{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:HX3MKKXEKR3ARE5EBBMZ4DB4HX","short_pith_number":"pith:HX3MKKXE","schema_version":"1.0","canonical_sha256":"3df6c52ae454760893a408599e0c3c3dd6f12e78d47f04603eacb66ec45f0238","source":{"kind":"arxiv","id":"2603.27714","version":2},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"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"},"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"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2603.27714","created_at":"2026-06-19T16:11:22.566869+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.27714v2","created_at":"2026-06-19T16:11:22.566869+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.27714","created_at":"2026-06-19T16:11:22.566869+00:00"},{"alias_kind":"pith_short_12","alias_value":"HX3MKKXEKR3A","created_at":"2026-06-19T16:11:22.566869+00:00"},{"alias_kind":"pith_short_16","alias_value":"HX3MKKXEKR3ARE5E","created_at":"2026-06-19T16:11:22.566869+00:00"},{"alias_kind":"pith_short_8","alias_value":"HX3MKKXE","created_at":"2026-06-19T16:11:22.566869+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HX3MKKXEKR3ARE5EBBMZ4DB4HX","json":"https://pith.science/pith/HX3MKKXEKR3ARE5EBBMZ4DB4HX.json","graph_json":"https://pith.science/api/pith-number/HX3MKKXEKR3ARE5EBBMZ4DB4HX/graph.json","events_json":"https://pith.science/api/pith-number/HX3MKKXEKR3ARE5EBBMZ4DB4HX/events.json","paper":"https://pith.science/paper/HX3MKKXE"},"agent_actions":{"view_html":"https://pith.science/pith/HX3MKKXEKR3ARE5EBBMZ4DB4HX","download_json":"https://pith.science/pith/HX3MKKXEKR3ARE5EBBMZ4DB4HX.json","view_paper":"https://pith.science/paper/HX3MKKXE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.27714&json=true","fetch_graph":"https://pith.science/api/pith-number/HX3MKKXEKR3ARE5EBBMZ4DB4HX/graph.json","fetch_events":"https://pith.science/api/pith-number/HX3MKKXEKR3ARE5EBBMZ4DB4HX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HX3MKKXEKR3ARE5EBBMZ4DB4HX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HX3MKKXEKR3ARE5EBBMZ4DB4HX/action/storage_attestation","attest_author":"https://pith.science/pith/HX3MKKXEKR3ARE5EBBMZ4DB4HX/action/author_attestation","sign_citation":"https://pith.science/pith/HX3MKKXEKR3ARE5EBBMZ4DB4HX/action/citation_signature","submit_replication":"https://pith.science/pith/HX3MKKXEKR3ARE5EBBMZ4DB4HX/action/replication_record"}},"created_at":"2026-06-19T16:11:22.566869+00:00","updated_at":"2026-06-19T16:11:22.566869+00:00"}