{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:5WQ75TR3OOAFXJNC3B3IPXKV7C","short_pith_number":"pith:5WQ75TR3","canonical_record":{"source":{"id":"1805.04147","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-10T19:42:58Z","cross_cats_sorted":[],"title_canon_sha256":"9234885897a17e52f83a600f06ba6196fba22c00511bcaffa8873846aaf2eb95","abstract_canon_sha256":"7c8742c8aca285a4ae64805c4caba1c2945c801eaeac810515c5318dc4bfff27"},"schema_version":"1.0"},"canonical_sha256":"eda1fece3b73805ba5a2d87687dd55f880a1ccf3bd7af203ad8784d758e7b4c4","source":{"kind":"arxiv","id":"1805.04147","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.04147","created_at":"2026-05-18T00:16:13Z"},{"alias_kind":"arxiv_version","alias_value":"1805.04147v1","created_at":"2026-05-18T00:16:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.04147","created_at":"2026-05-18T00:16:13Z"},{"alias_kind":"pith_short_12","alias_value":"5WQ75TR3OOAF","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5WQ75TR3OOAFXJNC","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5WQ75TR3","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:5WQ75TR3OOAFXJNC3B3IPXKV7C","target":"record","payload":{"canonical_record":{"source":{"id":"1805.04147","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-10T19:42:58Z","cross_cats_sorted":[],"title_canon_sha256":"9234885897a17e52f83a600f06ba6196fba22c00511bcaffa8873846aaf2eb95","abstract_canon_sha256":"7c8742c8aca285a4ae64805c4caba1c2945c801eaeac810515c5318dc4bfff27"},"schema_version":"1.0"},"canonical_sha256":"eda1fece3b73805ba5a2d87687dd55f880a1ccf3bd7af203ad8784d758e7b4c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:13.493146Z","signature_b64":"ousf5g/bQOPD/j+CY/7bzgeib3EgmPwVSXq3JpW7QQaZvSJ+yTYXG2IgLQC6uAVho6uUXN66Lt+86I980V5jDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eda1fece3b73805ba5a2d87687dd55f880a1ccf3bd7af203ad8784d758e7b4c4","last_reissued_at":"2026-05-18T00:16:13.492535Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:13.492535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.04147","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":"2026-05-18T00:16:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y+exgiTjnnVePNe7YtLMeHb78zlADdYnYy92REMkxayb3ZcBorgCObpSpMRm8rsxQ7jagNeNLQ1SOkoB3cWeDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T11:48:21.771705Z"},"content_sha256":"a963e49c109d35681f4d53ff87e97cddd03b4fef22c7e51dde7d4ab781567d1d","schema_version":"1.0","event_id":"sha256:a963e49c109d35681f4d53ff87e97cddd03b4fef22c7e51dde7d4ab781567d1d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:5WQ75TR3OOAFXJNC3B3IPXKV7C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New a priori analysis of first-order system least-squares finite element methods for parabolic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Michael Karkulik, Thomas F\\\"uhrer","submitted_at":"2018-05-10T19:42:58Z","abstract_excerpt":"We provide new insights into the a priori theory for a time-stepping scheme based on least-squares finite element methods for parabolic first-order systems. The elliptic part of the problem is of general reaction-convection-diffusion type. The new ingredient in the analysis is an elliptic projection operator defined via a non-symmetric bilinear form, although the main bilinear form corresponding to the least-squares functional is symmetric. This new operator allows to prove optimal error estimates in the natural norm associated to the problem and, under additional regularity assumptions, in th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04147","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":"2026-05-18T00:16:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZnaqV/MBDynD3AYQTCArSqoasKzWHEdUJaV3uTElhTzDQh7JXYL95EIk3W7keyo5WdfxawFeWS7aXdCV3i++CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T11:48:21.772055Z"},"content_sha256":"5db870b3274f639a00697beb99453b505a0a6296ca1c9b32d5c7ec1231aca2ae","schema_version":"1.0","event_id":"sha256:5db870b3274f639a00697beb99453b505a0a6296ca1c9b32d5c7ec1231aca2ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5WQ75TR3OOAFXJNC3B3IPXKV7C/bundle.json","state_url":"https://pith.science