{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FMQF5VNNILVLPY7SOT3QP3KQ7T","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":"264be597bad26b495ab7eaf2b511ac325447b1d164562877c13327c82a74bd48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-01-03T08:52:53Z","title_canon_sha256":"e8dd13ce87539a0ed02295e170ad5fb9b446e0e17b16bdfd24ddb318c391c0ca"},"schema_version":"1.0","source":{"id":"1101.0472","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.0472","created_at":"2026-05-18T04:32:10Z"},{"alias_kind":"arxiv_version","alias_value":"1101.0472v1","created_at":"2026-05-18T04:32:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.0472","created_at":"2026-05-18T04:32:10Z"},{"alias_kind":"pith_short_12","alias_value":"FMQF5VNNILVL","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FMQF5VNNILVLPY7S","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FMQF5VNN","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:aa3ab37536804ebc22389fe97076328221c0be54d55c2a8f62b01f142446c05d","target":"graph","created_at":"2026-05-18T04:32:10Z","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":"Let $\\frak g$ be a reductive Lie algebra over an algebraically closed field of characteristic 0 and $\\frak k$ be a reductive in $\\frak g$-subalgebra. Let $M$ be a finitely generated (possibly, infinite-dimensional) $\\frak g$-module. We say that $M$ is a $(\\frak g, \\frak k)$-module if $M$ is a direct sum of a (possibly, infinite) amount of simple finite-dimensional $\\frak k$-modules. We say that $M$ is of finite type if $M$ is a $(\\frak g, \\frak k)$-module and Hom$_\\frak k(V, M)<\\infty$ for any simple $\\frak k$-module $V$.\n  Let $X$ be a variety of all Borel subalgebras of $\\frak g$. Let $M$ be","authors_text":"Alexey V. Petukhov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-01-03T08:52:53Z","title":"Support varieties of $(\\frak g, \\frak k)$-modules of finite type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0472","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:b1274eeb75c9c8b6fea774b35207578d4ca40fd4fadcee8a8a3089d7d8bf0f0a","target":"record","created_at":"2026-05-18T04:32:10Z","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":"264be597bad26b495ab7eaf2b511ac325447b1d164562877c13327c82a74bd48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-01-03T08:52:53Z","title_canon_sha256":"e8dd13ce87539a0ed02295e170ad5fb9b446e0e17b16bdfd24ddb318c391c0ca"},"schema_version":"1.0","source":{"id":"1101.0472","kind":"arxiv","version":1}},"canonical_sha256":"2b205ed5ad42eab7e3f274f707ed50fccede747a55c76bfe31c43152060a2103","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b205ed5ad42eab7e3f274f707ed50fccede747a55c76bfe31c43152060a2103","first_computed_at":"2026-05-18T04:32:10.321838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:10.321838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7wGL1z5hrlBNRDYeS6LV6nOVzkOlI8wuoI+/7gAfNXcOmOIuBEzDjVnALwLcHKh7E7zSrkfXhfJhbuVOrU/1CA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:10.322281Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.0472","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1274eeb75c9c8b6fea774b35207578d4ca40fd4fadcee8a8a3089d7d8bf0f0a","sha256:aa3ab37536804ebc22389fe97076328221c0be54d55c2a8f62b01f142446c05d"],"state_sha256":"53206d7c1be849008785705b1c76c3a86f4981ab821ce67a9e82a6a50aa8853b"}