{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:G3XZJDLW2KPIRDEPM6T6W53MKM","short_pith_number":"pith:G3XZJDLW","canonical_record":{"source":{"id":"1009.3534","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-09-18T06:02:40Z","cross_cats_sorted":[],"title_canon_sha256":"4b8cf67542d7e5d5c749a16ff34a32a83a77ea14fc0dd3d69c8dfef683f5a752","abstract_canon_sha256":"e475a54290ce3d1bf12e2044951895b19cc594a4c7dfb331cbb2b560b069a9bd"},"schema_version":"1.0"},"canonical_sha256":"36ef948d76d29e888c8f67a7eb776c5311f6e6f66c70085f4c34d71ff91a201d","source":{"kind":"arxiv","id":"1009.3534","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.3534","created_at":"2026-05-18T04:40:44Z"},{"alias_kind":"arxiv_version","alias_value":"1009.3534v1","created_at":"2026-05-18T04:40:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3534","created_at":"2026-05-18T04:40:44Z"},{"alias_kind":"pith_short_12","alias_value":"G3XZJDLW2KPI","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"G3XZJDLW2KPIRDEP","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"G3XZJDLW","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:G3XZJDLW2KPIRDEPM6T6W53MKM","target":"record","payload":{"canonical_record":{"source":{"id":"1009.3534","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-09-18T06:02:40Z","cross_cats_sorted":[],"title_canon_sha256":"4b8cf67542d7e5d5c749a16ff34a32a83a77ea14fc0dd3d69c8dfef683f5a752","abstract_canon_sha256":"e475a54290ce3d1bf12e2044951895b19cc594a4c7dfb331cbb2b560b069a9bd"},"schema_version":"1.0"},"canonical_sha256":"36ef948d76d29e888c8f67a7eb776c5311f6e6f66c70085f4c34d71ff91a201d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:44.681611Z","signature_b64":"RNfgf1wNwZ0N5giHI49E9k28gIHNsOM4ncZiSXv7J9tO8cpXyVdg/fKouAb4mZIzr4drufHin1eLEnuFw8BbCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36ef948d76d29e888c8f67a7eb776c5311f6e6f66c70085f4c34d71ff91a201d","last_reissued_at":"2026-05-18T04:40:44.680932Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:44.680932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.3534","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:40:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BQ9wH7Pde/jptwcMsoguGrvbrQQ9/GjUlFuIQ7eH4qXdLLP+Hd+onMONmJS41kQ3X479aWjfxGjLD+bLefZaDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:57:31.618131Z"},"content_sha256":"ed083e10ee2aeb49cfb7c84a416a24a9d32d26b1832df76f2b281b1a012e8d2d","schema_version":"1.0","event_id":"sha256:ed083e10ee2aeb49cfb7c84a416a24a9d32d26b1832df76f2b281b1a012e8d2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:G3XZJDLW2KPIRDEPM6T6W53MKM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On cohomology and support varieties for Lie superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Irfan Bagci","submitted_at":"2010-09-18T06:02:40Z","abstract_excerpt":"Support varieties for Lie superalgebras over the complex numbers were introduced in \\cite{BKN1} using the relative cohomology. In this paper we discuss finite generation of the relative cohomology rings for Lie superalgebras, we formulate a definition for subalgebras which detect the cohomology, also discuss realizability of support varieties. In the last section as an application we compute the relative cohomology ring of the Lie superalgebra $\\overline{S}(n)$ relative to the graded zero component $\\overline{S}(n)_0$ and show that this ring is finitely generated. We also compute support varie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3534","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:40:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UbOaiouJ9mis79JyZL9q2Z+QN4MzCcaWicDk6iogmcv9fPnJTbGiN8x+lWKnlsn14wslx6P7pQZecbdxlyGbAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:57:31.618496Z"},"content_sha256":"68cf136747f4d1a7675eafbd4afa8742ebc24f0c01895ba07294567287584985","schema_version":"1.0","event_id":"sha256:68cf136747f4d1a7675eafbd4afa8742ebc24f0c01895ba07294567287584985"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G3XZJDLW2KPIRDEPM6T6W53MKM/bundle.json","state_url":"https://pith.science