{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:HX3MKKXEKR3ARE5EBBMZ4DB4HX","short_pith_number":"pith:HX3MKKXE","canonical_record":{"source":{"id":"2603.27714","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-03-29T14:34:27Z","cross_cats_sorted":["cs.NA","math.DG"],"title_canon_sha256":"06bbde0a3c1cce98b88ef57804fd38380f3a4f0a998c7b742f4ac917d4734f66","abstract_canon_sha256":"e4b284f62bc74fb5138eb5dcc67d49242f3187120a3bd62cd07f9b3870b9768b"},"schema_version":"1.0"},"canonical_sha256":"3df6c52ae454760893a408599e0c3c3dd6f12e78d47f04603eacb66ec45f0238","source":{"kind":"arxiv","id":"2603.27714","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.27714","created_at":"2026-06-19T16:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"2603.27714v2","created_at":"2026-06-19T16:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.27714","created_at":"2026-06-19T16:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"HX3MKKXEKR3A","created_at":"2026-06-19T16:11:22Z"},{"alias_kind":"pith_short_16","alias_value":"HX3MKKXEKR3ARE5E","created_at":"2026-06-19T16:11:22Z"},{"alias_kind":"pith_short_8","alias_value":"HX3MKKXE","created_at":"2026-06-19T16:11:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:HX3MKKXEKR3ARE5EBBMZ4DB4HX","target":"record","payload":{"canonical_record":{"source":{"id":"2603.27714","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-03-29T14:34:27Z","cross_cats_sorted":["cs.NA","math.DG"],"title_canon_sha256":"06bbde0a3c1cce98b88ef57804fd38380f3a4f0a998c7b742f4ac917d4734f66","abstract_canon_sha256":"e4b284f62bc74fb5138eb5dcc67d49242f3187120a3bd62cd07f9b3870b9768b"},"schema_version":"1.0"},"canonical_sha256":"3df6c52ae454760893a408599e0c3c3dd6f12e78d47f04603eacb66ec45f0238","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:11:22.567159Z","signature_b64":"VRecalOB/g9jnyyD1EN6oYPM8vmjJvXQlLaE4+0Xn5g7Heh/+psKOFjbvhE4OpqI0aoBgvbTa1fp1npl6tViBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3df6c52ae454760893a408599e0c3c3dd6f12e78d47f04603eacb66ec45f0238","last_reissued_at":"2026-06-19T16:11:22.566814Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:11:22.566814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2603.27714","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":"2026-06-19T16:11:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"070wGo93xcujndCL89niY1FAhRjCet4JZRFFaL7T+vYM3MhgXx2SNwCSjWyCFtYHIcJ/VoTe3Iz5GaAyZMLPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T18:11:04.733907Z"},"content_sha256":"f0a6ebb33f991964891b6b977d6a18f3aae5b7e6e4450358673f5c4fb8a38678","schema_version":"1.0","event_id":"sha256:f0a6ebb33f991964891b6b977d6a18f3aae5b7e6e4450358673f5c4fb8a38678"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:HX3MKKXEKR3ARE5EBBMZ4DB4HX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Releasing the pressure: High-order surface flow discretizations via discrete Helmholtz-Hodge decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.DG"],"primary_cat":"math.NA","authors_text":"Christoph Lehrenfeld, Max Wardetzky, Tim Br\\\"uers, Tim van Beeck","submitted_at":"2026-03-29T14:34:27Z","abstract_excerpt":"We present a discrete Helmholtz--Hodge decomposition for H(div)-conforming Brezzi--Douglas--Marini (BDM) finite elements on triangulated surfaces of arbitrary topology. The divergence-free BDM subspace is split L2-orthogonally into rotated gradients of a continuous streamfunction space and a finite-dimensional space of discrete harmonic fields whose dimension equals the first Betti number of the surface. Consequently, any incompressible flow discretized on this subspace can be reformulated with a scalar streamfunction and finitely many harmonic coefficients as the only unknowns. This eliminate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.27714","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/2603.27714/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":"2026-06-19T16:11:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WWWtocEKvQWgFfiguBPfAKd0RvdkKDw30qnGrvKJfSNlafdEGzcBNCV1XnVu7PsmZkfsahPW1vT82GhuxJ1cDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T18:11:04.734289Z"},"content_sha256":"9e254059a8259f074b0ff30a99c023dd9a897f9462e8dbffb5d34715e7e14883","schema_version":"1.0","event_id":"sha256:9e254059a8259f074b0ff30a99c023dd9a897f9462e8dbffb5d34715e7e14883"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HX3MKKXEKR3ARE5EBBMZ4DB4HX/bundle.json","state_url":"https://