{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:YAZO7HR4JNDBJW4QF6JYGACKGT","short_pith_number":"pith:YAZO7HR4","schema_version":"1.0","canonical_sha256":"c032ef9e3c4b4614db902f9383004a34cc601fae0be945f641aed839dfea1800","source":{"kind":"arxiv","id":"2605.31348","version":1},"attestation_state":"computed","paper":{"title":"Cohomology of Finite Element Stokes Complexes on Alfeld Splits","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Charles Parker, Pablo D. Brubeck, Yizhou Liang","submitted_at":"2026-05-29T14:26:52Z","abstract_excerpt":"We show that the cohomology of the finite element Stokes complex consisting of piecewise polynomials spaces on an Alfeld split mesh from Fu, Guzm\\'{a}n, & Neilan (2020, Math. Comp., 89, 1059--1091) is isomorphic to the cohomologies of the continuous Stokes and de Rham complexes. We also construct novel \"minimal\" conforming finite element complexes where the $H^1$-conforming space is the lowest-order space from Guzm\\'{a}n & Neilan (2018, SIAM J. Numer. Anal., 56, 2826--2844) and the $L^2$-conforming space is piecewise constants. These minimal complexes also have cohomologies isomorphic to the c"},"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":"2605.31348","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-05-29T14:26:52Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"0baf61af922e493f3373aa2d5c933dfd198ba47f8c6186a9e06946af72ac1097","abstract_canon_sha256":"465f531c6ff9e198cfa8aa72da04afa97a77797c08e68d0f85fa2d98ea2f3319"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-01T02:04:00.118230Z","signature_b64":"l4LeG0QU+/2TgCNF1C8zU4o87Ja22mdgl4dNK1Rh+PNfOrneONrvsL4MBJJXp+xZI90SqZPopiov+wIr95TRBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c032ef9e3c4b4614db902f9383004a34cc601fae0be945f641aed839dfea1800","last_reissued_at":"2026-06-01T02:04:00.117423Z","signature_status":"signed_v1","first_computed_at":"2026-06-01T02:04:00.117423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cohomology of Finite Element Stokes Complexes on Alfeld Splits","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Charles Parker, Pablo D. Brubeck, Yizhou Liang","submitted_at":"2026-05-29T14:26:52Z","abstract_excerpt":"We show that the cohomology of the finite element Stokes complex consisting of piecewise polynomials spaces on an Alfeld split mesh from Fu, Guzm\\'{a}n, & Neilan (2020, Math. Comp., 89, 1059--1091) is isomorphic to the cohomologies of the continuous Stokes and de Rham complexes. We also construct novel \"minimal\" conforming finite element complexes where the $H^1$-conforming space is the lowest-order space from Guzm\\'{a}n & Neilan (2018, SIAM J. Numer. Anal., 56, 2826--2844) and the $L^2$-conforming space is piecewise constants. These minimal complexes also have cohomologies isomorphic to the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.31348","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/2605.31348/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":"2605.31348","created_at":"2026-06-01T02:04:00.117561+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.31348v1","created_at":"2026-06-01T02:04:00.117561+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.31348","created_at":"2026-06-01T02:04:00.117561+00:00"},{"alias_kind":"pith_short_12","alias_value":"YAZO7HR4JNDB","created_at":"2026-06-01T02:04:00.117561+00:00"},{"alias_kind":"pith_short_16","alias_value":"YAZO7HR4JNDBJW4Q","created_at":"2026-06-01T02:04:00.117561+00:00"},{"alias_kind":"pith_short_8","alias_value":"YAZO7HR4","created_at":"2026-06-01T02:04:00.117561+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/YAZO7HR4JNDBJW4QF6JYGACKGT","json":"https://pith.science/pith/YAZO7HR4JNDBJW4QF6JYGACKGT.json","graph_json":"https://pith.science/api/pith-number/YAZO7HR4JNDBJW4QF6JYGACKGT/graph.json","events_json":"https://pith.science/api/pith-number/YAZO7HR4JNDBJW4QF6JYGACKGT/events.json","paper":"https://pith.science/paper/YAZO7HR4"},"agent_actions":{"view_html":"https://pith.science/pith/YAZO7HR4JNDBJW4QF6JYGACKGT","download_json":"https://pith.science/pith/YAZO7HR4JNDBJW4QF6JYGACKGT.json","view_paper":"https://pith.science/paper/YAZO7HR4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.31348&json=true","fetch_graph":"https://pith.science/api/pith-number/YAZO7HR4JNDBJW4QF6JYGACKGT/graph.json","fetch_events":"https://pith.science/api/pith-number/YAZO7HR4JNDBJW4QF6JYGACKGT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YAZO7HR4JNDBJW4QF6JYGACKGT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YAZO7HR4JNDBJW4QF6JYGACKGT/action/storage_attestation","attest_author":"https://pith.science/pith/YAZO7HR4JNDBJW4QF6JYGACKGT/action/author_attestation","sign_citation":"https://pith.science/pith/YAZO7HR4JNDBJW4QF6JYGACKGT/action/citation_signature","submit_replication":"https://pith.science/pith/YAZO7HR4JNDBJW4QF6JYGACKGT/action/replication_record"}},"created_at":"2026-06-01T02:04:00.117561+00:00","updated_at":"2026-06-01T02:04:00.117561+00:00"}