{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:SVCW365ZWJZSMNQUZU2FIYWGLD","short_pith_number":"pith:SVCW365Z","schema_version":"1.0","canonical_sha256":"95456dfbb9b273263614cd345462c658ef7fbea5c72c841bced35a78d484073f","source":{"kind":"arxiv","id":"1109.0894","version":1},"attestation_state":"computed","paper":{"title":"Generalized duality for k-forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Frank Klinker","submitted_at":"2011-09-05T13:29:37Z","abstract_excerpt":"We give the definition of a duality that is applicable to arbitrary $k$-forms. The operator that defines the duality depends on a fixed form $\\Omega$. Our definition extends in a very natural way the Hodge duality of $n$-forms in $2n$ dimensional spaces and the generalized duality of two-forms. We discuss the properties of the duality in the case where $\\Omega$ is invariant with respect to a subalgebra of $\\mathfrak{so}(V)$. Furthermore, we give examples for the invariant case as well as for the case of discrete symmetry."},"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":"1109.0894","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-05T13:29:37Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"670b5aeae803f0e16868ee70e22766031724b8a3db6f31835036e03ce8ccb6c7","abstract_canon_sha256":"60cffb3c04b1d44f7af964c81827828b799c6d6b68052f796b94147ae0c325fe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:06.428969Z","signature_b64":"vPM5Tip4laf1Atsg/ew9h42IyfFnBRCezS/L4BK6WFOpNFAbYsVATy0u3v1jVDEVAjyAQRrzcjKpcxAQZmk9BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95456dfbb9b273263614cd345462c658ef7fbea5c72c841bced35a78d484073f","last_reissued_at":"2026-05-18T04:14:06.428399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:06.428399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized duality for k-forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Frank Klinker","submitted_at":"2011-09-05T13:29:37Z","abstract_excerpt":"We give the definition of a duality that is applicable to arbitrary $k$-forms. The operator that defines the duality depends on a fixed form $\\Omega$. Our definition extends in a very natural way the Hodge duality of $n$-forms in $2n$ dimensional spaces and the generalized duality of two-forms. We discuss the properties of the duality in the case where $\\Omega$ is invariant with respect to a subalgebra of $\\mathfrak{so}(V)$. Furthermore, we give examples for the invariant case as well as for the case of discrete symmetry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0894","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":"1109.0894","created_at":"2026-05-18T04:14:06.428503+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.0894v1","created_at":"2026-05-18T04:14:06.428503+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0894","created_at":"2026-05-18T04:14:06.428503+00:00"},{"alias_kind":"pith_short_12","alias_value":"SVCW365ZWJZS","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"SVCW365ZWJZSMNQU","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"SVCW365Z","created_at":"2026-05-18T12:26:41.206345+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/SVCW365ZWJZSMNQUZU2FIYWGLD","json":"https://pith.science/pith/SVCW365ZWJZSMNQUZU2FIYWGLD.json","graph_json":"https://pith.science/api/pith-number/SVCW365ZWJZSMNQUZU2FIYWGLD/graph.json","events_json":"https://pith.science/api/pith-number/SVCW365ZWJZSMNQUZU2FIYWGLD/events.json","paper":"https://pith.science/paper/SVCW365Z"},"agent_actions":{"view_html":"https://pith.science/pith/SVCW365ZWJZSMNQUZU2FIYWGLD","download_json":"https://pith.science/pith/SVCW365ZWJZSMNQUZU2FIYWGLD.json","view_paper":"https://pith.science/paper/SVCW365Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.0894&json=true","fetch_graph":"https://pith.science/api/pith-number/SVCW365ZWJZSMNQUZU2FIYWGLD/graph.json","fetch_events":"https://pith.science/api/pith-number/SVCW365ZWJZSMNQUZU2FIYWGLD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SVCW365ZWJZSMNQUZU2FIYWGLD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SVCW365ZWJZSMNQUZU2FIYWGLD/action/storage_attestation","attest_author":"https://pith.science/pith/SVCW365ZWJZSMNQUZU2FIYWGLD/action/author_attestation","sign_citation":"https://pith.science/pith/SVCW365ZWJZSMNQUZU2FIYWGLD/action/citation_signature","submit_replication":"https://pith.science/pith/SVCW365ZWJZSMNQUZU2FIYWGLD/action/replication_record"}},"created_at":"2026-05-18T04:14:06.428503+00:00","updated_at":"2026-05-18T04:14:06.428503+00:00"}