/pith/5WQ75TR3OOAFXJNC3B3IPXKV7C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5WQ75TR3OOAFXJNC3B3IPXKV7C/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":"2026-05-20T11:48:21Z","links":{"resolver":"https://pith.science/pith/5WQ75TR3OOAFXJNC3B3IPXKV7C","bundle":"https://pith.science/pith/5WQ75TR3OOAFXJNC3B3IPXKV7C/bundle.json","state":"https://pith.science/pith/5WQ75TR3OOAFXJNC3B3IPXKV7C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5WQ75TR3OOAFXJNC3B3IPXKV7C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5WQ75TR3OOAFXJNC3B3IPXKV7C","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":"7c8742c8aca285a4ae64805c4caba1c2945c801eaeac810515c5318dc4bfff27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-10T19:42:58Z","title_canon_sha256":"9234885897a17e52f83a600f06ba6196fba22c00511bcaffa8873846aaf2eb95"},"schema_version":"1.0","source":{"id":"1805.04147","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.04147","created_at":"2026-05-18T00:16:13Z"},{"alias_kind":"arxiv_version","alias_value":"1805.04147v1","created_at":"2026-05-18T00:16:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.04147","created_at":"2026-05-18T00:16:13Z"},{"alias_kind":"pith_short_12","alias_value":"5WQ75TR3OOAF","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5WQ75TR3OOAFXJNC","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5WQ75TR3","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:5db870b3274f639a00697beb99453b505a0a6296ca1c9b32d5c7ec1231aca2ae","target":"graph","created_at":"2026-05-18T00:16:13Z","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 provide new insights into the a priori theory for a time-stepping scheme based on least-squares finite element methods for parabolic first-order systems. The elliptic part of the problem is of general reaction-convection-diffusion type. The new ingredient in the analysis is an elliptic projection operator defined via a non-symmetric bilinear form, although the main bilinear form corresponding to the least-squares functional is symmetric. This new operator allows to prove optimal error estimates in the natural norm associated to the problem and, under additional regularity assumptions, in th","authors_text":"Michael Karkulik, Thomas F\\\"uhrer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-10T19:42:58Z","title":"New a priori analysis of first-order system least-squares finite element methods for parabolic problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04147","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:a963e49c109d35681f4d53ff87e97cddd03b4fef22c7e51dde7d4ab781567d1d","target":"record","created_at":"2026-05-18T00:16:13Z","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":"7c8742c8aca285a4ae64805c4caba1c2945c801eaeac810515c5318dc4bfff27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-05-10T19:42:58Z","title_canon_sha256":"9234885897a17e52f83a600f06ba6196fba22c00511bcaffa8873846aaf2eb95"},"schema_version":"1.0","source":{"id":"1805.04147","kind":"arxiv","version":1}},"canonical_sha256":"eda1fece3b73805ba5a2d87687dd55f880a1ccf3bd7af203ad8784d758e7b4c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eda1fece3b73805ba5a2d87687dd55f880a1ccf3bd7af203ad8784d758e7b4c4","first_computed_at":"2026-05-18T00:16:13.492535Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:13.492535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ousf5g/bQOPD/j+CY/7bzgeib3EgmPwVSXq3JpW7QQaZvSJ+yTYXG2IgLQC6uAVho6uUXN66Lt+86I980V5jDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:13.493146Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.04147","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a963e49c109d35681f4d53ff87e97cddd03b4fef22c7e51dde7d4ab781567d1d","sha256:5db870b3274f639a00697beb99453b505a0a6296ca1c9b32d5c7ec1231aca2ae"],"state_sha256":"22564bc3597008dbc943d6581f4fafbe9d46376c6d1fb8baf1f3936c87be4428"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DgZyDbUfg96DgGUr0nUy0rUrDIjKYs7EKMpZtmTlUMUyA9M9Pz8N2MQgBttokocZvyqi8+gi5yK6WcpTlDWWCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T11:48:21.774104Z","bundle_sha256":"df19dec14b05c90fd7c842fc86a4cc010b310d36954586d47db68bbe0860f6d6"}}