{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JB55OK3BAGILNQ7ZZ6OGOTVT5J","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":"6334d209e41002043aebdbc426a297ce6e2cbcbf4387e67985ccd69a25a06711","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-04-07T14:21:41Z","title_canon_sha256":"b26fc37bc433657d3028973a3f1e18edf83245d7f6057664ce1497c1ed429181"},"schema_version":"1.0","source":{"id":"1804.02563","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.02563","created_at":"2026-05-17T23:58:14Z"},{"alias_kind":"arxiv_version","alias_value":"1804.02563v2","created_at":"2026-05-17T23:58:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.02563","created_at":"2026-05-17T23:58:14Z"},{"alias_kind":"pith_short_12","alias_value":"JB55OK3BAGIL","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JB55OK3BAGILNQ7Z","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JB55OK3B","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:ff9e8e3f81db6b557aeb3811b74cca401ebffa9d207f12474200a0dbadf8baaf","target":"graph","created_at":"2026-05-17T23:58:14Z","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":"We describe Borel and parabolic subalgebras of affine Lie superalgebras and study the Verma type modules associated to such subalgebras. We give necessary and sufficient conditions under which these modules are simple.","authors_text":"Lucas Calixto, Vyacheslav Futorny","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-04-07T14:21:41Z","title":"Highest weight modules for affine Lie superalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02563","kind":"arxiv","version":2},"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:ab14c5fdd39b295b2def730e2365dd02a3467a1ebd33af5679a50f7dc6697f4a","target":"record","created_at":"2026-05-17T23:58:14Z","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":"6334d209e41002043aebdbc426a297ce6e2cbcbf4387e67985ccd69a25a06711","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-04-07T14:21:41Z","title_canon_sha256":"b26fc37bc433657d3028973a3f1e18edf83245d7f6057664ce1497c1ed429181"},"schema_version":"1.0","source":{"id":"1804.02563","kind":"arxiv","version":2}},"canonical_sha256":"487bd72b610190b6c3f9cf9c674eb3ea423f5f58e247d3021f4bc215dddfa319","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"487bd72b610190b6c3f9cf9c674eb3ea423f5f58e247d3021f4bc215dddfa319","first_computed_at":"2026-05-17T23:58:14.415288Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:14.415288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"COstp4o1cmkp7YEbf/Yw+Ew/jpw1mrxRDo+ypYb/fxgx2sH9HgOeTDBbTtc8Z+X/dxfZFHU/1KqOl7CHW8RODA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:14.415791Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.02563","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab14c5fdd39b295b2def730e2365dd02a3467a1ebd33af5679a50f7dc6697f4a","sha256:ff9e8e3f81db6b557aeb3811b74cca401ebffa9d207f12474200a0dbadf8baaf"],"state_sha256":"d34a5a65bd5eb8ecfa377092fcb677cb4788cbe1550d833d9716daa07b653587"}