{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GPRRU5PDEOPF6YLIFPJRESW7HL","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":"49b985b1b3802255eaaf2557b9194e24b2de6b8f3343d8ff678bcc08daf5e86e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-05-24T11:10:55Z","title_canon_sha256":"1768e288e74b22f3cd03c44152a84677eb63d3b8983eafd095dd50427ba19b02"},"schema_version":"1.0","source":{"id":"1905.10147","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.10147","created_at":"2026-05-17T23:45:11Z"},{"alias_kind":"arxiv_version","alias_value":"1905.10147v1","created_at":"2026-05-17T23:45:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.10147","created_at":"2026-05-17T23:45:11Z"},{"alias_kind":"pith_short_12","alias_value":"GPRRU5PDEOPF","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"GPRRU5PDEOPF6YLI","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"GPRRU5PD","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:594a418b5ab3e3216f74d7e70841ff20719603c1124ff1fcd873d31c2c9097a5","target":"graph","created_at":"2026-05-17T23:45:11Z","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":"In this paper we study symmetric Leibniz and related algebras, namely symmetric dialgebras and symmetric Perm-algebras. We also calculate their Koszul duals, if not known. This will give us Lie-admissible algebras and new types of algebras, which we call commutative and associative admissible algebras. Finally we prove that all operads describing the considered algebras are Koszul.","authors_text":"Benedikt Hurle","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-05-24T11:10:55Z","title":"A diagram connecting Symmetric Leibniz algebras with Lie-admissible algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.10147","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:dc9fe87ad7c89a2c6da09e3f2c566663eb699a2ad73911309d236b37ce498792","target":"record","created_at":"2026-05-17T23:45:11Z","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":"49b985b1b3802255eaaf2557b9194e24b2de6b8f3343d8ff678bcc08daf5e86e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-05-24T11:10:55Z","title_canon_sha256":"1768e288e74b22f3cd03c44152a84677eb63d3b8983eafd095dd50427ba19b02"},"schema_version":"1.0","source":{"id":"1905.10147","kind":"arxiv","version":1}},"canonical_sha256":"33e31a75e3239e5f61682bd3124adf3ad11daf37531920fb7dc9a9c19b87a7fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33e31a75e3239e5f61682bd3124adf3ad11daf37531920fb7dc9a9c19b87a7fb","first_computed_at":"2026-05-17T23:45:11.214526Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:11.214526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v4jBG5vDY+oYOZiNOmFxO2Fct5vNNbzJdS5qCGk0pORNAPsD4rFcbhGPzHB6myO2MNXskcNv+LUNjOV4IYqxCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:11.215054Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.10147","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc9fe87ad7c89a2c6da09e3f2c566663eb699a2ad73911309d236b37ce498792","sha256:594a418b5ab3e3216f74d7e70841ff20719603c1124ff1fcd873d31c2c9097a5"],"state_sha256":"33021e90bfd20f479c2704fd825e523208617217c9273075496bc8d411ab79b7"}