{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:BD3GTMW4K52B3AHUJG7XNPMPIX","short_pith_number":"pith:BD3GTMW4","schema_version":"1.0","canonical_sha256":"08f669b2dc57741d80f449bf76bd8f45c9e22f25b6e31d4b67c88bc89800a547","source":{"kind":"arxiv","id":"1511.07055","version":2},"attestation_state":"computed","paper":{"title":"Homogeneous irreducible supermanifolds and graded Lie superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"A. Santi, D. V. Alekseevsky","submitted_at":"2015-11-22T19:29:44Z","abstract_excerpt":"A depth one grading $\\mathfrak{g}= \\mathfrak{g}^{-1}\\oplus \\mathfrak{g}^0 \\oplus \\mathfrak{g}^1 \\oplus \\cdots \\oplus \\mathfrak{g}^{\\ell}$ of a finite dimensional Lie superalgebra $\\mathfrak{g}$ is called nonlinear irreducible if the isotropy representation $\\mathrm{ad}_{\\mathfrak{g}^0}|_{\\mathfrak{g}^{-1}}$ is irreducible and $\\mathfrak{g}^1 \\neq (0)$. An example is the full prolongation of an irreducible linear Lie superalgebra $\\mathfrak{g}^0 \\subset \\mathfrak{gl}(\\mathfrak{g}^{-1})$ of finite type with non-trivial first prolongation. We prove that a complex Lie superalgebra $\\mathfrak{g}$ w"},"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":"1511.07055","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-11-22T19:29:44Z","cross_cats_sorted":["math.QA","math.RA"],"title_canon_sha256":"f22bb6f52b0951f7e4d45f45a421f2f0fb819476c6d991e85a4eb7c747936b19","abstract_canon_sha256":"bed83c9367895013a25f31394a89acd16f53f437096b57d36b17039dbb09c0fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:07.713711Z","signature_b64":"KIGJXJ1NRxwXvbI6sqd/hKD8DNegIuJnw+PFcB4JJacOxx/jqICRQQMb3K7UvzgehNyjj8RnaPvwMhNc+bEKCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08f669b2dc57741d80f449bf76bd8f45c9e22f25b6e31d4b67c88bc89800a547","last_reissued_at":"2026-05-18T00:20:07.713199Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:07.713199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homogeneous irreducible supermanifolds and graded Lie superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"A. Santi, D. V. Alekseevsky","submitted_at":"2015-11-22T19:29:44Z","abstract_excerpt":"A depth one grading $\\mathfrak{g}= \\mathfrak{g}^{-1}\\oplus \\mathfrak{g}^0 \\oplus \\mathfrak{g}^1 \\oplus \\cdots \\oplus \\mathfrak{g}^{\\ell}$ of a finite dimensional Lie superalgebra $\\mathfrak{g}$ is called nonlinear irreducible if the isotropy representation $\\mathrm{ad}_{\\mathfrak{g}^0}|_{\\mathfrak{g}^{-1}}$ is irreducible and $\\mathfrak{g}^1 \\neq (0)$. An example is the full prolongation of an irreducible linear Lie superalgebra $\\mathfrak{g}^0 \\subset \\mathfrak{gl}(\\mathfrak{g}^{-1})$ of finite type with non-trivial first prolongation. We prove that a complex Lie superalgebra $\\mathfrak{g}$ w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07055","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":""},"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":"1511.07055","created_at":"2026-05-18T00:20:07.713291+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.07055v2","created_at":"2026-05-18T00:20:07.713291+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07055","created_at":"2026-05-18T00:20:07.713291+00:00"},{"alias_kind":"pith_short_12","alias_value":"BD3GTMW4K52B","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BD3GTMW4K52B3AHU","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BD3GTMW4","created_at":"2026-05-18T12:29:14.074870+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/BD3GTMW4K52B3AHUJG7XNPMPIX","json":"https://pith.science/pith/BD3GTMW4K52B3AHUJG7XNPMPIX.json","graph_json":"https://pith.science/api/pith-number/BD3GTMW4K52B3AHUJG7XNPMPIX/graph.json","events_json":"https://pith.science/api/pith-number/BD3GTMW4K52B3AHUJG7XNPMPIX/events.json","paper":"https://pith.science/paper/BD3GTMW4"},"agent_actions":{"view_html":"https://pith.science/pith/BD3GTMW4K52B3AHUJG7XNPMPIX","download_json":"https://pith.science/pith/BD3GTMW4K52B3AHUJG7XNPMPIX.json","view_paper":"https://pith.science/paper/BD3GTMW4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.07055&json=true","fetch_graph":"https://pith.science/api/pith-number/BD3GTMW4K52B3AHUJG7XNPMPIX/graph.json","fetch_events":"https://pith.science/api/pith-number/BD3GTMW4K52B3AHUJG7XNPMPIX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BD3GTMW4K52B3AHUJG7XNPMPIX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BD3GTMW4K52B3AHUJG7XNPMPIX/action/storage_attestation","attest_author":"https://pith.science/pith/BD3GTMW4K52B3AHUJG7XNPMPIX/action/author_attestation","sign_citation":"https://pith.science/pith/BD3GTMW4K52B3AHUJG7XNPMPIX/action/citation_signature","submit_replication":"https://pith.science/pith/BD3GTMW4K52B3AHUJG7XNPMPIX/action/replication_record"}},"created_at":"2026-05-18T00:20:07.713291+00:00","updated_at":"2026-05-18T00:20:07.713291+00:00"}