{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6CFUHODBYWQTLJ6NQ2J4JAOE2F","short_pith_number":"pith:6CFUHODB","schema_version":"1.0","canonical_sha256":"f08b43b861c5a135a7cd8693c481c4d15f83b10ef4e7e5d189375b44da4ab160","source":{"kind":"arxiv","id":"1507.01329","version":1},"attestation_state":"computed","paper":{"title":"Invariants of the orthosymplectic Lie superalgebra and super Pfaffians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"G.I. Lehrer, R.B. Zhang","submitted_at":"2015-07-06T05:34:31Z","abstract_excerpt":"Given a complex orthosymplectic superspace $V$, the orthosymplectic Lie superalgebra $\\mathfrak {osp}(V)$ and general linear algebra ${\\mathfrak {gl}}_N$ both act naturally on the coordinate super-ring $\\mathcal{S}(N)$ of the dual space of $V\\otimes{\\mathbb C}^N$, and their actions commute. Hence the subalgebra $\\mathcal{S}(N)^{\\mathfrak {osp}(V)}$ of $\\mathfrak {osp}(V)$-invariants in $\\mathcal{S}(N)$ has a ${\\mathfrak {gl}}_N$-module structure. We introduce the space of super Pfaffians as a simple ${\\mathfrak {gl}}_N$-submodule of $\\mathcal{S}(N)^{\\mathfrak {osp}(V)}$, give an explicit formu"},"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":"1507.01329","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-06T05:34:31Z","cross_cats_sorted":[],"title_canon_sha256":"4a20b1798f09229bcfd6c90388a12fcfd5337cf3dff8aa785323cec944b41d87","abstract_canon_sha256":"817f91346f46bd72fc98cecfb08546063d52fe32eb7b7e2ab3dab708e23516c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:17.265279Z","signature_b64":"3AQAXOxUSYAVsLg6SOdPaHqvwRKJbSw0nyyPRUixfhQkoYkhu6D5IcrT8P9ks/Zkzf2nt0IEtzsiXOD03XpdDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f08b43b861c5a135a7cd8693c481c4d15f83b10ef4e7e5d189375b44da4ab160","last_reissued_at":"2026-05-18T01:37:17.264573Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:17.264573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariants of the orthosymplectic Lie superalgebra and super Pfaffians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"G.I. Lehrer, R.B. Zhang","submitted_at":"2015-07-06T05:34:31Z","abstract_excerpt":"Given a complex orthosymplectic superspace $V$, the orthosymplectic Lie superalgebra $\\mathfrak {osp}(V)$ and general linear algebra ${\\mathfrak {gl}}_N$ both act naturally on the coordinate super-ring $\\mathcal{S}(N)$ of the dual space of $V\\otimes{\\mathbb C}^N$, and their actions commute. Hence the subalgebra $\\mathcal{S}(N)^{\\mathfrak {osp}(V)}$ of $\\mathfrak {osp}(V)$-invariants in $\\mathcal{S}(N)$ has a ${\\mathfrak {gl}}_N$-module structure. We introduce the space of super Pfaffians as a simple ${\\mathfrak {gl}}_N$-submodule of $\\mathcal{S}(N)^{\\mathfrak {osp}(V)}$, give an explicit formu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01329","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":"1507.01329","created_at":"2026-05-18T01:37:17.264699+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.01329v1","created_at":"2026-05-18T01:37:17.264699+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01329","created_at":"2026-05-18T01:37:17.264699+00:00"},{"alias_kind":"pith_short_12","alias_value":"6CFUHODBYWQT","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6CFUHODBYWQTLJ6N","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6CFUHODB","created_at":"2026-05-18T12:29:07.941421+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/6CFUHODBYWQTLJ6NQ2J4JAOE2F","json":"https://pith.science/pith/6CFUHODBYWQTLJ6NQ2J4JAOE2F.json","graph_json":"https://pith.science/api/pith-number/6CFUHODBYWQTLJ6NQ2J4JAOE2F/graph.json","events_json":"https://pith.science/api/pith-number/6CFUHODBYWQTLJ6NQ2J4JAOE2F/events.json","paper":"https://pith.science/paper/6CFUHODB"},"agent_actions":{"view_html":"https://pith.science/pith/6CFUHODBYWQTLJ6NQ2J4JAOE2F","download_json":"https://pith.science/pith/6CFUHODBYWQTLJ6NQ2J4JAOE2F.json","view_paper":"https://pith.science/paper/6CFUHODB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.01329&json=true","fetch_graph":"https://pith.science/api/pith-number/6CFUHODBYWQTLJ6NQ2J4JAOE2F/graph.json","fetch_events":"https://pith.science/api/pith-number/6CFUHODBYWQTLJ6NQ2J4JAOE2F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6CFUHODBYWQTLJ6NQ2J4JAOE2F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6CFUHODBYWQTLJ6NQ2J4JAOE2F/action/storage_attestation","attest_author":"https://pith.science/pith/6CFUHODBYWQTLJ6NQ2J4JAOE2F/action/author_attestation","sign_citation":"https://pith.science/pith/6CFUHODBYWQTLJ6NQ2J4JAOE2F/action/citation_signature","submit_replication":"https://pith.science/pith/6CFUHODBYWQTLJ6NQ2J4JAOE2F/action/replication_record"}},"created_at":"2026-05-18T01:37:17.264699+00:00","updated_at":"2026-05-18T01:37:17.264699+00:00"}