{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EWULKUU52LAGU5KZ6L6QRAADHB","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":"ffa9d4269d554209a987051e4df7e0abf0b743e5f35e9992dfed0e10808bd377","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-12-13T20:48:34Z","title_canon_sha256":"4ae0aa885ade133e981a9ed3b2dcf119d6b5d0d619e972a23bcbd81ca6a430cc"},"schema_version":"1.0","source":{"id":"1312.3935","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3935","created_at":"2026-05-18T03:04:47Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3935v1","created_at":"2026-05-18T03:04:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3935","created_at":"2026-05-18T03:04:47Z"},{"alias_kind":"pith_short_12","alias_value":"EWULKUU52LAG","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EWULKUU52LAGU5KZ","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EWULKUU5","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:e046e055082786551652464467abe54b583fd1390a0445a2081c884eea7b4ff2","target":"graph","created_at":"2026-05-18T03:04:47Z","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 study a series of real nonassociative algebras $\\mathbb{O}_{p,q}$ introduced in $[5]$. These algebras have a natural $\\mathbb{Z}_2^n$-grading, where $n=p+q$, and they are characterized by a cubic form over the field $\\mathbb{Z}_2$. We establish all the possible isomorphisms between the algebras $\\mathbb{O}_{p,q}$ preserving the structure of $\\mathbb{Z}_2^n$-graded algebra. The classification table of $\\mathbb{O}_{p,q}$ is quite similar to that of the real Clifford algebras $\\mathrm{Cl}_{p,q}$, the main difference is that the algebras $\\mathbb{O}_{n,0}$ and $\\mathbb{O}_{0,n}$ are exceptional","authors_text":"Marie Kreusch, Sophie Morier-Genoud","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-12-13T20:48:34Z","title":"Classification of the algebras $\\mathbb{O}_{p,q}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3935","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":"sha256:113894403c57c97b82eb294b1faac722aace1e20a709889dd2030f66d52710cb","target":"record","created_at":"2026-05-18T03:04:47Z","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":"ffa9d4269d554209a987051e4df7e0abf0b743e5f35e9992dfed0e10808bd377","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-12-13T20:48:34Z","title_canon_sha256":"4ae0aa885ade133e981a9ed3b2dcf119d6b5d0d619e972a23bcbd81ca6a430cc"},"schema_version":"1.0","source":{"id":"1312.3935","kind":"arxiv","version":1}},"canonical_sha256":"25a8b5529dd2c06a7559f2fd088003384533183c67ccb3d2ef34e3da7286bbc5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25a8b5529dd2c06a7559f2fd088003384533183c67ccb3d2ef34e3da7286bbc5","first_computed_at":"2026-05-18T03:04:47.096182Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:47.096182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eCmfZ48D3C6cLgbAo4VDDPnmJh1EQxnV60Z6CengCkVy8GVEhERyVVjq2tPU/rekcPvMaWP7sF2EUtDDVu/tAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:47.096799Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.3935","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:113894403c57c97b82eb294b1faac722aace1e20a709889dd2030f66d52710cb","sha256:e046e055082786551652464467abe54b583fd1390a0445a2081c884eea7b4ff2"],"state_sha256":"4c056feb33d94a2e56b6351b19244c3dfa30c38e0d6f56438d330fe571e015ed"}