{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:ZRUQPOFLGOJA6HHHQPEFBKRV6V","short_pith_number":"pith:ZRUQPOFL","canonical_record":{"source":{"id":"2509.17899","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-09-22T15:27:29Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"4e990d0d4e55000f2d6aa33d23b16bf87fe3f7fedc78e0db3c431b3e43e8e0ae","abstract_canon_sha256":"f9ba5080e98621f31a7d13c0facc4963f8c3e8393a5f7ff7329665b68bb09975"},"schema_version":"1.0"},"canonical_sha256":"cc6907b8ab33920f1ce783c850aa35f547b579dd4620d212e6fb9433ec9d1704","source":{"kind":"arxiv","id":"2509.17899","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.17899","created_at":"2026-06-26T00:15:22Z"},{"alias_kind":"arxiv_version","alias_value":"2509.17899v2","created_at":"2026-06-26T00:15:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.17899","created_at":"2026-06-26T00:15:22Z"},{"alias_kind":"pith_short_12","alias_value":"ZRUQPOFLGOJA","created_at":"2026-06-26T00:15:22Z"},{"alias_kind":"pith_short_16","alias_value":"ZRUQPOFLGOJA6HHH","created_at":"2026-06-26T00:15:22Z"},{"alias_kind":"pith_short_8","alias_value":"ZRUQPOFL","created_at":"2026-06-26T00:15:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:ZRUQPOFLGOJA6HHHQPEFBKRV6V","target":"record","payload":{"canonical_record":{"source":{"id":"2509.17899","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-09-22T15:27:29Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"4e990d0d4e55000f2d6aa33d23b16bf87fe3f7fedc78e0db3c431b3e43e8e0ae","abstract_canon_sha256":"f9ba5080e98621f31a7d13c0facc4963f8c3e8393a5f7ff7329665b68bb09975"},"schema_version":"1.0"},"canonical_sha256":"cc6907b8ab33920f1ce783c850aa35f547b579dd4620d212e6fb9433ec9d1704","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-26T00:15:22.704780Z","signature_b64":"P9JuyoFCKZFhtjqsvdXgbgiHikeNfXwWT0/S1JHQy8+QZlMbS14ceYD2aOMWWCjMPOAiU6JuvSU43JEqJdh5CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc6907b8ab33920f1ce783c850aa35f547b579dd4620d212e6fb9433ec9d1704","last_reissued_at":"2026-06-26T00:15:22.704347Z","signature_status":"signed_v1","first_computed_at":"2026-06-26T00:15:22.704347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.17899","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-26T00:15:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6MYLQe2EVyziSHvjFRfMb5Kuoz9kK1KDKvkKh4nOOuI9Ckb9N0afeGSxps9rKl5UntAvGGQuUYiEp3U7va7KBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T02:46:54.418800Z"},"content_sha256":"021bf35a2137a751f7813ebad6b44dc06e5e1bd52402bb1c3c2992d3299b8fac","schema_version":"1.0","event_id":"sha256:021bf35a2137a751f7813ebad6b44dc06e5e1bd52402bb1c3c2992d3299b8fac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:ZRUQPOFLGOJA6HHHQPEFBKRV6V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scott-Vogelius element and iterated penalty method for inhomogeneous Dirichlet boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Franziska Eickmann, L. Ridgway Scott, Tabea Tscherpel","submitted_at":"2025-09-22T15:27:29Z","abstract_excerpt":"We present quasi-optimal a priori error estimates for general mixed finite element methods to approximate solutions of the Stokes problem subject to inhomogeneous Dirichlet boundary conditions. For the Scott--Vogelius element this yields pressure-robust a priori error stimates. Due to the exact divergence constraint, this requires a compatibility condition for the boundary data to hold. A key tool is a modified Fortin operator, capable of preserving this compatibility condition. Furthermore, we analyse the iterated penalty method, an Uzawa-type algorithm and we show its convergence and asympto"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.17899","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.17899/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-26T00:15:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uvGb8epNTwyBZI+LkOkf799LCGs/uHrXl8AaQ2rRSUm7QoEoPmDLAabiCjL2rQjwv3m1OnASQyEZLRYq0AFjAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T02:46:54.419330Z"},"content_sha256":"4401cf896b847b9fd91ca518d692b801cada036f3522785118a5df795447ff59","schema_version":"1.0","event_id":"sha256:4401cf896b847b9fd91ca518d692b801cada036f3522785118a5df795447ff59"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZRUQPOFLGOJA6HHHQPEFBKRV6V/bundle.json","state_url":"https://pith.science/pith/ZRUQPOFLGOJA6HHHQPEFBKRV6V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZRUQPOFLGOJA6HHHQPEFBKRV6V/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":"2026-08-23T02:46:54Z","links":{"resolver":"https://pith.science/pith/ZRUQPOFLGOJA6HHHQPEFBKRV6V","bundle":"https://pith.science/pith/ZRUQPOFLGOJA6HHHQPEFBKRV6V/bundle.json","state":"https://pith.science/pith/ZRUQPOFLGOJA6HHHQPEFBKRV6V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZRUQPOFLGOJA6HHHQPEFBKRV6V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZRUQPOFLGOJA6HHHQPEFBKRV6V","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":"f9ba5080e98621f31a7d13c0facc4963f8c3e8393a5f7ff7329665b68bb09975","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-09-22T15:27:29Z","title_canon_sha256":"4e990d0d4e55000f2d6aa33d23b16bf87fe3f7fedc78e0db3c431b3e43e8e0ae"},"schema_version":"1.0","source":{"id":"2509.17899","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.17899","created_at":"2026-06-26T00:15:22Z"},{"alias_kind":"arxiv_version","alias_value":"2509.17899v2","created_at":"2026-06-26T00:15:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.17899","created_at":"2026-06-26T00:15:22Z"},{"alias_kind":"pith_short_12","alias_value":"ZRUQPOFLGOJA","created_at":"2026-06-26T00:15:22Z"},{"alias_kind":"pith_short_16","alias_value":"ZRUQPOFLGOJA6HHH","created_at":"2026-06-26T00:15:22Z"},{"alias_kind":"pith_short_8","alias_value":"ZRUQPOFL","created_at":"2026-06-26T00:15:22Z"}],"graph_snapshots":[{"event_id":"sha256:4401cf896b847b9fd91ca518d692b801cada036f3522785118a5df795447ff59","target":"graph","created_at":"2026-06-26T00:15:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2509.17899/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present quasi-optimal a priori error estimates for general mixed finite element methods to approximate solutions of the Stokes problem subject to inhomogeneous Dirichlet boundary conditions. For the Scott--Vogelius element this yields pressure-robust a priori error stimates. Due to the exact divergence constraint, this requires a compatibility condition for the boundary data to hold. A key tool is a modified Fortin operator, capable of preserving this compatibility condition. Furthermore, we analyse the iterated penalty method, an Uzawa-type algorithm and we show its convergence and asympto","authors_text":"Franziska Eickmann, L. Ridgway Scott, Tabea Tscherpel","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-09-22T15:27:29Z","title":"Scott-Vogelius element and iterated penalty method for inhomogeneous Dirichlet boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.17899","kind":"arxiv","version":2},"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":"sha256:021bf35a2137a751f7813ebad6b44dc06e5e1bd52402bb1c3c2992d3299b8fac","target":"record","created_at":"2026-06-26T00:15:22Z","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":"f9ba5080e98621f31a7d13c0facc4963f8c3e8393a5f7ff7329665b68bb09975","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-09-22T15:27:29Z","title_canon_sha256":"4e990d0d4e55000f2d6aa33d23b16bf87fe3f7fedc78e0db3c431b3e43e8e0ae"},"schema_version":"1.0","source":{"id":"2509.17899","kind":"arxiv","version":2}},"canonical_sha256":"cc6907b8ab33920f1ce783c850aa35f547b579dd4620d212e6fb9433ec9d1704","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc6907b8ab33920f1ce783c850aa35f547b579dd4620d212e6fb9433ec9d1704","first_computed_at":"2026-06-26T00:15:22.704347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T00:15:22.704347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P9JuyoFCKZFhtjqsvdXgbgiHikeNfXwWT0/S1JHQy8+QZlMbS14ceYD2aOMWWCjMPOAiU6JuvSU43JEqJdh5CQ==","signature_status":"signed_v1","signed_at":"2026-06-26T00:15:22.704780Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.17899","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:021bf35a2137a751f7813ebad6b44dc06e5e1bd52402bb1c3c2992d3299b8fac","sha256:4401cf896b847b9fd91ca518d692b801cada036f3522785118a5df795447ff59"],"state_sha256":"123910701ea5cacad756c2cd2a72a0afd6b9133ec6ceaef6a082d0868d02955c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WnWH6Ej4zi8vk86JV2TkekkV/9YgrbrE0To0ZUEzrE1mXlBnSwU6peLad65NI7PoggKtuWTRzUrHFWKxtCUFCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T02:46:54.424167Z","bundle_sha256":"5149d061fa18df7f3cd2f1cfc811a6fcbd4e1283cf444ee9059be037238a4f9d"}}