_version":"1.0","event_id":"sha256:f9416ae5e4688f2e77981d9d3e54ed07a64e3ad044d8b9918d6eaa6ff3f5cf69"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OATJAAQVJDY7NZD2P2FHLIBATM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Error estimates for stabilized finite element methods applied to ill-posed problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Erik Burman","submitted_at":"2014-06-17T14:09:26Z","abstract_excerpt":"We propose an analysis for the stabilized finite element methods proposed in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive, and ill-posed problems. Part I: Elliptic equations. SIAM J. Sci. Comput., 35(6) 2013, valid in the case of ill-posed problems for which only weak continuous dependence can be assumed. A priori and a posteriori error estimates are obtained without assuming coercivity or inf-sup stability of the continuous problem. A numerical example illustrates the theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4371","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":"2026-05-18T02:49:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VQ9pyMNA4uGPhiGWxuQO/CChMUgKI1RH4KVs61PVOBkOXK2VHsMF7FlYwfs1FwyTpJLf4OIlWOPqXRSDHo3ODQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:50:22.502017Z"},"content_sha256":"ee4483a12e48c21cf39daacd16d62f6f43bed732df92d7609df5be6127c0daae","schema_version":"1.0","event_id":"sha256:ee4483a12e48c21cf39daacd16d62f6f43bed732df92d7609df5be6127c0daae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OATJAAQVJDY7NZD2P2FHLIBATM/bundle.json","state_url":"https://pith.science/pith/OATJAAQVJDY7NZD2P2FHLIBATM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OATJAAQVJDY7NZD2P2FHLIBATM/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":"2026-05-27T15:50:22Z","links":{"resolver":"https://pith.science/pith/OATJAAQVJDY7NZD2P2FHLIBATM","bundle":"https://pith.science/pith/OATJAAQVJDY7NZD2P2FHLIBATM/bundle.json","state":"https://pith.science/pith/OATJAAQVJDY7NZD2P2FHLIBATM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OATJAAQVJDY7NZD2P2FHLIBATM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OATJAAQVJDY7NZD2P2FHLIBATM","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":"5ffd6b7634530157ff3ed9a03aa79d4225206e25bd60c77dec0a5332fe4943d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-17T14:09:26Z","title_canon_sha256":"edd63be59259e6601bbec1b5e5002343472ff17b6c84f4a2a245e1bc93e88808"},"schema_version":"1.0","source":{"id":"1406.4371","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4371","created_at":"2026-05-18T02:49:37Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4371v1","created_at":"2026-05-18T02:49:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4371","created_at":"2026-05-18T02:49:37Z"},{"alias_kind":"pith_short_12","alias_value":"OATJAAQVJDY7","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OATJAAQVJDY7NZD2","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OATJAAQV","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:ee4483a12e48c21cf39daacd16d62f6f43bed732df92d7609df5be6127c0daae","target":"graph","created_at":"2026-05-18T02:49:37Z","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 propose an analysis for the stabilized finite element methods proposed in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive, and ill-posed problems. Part I: Elliptic equations. SIAM J. Sci. Comput., 35(6) 2013, valid in the case of ill-posed problems for which only weak continuous dependence can be assumed. A priori and a posteriori error estimates are obtained without assuming coercivity or inf-sup stability of the continuous problem. A numerical example illustrates the theory.","authors_text":"Erik Burman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-17T14:09:26Z","title":"Error estimates for stabilized finite element methods applied to ill-posed problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4371","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:f9416ae5e4688f2e77981d9d3e54ed07a64e3ad044d8b9918d6eaa6ff3f5cf69","target":"record","created_at":"2026-05-18T02:49:37Z","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":"5ffd6b7634530157ff3ed9a03aa79d4225206e25bd60c77dec0a5332fe4943d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-17T14:09:26Z","title_canon_sha256":"edd63be59259e6601bbec1b5e5002343472ff17b6c84f4a2a245e1bc93e88808"},"schema_version":"1.0","source":{"id":"1406.4371","kind":"arxiv","version":1}},"canonical_sha256":"702690021548f1f6e47a7e8a75a0209b13cf31e901bca34d24f631f2f98ff14c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"702690021548f1f6e47a7e8a75a0209b13cf31e901bca34d24f631f2f98ff14c","first_computed_at":"2026-05-18T02:49:37.713185Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:37.713185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sxmi0iY/M6XcY0sZf/7UTgvIrsIeknYmjKV0CFer5hhLvMIuFLo8ZFtlXQo8/7292PTClhSo1cyk+9sbkEtrBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:37.713676Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.4371","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9416ae5e4688f2e77981d9d3e54ed07a64e3ad044d8b9918d6eaa6ff3f5cf69","sha256:ee4483a12e48c21cf39daacd16d62f6f43bed732df92d7609df5be6127c0daae"],"state_sha256":"c91db4b64477613435967325639979ca3c672241c93c7c76e01e856f703cc7d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vkEo7oGcqnsi8AzZYVX/P0wKYyPoft03ks140V0gXPh+XrWlafSETHP3v/y/arhHmxTAJFgpQ+hF4vvZ1kQbDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T15:50:22.505196Z","bundle_sha256":"f0caec1e412ceefad20a23a90dd35e1d274e219ccde2203542b63be6b222ac0a"}}