{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:KIO3XKWP3CKWVKEQOEX5RHHZG2","short_pith_number":"pith:KIO3XKWP","canonical_record":{"source":{"id":"2411.14561","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-21T20:18:34Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"d78b9a0e8d433ac77ef4fae9af9f4880c14f1e040cdb622b373b2d73cb4f3500","abstract_canon_sha256":"d45ffec53137b947569975b01a59ea79a6b72a98f82df04520d2cedd0c4511d7"},"schema_version":"1.0"},"canonical_sha256":"521dbbaacfd8956aa890712fd89cf9369b941b1d8fd674f09bd7c81fb590bf75","source":{"kind":"arxiv","id":"2411.14561","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.14561","created_at":"2026-07-05T09:38:53Z"},{"alias_kind":"arxiv_version","alias_value":"2411.14561v1","created_at":"2026-07-05T09:38:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14561","created_at":"2026-07-05T09:38:53Z"},{"alias_kind":"pith_short_12","alias_value":"KIO3XKWP3CKW","created_at":"2026-07-05T09:38:53Z"},{"alias_kind":"pith_short_16","alias_value":"KIO3XKWP3CKWVKEQ","created_at":"2026-07-05T09:38:53Z"},{"alias_kind":"pith_short_8","alias_value":"KIO3XKWP","created_at":"2026-07-05T09:38:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:KIO3XKWP3CKWVKEQOEX5RHHZG2","target":"record","payload":{"canonical_record":{"source":{"id":"2411.14561","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-21T20:18:34Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"d78b9a0e8d433ac77ef4fae9af9f4880c14f1e040cdb622b373b2d73cb4f3500","abstract_canon_sha256":"d45ffec53137b947569975b01a59ea79a6b72a98f82df04520d2cedd0c4511d7"},"schema_version":"1.0"},"canonical_sha256":"521dbbaacfd8956aa890712fd89cf9369b941b1d8fd674f09bd7c81fb590bf75","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:38:53.198887Z","signature_b64":"FXWCnXZdFU+k8FwrHIzeG+qH85sUaVtO519/uVG8b4RkkDhY6wEnLIHV6jj7Ic/4MT266h4RFa7VkJfKtDFTCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"521dbbaacfd8956aa890712fd89cf9369b941b1d8fd674f09bd7c81fb590bf75","last_reissued_at":"2026-07-05T09:38:53.198498Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:38:53.198498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.14561","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":"2026-07-05T09:38:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lOJGtLn+OtFZDHWOzghfCoA14bWHzZToIJnm7cGB1/SlI1y3PBV2wpKj1pHMk3HgF/pc21C8tMI8SUGDBczoBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T22:47:58.238980Z"},"content_sha256":"9dcbf84fdc158fbe03a923225458869d09b7ef743b9fa80d74aeddda9bc8a444","schema_version":"1.0","event_id":"sha256:9dcbf84fdc158fbe03a923225458869d09b7ef743b9fa80d74aeddda9bc8a444"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:KIO3XKWP3CKWVKEQOEX5RHHZG2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Will Pazner","submitted_at":"2024-11-21T20:18:34Z","abstract_excerpt":"In this paper, we construct and analyze preconditioners for the interior penalty discontinuous Galerkin discretization posed in the space $H(\\mathrm{div})$. These discretizations are used as one component in exactly divergence-free pressure-robust discretizations for the Stokes problem. Three preconditioners are presently considered: a subspace correction preconditioner using vertex patches and the lowest-order $H^1$-conforming space as a coarse space, a fictitious space preconditioner using the degree-$p$ discontinuous Galerkin space, and an auxiliary space preconditioner using the degree-$(p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14561","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.14561/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":"2026-07-05T09:38:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7XKxBtT/rNRcWFRCYbDAe1HGCXJd6r4vMZHv2c8WfZfOBkcjXIDck1CKXH8QH6XyMNJZTlcQ0JH17dE/DPzuDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T22:47:58.240447Z"},"content_sha256":"f12abef45c72ee38442a504cb866fba43d35c178726234d06e0650fcf791eed5","schema_version":"1.0","event_id":"sha256:f12abef45c72ee38442a504cb866fba43d35c178726234d06e0650fcf791eed5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KIO3XKWP3CKWVKEQOEX5RHHZG2/bundle.json","state