{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:EXN3E4753PB6USSWHXEFDRRVCE","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":"187b72c0c35c39c758482dfa1a950e74aff2f704ef9342bd8337dc6efbd1e401","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-06-05T11:24:55Z","title_canon_sha256":"dc6a511ed1463a90b3da7b00df8a6304478b69eb1979d5bf70f5a746a16208e7"},"schema_version":"1.0","source":{"id":"1906.01948","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.01948","created_at":"2026-05-17T23:44:05Z"},{"alias_kind":"arxiv_version","alias_value":"1906.01948v1","created_at":"2026-05-17T23:44:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.01948","created_at":"2026-05-17T23:44:05Z"},{"alias_kind":"pith_short_12","alias_value":"EXN3E4753PB6","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"EXN3E4753PB6USSW","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"EXN3E475","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:ad2efd87cb6aeb3e0cb4a40d0d87cba22db70fc3efb4e1174a6c217bd49c8846","target":"graph","created_at":"2026-05-17T23:44:05Z","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 explicitly the Grothendieck rings of finite-dimensional representations of the periplectic Lie superalgebras. In particular, the Grothendieck ring of the Lie supergroup $P(n)$ is isomorphic to the ring of symmetric polynomials in $x_1^{\\pm 1}, \\ldots, x_n^{\\pm 1}$ whose evaluation $x_1=x_2^{-1}=t$ is independent of $t$.","authors_text":"Mee Seong Im, Shifra Reif, Vera Serganova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-06-05T11:24:55Z","title":"Grothendieck rings of periplectic Lie superalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01948","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:cb2d8e723890f1a22e22e0163d88a48f45c6142baccc58e4cb85b2b7528c41ce","target":"record","created_at":"2026-05-17T23:44:05Z","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":"187b72c0c35c39c758482dfa1a950e74aff2f704ef9342bd8337dc6efbd1e401","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-06-05T11:24:55Z","title_canon_sha256":"dc6a511ed1463a90b3da7b00df8a6304478b69eb1979d5bf70f5a746a16208e7"},"schema_version":"1.0","source":{"id":"1906.01948","kind":"arxiv","version":1}},"canonical_sha256":"25dbb273fddbc3ea4a563dc851c635110464068c2f6f707b7185991cba14694e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25dbb273fddbc3ea4a563dc851c635110464068c2f6f707b7185991cba14694e","first_computed_at":"2026-05-17T23:44:05.663646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:05.663646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U+xeZHpf4oV9Ao4YByfRZMVR3bzOj2cSV3ISCoXs49L3k60kf67y4lHZJjZZNMI5RJRta3W6JIwnhZ19H+OxBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:05.664375Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.01948","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb2d8e723890f1a22e22e0163d88a48f45c6142baccc58e4cb85b2b7528c41ce","sha256:ad2efd87cb6aeb3e0cb4a40d0d87cba22db70fc3efb4e1174a6c217bd49c8846"],"state_sha256":"8e63642931a828d25329bedd87a53d6466b6daa27f9157805a8a65eceea4c9d1"}