pith.science/pith/HX3MKKXEKR3ARE5EBBMZ4DB4HX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HX3MKKXEKR3ARE5EBBMZ4DB4HX/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":"2026-06-21T18:11:04Z","links":{"resolver":"https://pith.science/pith/HX3MKKXEKR3ARE5EBBMZ4DB4HX","bundle":"https://pith.science/pith/HX3MKKXEKR3ARE5EBBMZ4DB4HX/bundle.json","state":"https://pith.science/pith/HX3MKKXEKR3ARE5EBBMZ4DB4HX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HX3MKKXEKR3ARE5EBBMZ4DB4HX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HX3MKKXEKR3ARE5EBBMZ4DB4HX","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":"e4b284f62bc74fb5138eb5dcc67d49242f3187120a3bd62cd07f9b3870b9768b","cross_cats_sorted":["cs.NA","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-03-29T14:34:27Z","title_canon_sha256":"06bbde0a3c1cce98b88ef57804fd38380f3a4f0a998c7b742f4ac917d4734f66"},"schema_version":"1.0","source":{"id":"2603.27714","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.27714","created_at":"2026-06-19T16:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"2603.27714v2","created_at":"2026-06-19T16:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.27714","created_at":"2026-06-19T16:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"HX3MKKXEKR3A","created_at":"2026-06-19T16:11:22Z"},{"alias_kind":"pith_short_16","alias_value":"HX3MKKXEKR3ARE5E","created_at":"2026-06-19T16:11:22Z"},{"alias_kind":"pith_short_8","alias_value":"HX3MKKXE","created_at":"2026-06-19T16:11:22Z"}],"graph_snapshots":[{"event_id":"sha256:9e254059a8259f074b0ff30a99c023dd9a897f9462e8dbffb5d34715e7e14883","target":"graph","created_at":"2026-06-19T16:11:22Z","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/2603.27714/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a discrete Helmholtz--Hodge decomposition for H(div)-conforming Brezzi--Douglas--Marini (BDM) finite elements on triangulated surfaces of arbitrary topology. The divergence-free BDM subspace is split L2-orthogonally into rotated gradients of a continuous streamfunction space and a finite-dimensional space of discrete harmonic fields whose dimension equals the first Betti number of the surface. Consequently, any incompressible flow discretized on this subspace can be reformulated with a scalar streamfunction and finitely many harmonic coefficients as the only unknowns. This eliminate","authors_text":"Christoph Lehrenfeld, Max Wardetzky, Tim Br\\\"uers, Tim van Beeck","cross_cats":["cs.NA","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-03-29T14:34:27Z","title":"Releasing the pressure: High-order surface flow discretizations via discrete Helmholtz-Hodge decompositions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.27714","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:f0a6ebb33f991964891b6b977d6a18f3aae5b7e6e4450358673f5c4fb8a38678","target":"record","created_at":"2026-06-19T16:11:22Z","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":"e4b284f62bc74fb5138eb5dcc67d49242f3187120a3bd62cd07f9b3870b9768b","cross_cats_sorted":["cs.NA","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-03-29T14:34:27Z","title_canon_sha256":"06bbde0a3c1cce98b88ef57804fd38380f3a4f0a998c7b742f4ac917d4734f66"},"schema_version":"1.0","source":{"id":"2603.27714","kind":"arxiv","version":2}},"canonical_sha256":"3df6c52ae454760893a408599e0c3c3dd6f12e78d47f04603eacb66ec45f0238","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3df6c52ae454760893a408599e0c3c3dd6f12e78d47f04603eacb66ec45f0238","first_computed_at":"2026-06-19T16:11:22.566814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:22.566814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VRecalOB/g9jnyyD1EN6oYPM8vmjJvXQlLaE4+0Xn5g7Heh/+psKOFjbvhE4OpqI0aoBgvbTa1fp1npl6tViBQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:22.567159Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.27714","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0a6ebb33f991964891b6b977d6a18f3aae5b7e6e4450358673f5c4fb8a38678","sha256:9e254059a8259f074b0ff30a99c023dd9a897f9462e8dbffb5d34715e7e14883"],"state_sha256":"750cb641f1108a21cd72e622c018bf22c0586801e92a9d3ed36566452bff4727"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NBd1cXvGfop7sjKq2bf52Grb9x/8jgh0m4O49StTdy+L+fBkxBy+S/kRptOLzjB/Q2qIUiJWAzGyJ41hrTa1BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T18:11:04.736463Z","bundle_sha256":"082adaedaecdc3cc59f62299338a6df374d87fb1284d6a02531632d4db7d025c"}}