{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:RBMUTI6C2RJQ2SYQKWXQYKN7QJ","short_pith_number":"pith:RBMUTI6C","schema_version":"1.0","canonical_sha256":"885949a3c2d4530d4b1055af0c29bf824fee700d67db371ee907e2543ea35dfe","source":{"kind":"arxiv","id":"1507.08464","version":1},"attestation_state":"computed","paper":{"title":"Inequalities of Babu\\v{s}ka-Aziz and Friedrichs-Velte for differential forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Martin Costabel (IRMAR)","submitted_at":"2015-07-30T11:38:48Z","abstract_excerpt":"For sufficiently smooth bounded plane domains, the equivalence between the inequalities of Babu{\\v s}ka --Aziz for right inverses of the divergence and of Friedrichs on conjugate harmonic functions was shown by Horgan and Payne in 1983 [7]. In a previous paper [4] we proved that this equivalence, and the equality between the associated constants, is true without any regularity condition on the domain. In three dimensions, Velte [9] studied a generalization of the notion of conjugate harmonic functions and corresponding generalizations of Friedrich's inequality, and he showed for sufficiently s"},"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":"1507.08464","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-30T11:38:48Z","cross_cats_sorted":[],"title_canon_sha256":"3a4ee2cee6b2a5a025bd6c8114327c4ab6e717511be1f90e9bf79e816b0e3e2b","abstract_canon_sha256":"728312639cb808681380eb31e27c4e3f0b2b5f8925ad51948eb4418541c72e1b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:06.375104Z","signature_b64":"rtBx+QGZTZFUOp/v8b9szVKcE+rhJPoz/yqvjxlxwTSbsBKzlbEf+Qns9mayfr7Wcl8oAhmq+Jv5DawEy6fYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"885949a3c2d4530d4b1055af0c29bf824fee700d67db371ee907e2543ea35dfe","last_reissued_at":"2026-05-18T01:36:06.374665Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:06.374665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inequalities of Babu\\v{s}ka-Aziz and Friedrichs-Velte for differential forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Martin Costabel (IRMAR)","submitted_at":"2015-07-30T11:38:48Z","abstract_excerpt":"For sufficiently smooth bounded plane domains, the equivalence between the inequalities of Babu{\\v s}ka --Aziz for right inverses of the divergence and of Friedrichs on conjugate harmonic functions was shown by Horgan and Payne in 1983 [7]. In a previous paper [4] we proved that this equivalence, and the equality between the associated constants, is true without any regularity condition on the domain. In three dimensions, Velte [9] studied a generalization of the notion of conjugate harmonic functions and corresponding generalizations of Friedrich's inequality, and he showed for sufficiently s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08464","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":""},"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":"1507.08464","created_at":"2026-05-18T01:36:06.374723+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.08464v1","created_at":"2026-05-18T01:36:06.374723+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08464","created_at":"2026-05-18T01:36:06.374723+00:00"},{"alias_kind":"pith_short_12","alias_value":"RBMUTI6C2RJQ","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"RBMUTI6C2RJQ2SYQ","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"RBMUTI6C","created_at":"2026-05-18T12:29:39.896362+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/RBMUTI6C2RJQ2SYQKWXQYKN7QJ","json":"https://pith.science/pith/RBMUTI6C2RJQ2SYQKWXQYKN7QJ.json","graph_json":"https://pith.science/api/pith-number/RBMUTI6C2RJQ2SYQKWXQYKN7QJ/graph.json","events_json":"https://pith.science/api/pith-number/RBMUTI6C2RJQ2SYQKWXQYKN7QJ/events.json","paper":"https://pith.science/paper/RBMUTI6C"},"agent_actions":{"view_html":"https://pith.science/pith/RBMUTI6C2RJQ2SYQKWXQYKN7QJ","download_json":"https://pith.science/pith/RBMUTI6C2RJQ2SYQKWXQYKN7QJ.json","view_paper":"https://pith.science/paper/RBMUTI6C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.08464&json=true","fetch_graph":"https://pith.science/api/pith-number/RBMUTI6C2RJQ2SYQKWXQYKN7QJ/graph.json","fetch_events":"https://pith.science/api/pith-number/RBMUTI6C2RJQ2SYQKWXQYKN7QJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RBMUTI6C2RJQ2SYQKWXQYKN7QJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RBMUTI6C2RJQ2SYQKWXQYKN7QJ/action/storage_attestation","attest_author":"https://pith.science/pith/RBMUTI6C2RJQ2SYQKWXQYKN7QJ/action/author_attestation","sign_citation":"https://pith.science/pith/RBMUTI6C2RJQ2SYQKWXQYKN7QJ/action/citation_signature","submit_replication":"https://pith.science/pith/RBMUTI6C2RJQ2SYQKWXQYKN7QJ/action/replication_record"}},"created_at":"2026-05-18T01:36:06.374723+00:00","updated_at":"2026-05-18T01:36:06.374723+00:00"}