{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:R6HKWAHNWQL6LFFSXUEN2BDTTM","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":"49248f92168076116ecf87bcd8ac106fe5c5cd69b30e2a270aa1c06ab01708c0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2023-11-17T07:34:02Z","title_canon_sha256":"aaf384d051b05c2106448c0bb39516b43d7dedb3ae959406cc1cda2fba613c80"},"schema_version":"1.0","source":{"id":"2401.08592","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.08592","created_at":"2026-07-05T07:34:18Z"},{"alias_kind":"arxiv_version","alias_value":"2401.08592v1","created_at":"2026-07-05T07:34:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.08592","created_at":"2026-07-05T07:34:18Z"},{"alias_kind":"pith_short_12","alias_value":"R6HKWAHNWQL6","created_at":"2026-07-05T07:34:18Z"},{"alias_kind":"pith_short_16","alias_value":"R6HKWAHNWQL6LFFS","created_at":"2026-07-05T07:34:18Z"},{"alias_kind":"pith_short_8","alias_value":"R6HKWAHN","created_at":"2026-07-05T07:34:18Z"}],"graph_snapshots":[{"event_id":"sha256:e5b24762086ec4e547afeddc4e7b17060d59b3a20956a4b20e54e3d8a1ff03f6","target":"graph","created_at":"2026-07-05T07:34:18Z","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/2401.08592/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the double extension of a restricted quadratic Hom-Lie algebra $(V,[\\cdot,\\cdot]_{V},\\alpha_{V},B_{V})$, which is an enlargement of $V$ by means of a central extension and a restricted derivation $\\mathscr{D}$. In particular, we prove that the double extension of a restricted quadratic Hom-Lie algebra $V$ with a $\\mathscr{D}$-invariant bilinear form $B_{V}$ is restricted. Conversely, any irreducible restricted quadratic Hom-Lie algebra with nonzero center is proved to be the double extension of another restricted quadratic Hom-Lie algebra.","authors_text":"Dan Mao, Liangyun Chen, Zeyu Hao","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2023-11-17T07:34:02Z","title":"Double Extensions of Multiplicative Restricted Hom-Lie Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.08592","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:aaf11ddb9e66464b86668e874715ce4c17e7a95cde3c2897e88141c92edb3352","target":"record","created_at":"2026-07-05T07:34:18Z","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":"49248f92168076116ecf87bcd8ac106fe5c5cd69b30e2a270aa1c06ab01708c0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2023-11-17T07:34:02Z","title_canon_sha256":"aaf384d051b05c2106448c0bb39516b43d7dedb3ae959406cc1cda2fba613c80"},"schema_version":"1.0","source":{"id":"2401.08592","kind":"arxiv","version":1}},"canonical_sha256":"8f8eab00edb417e594b2bd08dd04739b1b10379deb7a877e78dec9a456f989ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f8eab00edb417e594b2bd08dd04739b1b10379deb7a877e78dec9a456f989ef","first_computed_at":"2026-07-05T07:34:18.560675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:34:18.560675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uHFP8xWxaGbWAwHdC2BTWM+dlZXkbQzuDAJX9dJbGVdQHSlIT/IhItnCJqeZeBciJ/cosuRiwfFdozzACDvOBA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:34:18.561085Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.08592","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aaf11ddb9e66464b86668e874715ce4c17e7a95cde3c2897e88141c92edb3352","sha256:e5b24762086ec4e547afeddc4e7b17060d59b3a20956a4b20e54e3d8a1ff03f6"],"state_sha256":"83951609f6851d16140a6c418bb0c0b917388f713c2d6d156b27fa00a958cc29"}