{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QNGAMBF544VSJ6CANBJ5XYRHJV","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":"5aca504fcfca4fbb0fbda852f858ae0d5b056803021c5d05754823204ac8f459","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-01-13T15:06:33Z","title_canon_sha256":"b5078ca3fb58461dbb037674b911c348fb321f8ea7d99a088f48582908907c04"},"schema_version":"1.0","source":{"id":"1301.2781","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2781","created_at":"2026-07-05T09:07:21Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2781v4","created_at":"2026-07-05T09:07:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2781","created_at":"2026-07-05T09:07:21Z"},{"alias_kind":"pith_short_12","alias_value":"QNGAMBF544VS","created_at":"2026-07-05T09:07:21Z"},{"alias_kind":"pith_short_16","alias_value":"QNGAMBF544VSJ6CA","created_at":"2026-07-05T09:07:21Z"},{"alias_kind":"pith_short_8","alias_value":"QNGAMBF5","created_at":"2026-07-05T09:07:21Z"}],"graph_snapshots":[{"event_id":"sha256:e50a6a00b76d4b0125a1447bf929699b0bf2487e12d87f7edc08f9f7860b198b","target":"graph","created_at":"2026-07-05T09:07:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1301.2781/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Of four types of Kaplansky algebras, type-2 and type-4 algebras have previously unobserved $\\mathbb{Z}/2$-gradings: nonlinear in roots. A method assigning a simple Lie superalgebra to every $\\mathbb{Z}/2$-graded simple Lie algebra in characteristic 2 is illustrated by seven new series. Type-2 algebras and one of the two type-4 algebras are demystified as nontrivial deforms (the results of deformations) of the alternate Hamiltonian algebras. The type-1 Kaplansky algebra is recognized as the derived of the nonalternate version of the Hamiltonian Lie algebra, the one that preserves a tensorial 2-","authors_text":"Alexei Lebedev, Dimitry Leites, Irina Shchepochkina, Sofiane Bouarroudj","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-01-13T15:06:33Z","title":"Lie algebra deformations in characteristic 2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2781","kind":"arxiv","version":4},"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:c9116626c98a0b54485074475d0b013b05d82c80c39e5e7d070c4e3b8caba027","target":"record","created_at":"2026-07-05T09:07:21Z","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":"5aca504fcfca4fbb0fbda852f858ae0d5b056803021c5d05754823204ac8f459","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-01-13T15:06:33Z","title_canon_sha256":"b5078ca3fb58461dbb037674b911c348fb321f8ea7d99a088f48582908907c04"},"schema_version":"1.0","source":{"id":"1301.2781","kind":"arxiv","version":4}},"canonical_sha256":"834c0604bde72b24f8406853dbe2274d691333fca1ab6b7a034bbe7b2620618f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"834c0604bde72b24f8406853dbe2274d691333fca1ab6b7a034bbe7b2620618f","first_computed_at":"2026-07-05T09:07:21.867432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:07:21.867432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zmYFrGjSfzW94L3gtRnHFWc0GuP2AAjVEqgFufskcYd/eNp8G8U67aaC6+WJv3NWuPVwdhTgD39KauUl5lhwBw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:07:21.867844Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2781","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9116626c98a0b54485074475d0b013b05d82c80c39e5e7d070c4e3b8caba027","sha256:e50a6a00b76d4b0125a1447bf929699b0bf2487e12d87f7edc08f9f7860b198b"],"state_sha256":"128d134638c56706aecd7cb5ee8e0325fb74f0b5ed97cc27386c7d876426c62b"}