{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NZLQCMHISOMACHCIPL3ZX3OWPW","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":"d681bacdeb7fa75692f982ab2ce2213fce65e0bc1d583b7054aaa9fbc5c1d8a9","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-03-20T00:18:38Z","title_canon_sha256":"7abb14ea9427059624b8a63e240977002cf8304acc5d8e6dbc5aa3d4a44c65fe"},"schema_version":"1.0","source":{"id":"1303.4797","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4797","created_at":"2026-05-18T03:30:24Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4797v1","created_at":"2026-05-18T03:30:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4797","created_at":"2026-05-18T03:30:24Z"},{"alias_kind":"pith_short_12","alias_value":"NZLQCMHISOMA","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"NZLQCMHISOMACHCI","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"NZLQCMHI","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:751656eef075b105df414fbb219ec2b089e3fe5b3d24179a641ae55991a6284d","target":"graph","created_at":"2026-05-18T03:30:24Z","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 $g$ be an exceptional Lie superalgebra, and let $p$ be the maximal parabolic subalgebra which contains the distinguished Borel subalgebra and has a purely even Levi subalgebra. For any parabolic Verma module in the parabolic category $O^p$, it is shown that the Jantzen filtration is the unique Loewy filtration, and the decomposition numbers of the layers of the filtration are determined by the coefficients of inverse Kazhdan-Lusztig polynomials. An explicit description of the submodule lattices of the parabolic Verma modules is given, and formulae for characters and dimensions of the finit","authors_text":"R.B. Zhang, Yucai Su","cross_cats":["math-ph","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-03-20T00:18:38Z","title":"Generalised Jantzen filtration of Lie superalgebras II: the exceptional cases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4797","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":"sha256:60d9d4d80a443be7e87c18e6610252b15564db38d2cd3467967ab6ecc9f16e4b","target":"record","created_at":"2026-05-18T03:30:24Z","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":"d681bacdeb7fa75692f982ab2ce2213fce65e0bc1d583b7054aaa9fbc5c1d8a9","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-03-20T00:18:38Z","title_canon_sha256":"7abb14ea9427059624b8a63e240977002cf8304acc5d8e6dbc5aa3d4a44c65fe"},"schema_version":"1.0","source":{"id":"1303.4797","kind":"arxiv","version":1}},"canonical_sha256":"6e570130e89398011c487af79bedd67d9b415543b78bdd3c4e46ffbe6a98f53b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e570130e89398011c487af79bedd67d9b415543b78bdd3c4e46ffbe6a98f53b","first_computed_at":"2026-05-18T03:30:24.829896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:24.829896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uuPzUfyqDKvpRASTIrhelkEhJgCtxUvqMcyOYNlQc/ApPH/iaI5q3g0Sk6ePBcYsP7MhhLUYH1vGKjDmmCEGDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:24.830516Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.4797","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60d9d4d80a443be7e87c18e6610252b15564db38d2cd3467967ab6ecc9f16e4b","sha256:751656eef075b105df414fbb219ec2b089e3fe5b3d24179a641ae55991a6284d"],"state_sha256":"1e74cb85a4dfb9549a965d2fef4f0931db20d53e404c9891707dcd93b3580406"}