/pith/G3XZJDLW2KPIRDEPM6T6W53MKM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G3XZJDLW2KPIRDEPM6T6W53MKM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T10:57:31Z","links":{"resolver":"https://pith.science/pith/G3XZJDLW2KPIRDEPM6T6W53MKM","bundle":"https://pith.science/pith/G3XZJDLW2KPIRDEPM6T6W53MKM/bundle.json","state":"https://pith.science/pith/G3XZJDLW2KPIRDEPM6T6W53MKM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G3XZJDLW2KPIRDEPM6T6W53MKM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:G3XZJDLW2KPIRDEPM6T6W53MKM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e475a54290ce3d1bf12e2044951895b19cc594a4c7dfb331cbb2b560b069a9bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-09-18T06:02:40Z","title_canon_sha256":"4b8cf67542d7e5d5c749a16ff34a32a83a77ea14fc0dd3d69c8dfef683f5a752"},"schema_version":"1.0","source":{"id":"1009.3534","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.3534","created_at":"2026-05-18T04:40:44Z"},{"alias_kind":"arxiv_version","alias_value":"1009.3534v1","created_at":"2026-05-18T04:40:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3534","created_at":"2026-05-18T04:40:44Z"},{"alias_kind":"pith_short_12","alias_value":"G3XZJDLW2KPI","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"G3XZJDLW2KPIRDEP","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"G3XZJDLW","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:68cf136747f4d1a7675eafbd4afa8742ebc24f0c01895ba07294567287584985","target":"graph","created_at":"2026-05-18T04:40:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Support varieties for Lie superalgebras over the complex numbers were introduced in \\cite{BKN1} using the relative cohomology. In this paper we discuss finite generation of the relative cohomology rings for Lie superalgebras, we formulate a definition for subalgebras which detect the cohomology, also discuss realizability of support varieties. In the last section as an application we compute the relative cohomology ring of the Lie superalgebra $\\overline{S}(n)$ relative to the graded zero component $\\overline{S}(n)_0$ and show that this ring is finitely generated. We also compute support varie","authors_text":"Irfan Bagci","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-09-18T06:02:40Z","title":"On cohomology and support varieties for Lie superalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3534","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ed083e10ee2aeb49cfb7c84a416a24a9d32d26b1832df76f2b281b1a012e8d2d","target":"record","created_at":"2026-05-18T04:40:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e475a54290ce3d1bf12e2044951895b19cc594a4c7dfb331cbb2b560b069a9bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-09-18T06:02:40Z","title_canon_sha256":"4b8cf67542d7e5d5c749a16ff34a32a83a77ea14fc0dd3d69c8dfef683f5a752"},"schema_version":"1.0","source":{"id":"1009.3534","kind":"arxiv","version":1}},"canonical_sha256":"36ef948d76d29e888c8f67a7eb776c5311f6e6f66c70085f4c34d71ff91a201d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36ef948d76d29e888c8f67a7eb776c5311f6e6f66c70085f4c34d71ff91a201d","first_computed_at":"2026-05-18T04:40:44.680932Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:44.680932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RNfgf1wNwZ0N5giHI49E9k28gIHNsOM4ncZiSXv7J9tO8cpXyVdg/fKouAb4mZIzr4drufHin1eLEnuFw8BbCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:44.681611Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.3534","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed083e10ee2aeb49cfb7c84a416a24a9d32d26b1832df76f2b281b1a012e8d2d","sha256:68cf136747f4d1a7675eafbd4afa8742ebc24f0c01895ba07294567287584985"],"state_sha256":"db15287801b769bffd461168397924febcebd29a7e6f3846fd1d9da494e83fa0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bBZiyDKJi8C2hJAd/5KRvQjr6D61jJqnQTVkB7n6MKkVCu92poyYb/SKXkfMjwTvVfVeuu7XdjHgT+MMbPGdBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T10:57:31.620397Z","bundle_sha256":"48ee4629a955d76fd0886457777a963ac90f0b6a34478161b140c56a52c0694d"}}