{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:YQKR2LS7OIVXB2B3NDTWUDND76","short_pith_number":"pith:YQKR2LS7","canonical_record":{"source":{"id":"1610.05017","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-17T08:56:04Z","cross_cats_sorted":[],"title_canon_sha256":"be6a81c8cdf5bde02c211a39b21b2e3f6e2ec165123e234db1033999536921ab","abstract_canon_sha256":"5efcb76a98be123c8ef6d6953fa2857dd34ef7002c08debe91a79052e997aa82"},"schema_version":"1.0"},"canonical_sha256":"c4151d2e5f722b70e83b68e76a0da3ff910a28826147a796211dd30f152bf6fc","source":{"kind":"arxiv","id":"1610.05017","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05017","created_at":"2026-05-18T00:43:39Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05017v3","created_at":"2026-05-18T00:43:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05017","created_at":"2026-05-18T00:43:39Z"},{"alias_kind":"pith_short_12","alias_value":"YQKR2LS7OIVX","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YQKR2LS7OIVXB2B3","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YQKR2LS7","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:YQKR2LS7OIVXB2B3NDTWUDND76","target":"record","payload":{"canonical_record":{"source":{"id":"1610.05017","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-17T08:56:04Z","cross_cats_sorted":[],"title_canon_sha256":"be6a81c8cdf5bde02c211a39b21b2e3f6e2ec165123e234db1033999536921ab","abstract_canon_sha256":"5efcb76a98be123c8ef6d6953fa2857dd34ef7002c08debe91a79052e997aa82"},"schema_version":"1.0"},"canonical_sha256":"c4151d2e5f722b70e83b68e76a0da3ff910a28826147a796211dd30f152bf6fc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:39.587800Z","signature_b64":"kddSl8xv/qy7wr+n5E4lmioImHS6TNmJnqK/933UdXc8hDwlguiQy/Evzk22doKMwozzA68qyO7Ddw3QJ9j5Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4151d2e5f722b70e83b68e76a0da3ff910a28826147a796211dd30f152bf6fc","last_reissued_at":"2026-05-18T00:43:39.587396Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:39.587396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.05017","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:43:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AKvl2kTjsCMs1zfaoaeUJUd8bEZf6RyMFklDHoGeByT2TDPRlDGKJzIN9ezZnpBylcYx5dpiZc07/xPOlGd0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:08:19.724948Z"},"content_sha256":"7ba4d905fdacf0cf3c8088720501ca27c56c85a72e996f1fb2d1715a6a52e79e","schema_version":"1.0","event_id":"sha256:7ba4d905fdacf0cf3c8088720501ca27c56c85a72e996f1fb2d1715a6a52e79e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:YQKR2LS7OIVXB2B3NDTWUDND76","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis of the grad-div stabilization for the time-dependent Navier-Stokes equations with inf-sup stable finite elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Bosco Garc\\'ia-Archilla, Javier de Frutos, Julia Novo, Volker John","submitted_at":"2016-10-17T08:56:04Z","abstract_excerpt":"This paper studies inf-sup stable finite element discretizations of the evolutionary Navier--Stokes equations with a grad-div type stabilization. The analysis covers both the case in which the solution is assumed to be smooth and consequently has to satisfy nonlocal compatibility conditions as well as the practically relevant situation in which the nonlocal compatibility conditions are not satisfied. The constants in the error bounds obtained do not depend on negative powers of the viscosity. Taking into account the loss of regularity suffered by the solution of the Navier--Stokes equations at"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05017","kind":"arxiv","version":3},"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":"2026-05-18T00:43:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OG3IysYcA4u5xmTZu4tblHxfL6JzNBEC904lYzZK4FzMqMF+GpYNTgMl4RpokwGa6aB6rIvKq5pfRcYAInGVAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:08:19.725388Z"},"content_sha256":"eac0e54d9d4724b25e77bb126cff0da96361aaa68bd849c5583d1d60252c27c5","schema_version":"1.0","event_id":"sha256:eac0e54d9d4724b25e77bb126cff0da96361aaa68bd849c5583d1d60252c27c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YQKR2LS7OIVXB2B3NDTWUDND76/bundle.json","state_url":"https://pith.science/pith/YQKR2LS7OIVXB2B3NDTWUDND76/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YQKR2LS7OIVXB2B3NDTWUDND76/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":"2026-05-25T20:08:19Z","links":{"resolver":"https://pith.science/pith/YQKR2LS7OIVXB2B3NDTWUDND76","bundle":"https://pith.science/pith/YQKR2LS7OIVXB2B3NDTWUDND76/bundle.json","state":"https://pith.science/pith/YQKR2LS7OIVXB2B3NDTWUDND76/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YQKR2LS7OIVXB2B3NDTWUDND76/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YQKR2LS7OIVXB2B3NDTWUDND76","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":"5efcb76a98be123c8ef6d6953fa2857dd34ef7002c08debe91a79052e997aa82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-17T08:56:04Z","title_canon_sha256":"be6a81c8cdf5bde02c211a39b21b2e3f6e2ec165123e234db1033999536921ab"},"schema_version":"1.0","source":{"id":"1610.05017","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05017","created_at":"2026-05-18T00:43:39Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05017v3","created_at":"2026-05-18T00:43:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05017","created_at":"2026-05-18T00:43:39Z"},{"alias_kind":"pith_short_12","alias_value":"YQKR2LS7OIVX","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YQKR2LS7OIVXB2B3","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YQKR2LS7","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:eac0e54d9d4724b25e77bb126cff0da96361aaa68bd849c5583d1d60252c27c5","target":"graph","created_at":"2026-05-18T00:43:39Z","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 studies inf-sup stable finite element discretizations of the evolutionary Navier--Stokes equations with a grad-div type stabilization. The analysis covers both the case in which the solution is assumed to be smooth and consequently has to satisfy nonlocal compatibility conditions as well as the practically relevant situation in which the nonlocal compatibility conditions are not satisfied. The constants in the error bounds obtained do not depend on negative powers of the viscosity. Taking into account the loss of regularity suffered by the solution of the Navier--Stokes equations at","authors_text":"Bosco Garc\\'ia-Archilla, Javier de Frutos, Julia Novo, Volker John","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-17T08:56:04Z","title":"Analysis of the grad-div stabilization for the time-dependent Navier-Stokes equations with inf-sup stable finite elements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05017","kind":"arxiv","version":3},"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":"sha256:7ba4d905fdacf0cf3c8088720501ca27c56c85a72e996f1fb2d1715a6a52e79e","target":"record","created_at":"2026-05-18T00:43:39Z","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":"5efcb76a98be123c8ef6d6953fa2857dd34ef7002c08debe91a79052e997aa82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-17T08:56:04Z","title_canon_sha256":"be6a81c8cdf5bde02c211a39b21b2e3f6e2ec165123e234db1033999536921ab"},"schema_version":"1.0","source":{"id":"1610.05017","kind":"arxiv","version":3}},"canonical_sha256":"c4151d2e5f722b70e83b68e76a0da3ff910a28826147a796211dd30f152bf6fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4151d2e5f722b70e83b68e76a0da3ff910a28826147a796211dd30f152bf6fc","first_computed_at":"2026-05-18T00:43:39.587396Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:39.587396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kddSl8xv/qy7wr+n5E4lmioImHS6TNmJnqK/933UdXc8hDwlguiQy/Evzk22doKMwozzA68qyO7Ddw3QJ9j5Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:39.587800Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.05017","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ba4d905fdacf0cf3c8088720501ca27c56c85a72e996f1fb2d1715a6a52e79e","sha256:eac0e54d9d4724b25e77bb126cff0da96361aaa68bd849c5583d1d60252c27c5"],"state_sha256":"9dd27fc5e5a075b7b283932945e0a14b4fc2d1b9891c6c09cd60f7ee0949285b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eRhpfgw8fXar5bV1QNRaceR6XmRnx2ixvGlNeccsLE+iGE6uD2ATWHbnJf1DXu6JHWUX3nAzXrpOWq4CtqtDDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T20:08:19.728395Z","bundle_sha256":"d427b4ba720283dd5c4002929345ac9548e96953e75226b200d0b318b0bfa22b"}}