_url":"https://pith.science/pith/KIO3XKWP3CKWVKEQOEX5RHHZG2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KIO3XKWP3CKWVKEQOEX5RHHZG2/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":"2026-08-13T22:47:58Z","links":{"resolver":"https://pith.science/pith/KIO3XKWP3CKWVKEQOEX5RHHZG2","bundle":"https://pith.science/pith/KIO3XKWP3CKWVKEQOEX5RHHZG2/bundle.json","state":"https://pith.science/pith/KIO3XKWP3CKWVKEQOEX5RHHZG2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KIO3XKWP3CKWVKEQOEX5RHHZG2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:KIO3XKWP3CKWVKEQOEX5RHHZG2","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":"d45ffec53137b947569975b01a59ea79a6b72a98f82df04520d2cedd0c4511d7","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-21T20:18:34Z","title_canon_sha256":"d78b9a0e8d433ac77ef4fae9af9f4880c14f1e040cdb622b373b2d73cb4f3500"},"schema_version":"1.0","source":{"id":"2411.14561","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.14561","created_at":"2026-07-05T09:38:53Z"},{"alias_kind":"arxiv_version","alias_value":"2411.14561v1","created_at":"2026-07-05T09:38:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14561","created_at":"2026-07-05T09:38:53Z"},{"alias_kind":"pith_short_12","alias_value":"KIO3XKWP3CKW","created_at":"2026-07-05T09:38:53Z"},{"alias_kind":"pith_short_16","alias_value":"KIO3XKWP3CKWVKEQ","created_at":"2026-07-05T09:38:53Z"},{"alias_kind":"pith_short_8","alias_value":"KIO3XKWP","created_at":"2026-07-05T09:38:53Z"}],"graph_snapshots":[{"event_id":"sha256:f12abef45c72ee38442a504cb866fba43d35c178726234d06e0650fcf791eed5","target":"graph","created_at":"2026-07-05T09:38:53Z","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/2411.14561/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we construct and analyze preconditioners for the interior penalty discontinuous Galerkin discretization posed in the space $H(\\mathrm{div})$. These discretizations are used as one component in exactly divergence-free pressure-robust discretizations for the Stokes problem. Three preconditioners are presently considered: a subspace correction preconditioner using vertex patches and the lowest-order $H^1$-conforming space as a coarse space, a fictitious space preconditioner using the degree-$p$ discontinuous Galerkin space, and an auxiliary space preconditioner using the degree-$(p","authors_text":"Will Pazner","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14561","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":"sha256:9dcbf84fdc158fbe03a923225458869d09b7ef743b9fa80d74aeddda9bc8a444","target":"record","created_at":"2026-07-05T09:38:53Z","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":"d45ffec53137b947569975b01a59ea79a6b72a98f82df04520d2cedd0c4511d7","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-21T20:18:34Z","title_canon_sha256":"d78b9a0e8d433ac77ef4fae9af9f4880c14f1e040cdb622b373b2d73cb4f3500"},"schema_version":"1.0","source":{"id":"2411.14561","kind":"arxiv","version":1}},"canonical_sha256":"521dbbaacfd8956aa890712fd89cf9369b941b1d8fd674f09bd7c81fb590bf75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"521dbbaacfd8956aa890712fd89cf9369b941b1d8fd674f09bd7c81fb590bf75","first_computed_at":"2026-07-05T09:38:53.198498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:38:53.198498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FXWCnXZdFU+k8FwrHIzeG+qH85sUaVtO519/uVG8b4RkkDhY6wEnLIHV6jj7Ic/4MT266h4RFa7VkJfKtDFTCw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:38:53.198887Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.14561","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9dcbf84fdc158fbe03a923225458869d09b7ef743b9fa80d74aeddda9bc8a444","sha256:f12abef45c72ee38442a504cb866fba43d35c178726234d06e0650fcf791eed5"],"state_sha256":"73d2029538333ebbd21caa78af7f178dac710a90dc2d01719fa381f982e28e04"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"48jb5LycERhp7liIG7jdFsn5ZK+KPYR1sM73oOSMTTsl9pvkw1R4+ALj1N36I2ACbxhC4Gun9uaR0w7nTWRhDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T22:47:58.270031Z","bundle_sha256":"f29be29980368a6bbf3ba2642bbc9b0d4a7f8a4a2f8aadbba9722cc59774e9a9"}}