{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:CRO5G7VGSYYFEDGOFJTKHCH6WS","short_pith_number":"pith:CRO5G7VG","schema_version":"1.0","canonical_sha256":"145dd37ea69630520cce2a66a388feb48a9a4a447c85a7f446d4fc026a50e279","source":{"kind":"arxiv","id":"1104.3824","version":1},"attestation_state":"computed","paper":{"title":"A 3-Calabi-Yau algebra with G_2 symmetry constructed from the octonions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"S. Paul Smith","submitted_at":"2011-04-19T18:17:08Z","abstract_excerpt":"This paper concerns an associative graded algebra A that is the enveloping algebra of a Lie algebra with exponential growth. The algebra A is 3-Calabi-Yau. There is a Z-form of A so for every field k there is an algebra A_k. An algebraic group of type G_2 acts as degree-preserving automorphisms of A.\n  The algebra A is generated by 7 elements modulo 7 homogeneous quadratic relations. It can be constructed from the octonions; the same construction applied to the quaternions produces the commutative polynomial ring in 3 variables.\n  If V is the 7-dimensional irreducible representation of the com"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1104.3824","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-04-19T18:17:08Z","cross_cats_sorted":[],"title_canon_sha256":"451c61244364cb63da1a5f8e1def9f9f160a4751e60724a275e7df2d3983bdc1","abstract_canon_sha256":"394b467165118743926b8dc0d4b873d3eff71b6abc8a07b5228705d3144021ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:55.634491Z","signature_b64":"EcnhvOAgVJU2IjVDxUsaR1/h0hbkrtGCHc9M4Xztu5k0wejOgm79pU0AE8H6GvzMVqXVacdpafDyG2ZkLwaXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"145dd37ea69630520cce2a66a388feb48a9a4a447c85a7f446d4fc026a50e279","last_reissued_at":"2026-05-18T04:23:55.634089Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:55.634089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A 3-Calabi-Yau algebra with G_2 symmetry constructed from the octonions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"S. Paul Smith","submitted_at":"2011-04-19T18:17:08Z","abstract_excerpt":"This paper concerns an associative graded algebra A that is the enveloping algebra of a Lie algebra with exponential growth. The algebra A is 3-Calabi-Yau. There is a Z-form of A so for every field k there is an algebra A_k. An algebraic group of type G_2 acts as degree-preserving automorphisms of A.\n  The algebra A is generated by 7 elements modulo 7 homogeneous quadratic relations. It can be constructed from the octonions; the same construction applied to the quaternions produces the commutative polynomial ring in 3 variables.\n  If V is the 7-dimensional irreducible representation of the com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3824","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1104.3824","created_at":"2026-05-18T04:23:55.634159+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.3824v1","created_at":"2026-05-18T04:23:55.634159+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3824","created_at":"2026-05-18T04:23:55.634159+00:00"},{"alias_kind":"pith_short_12","alias_value":"CRO5G7VGSYYF","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"CRO5G7VGSYYFEDGO","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"CRO5G7VG","created_at":"2026-05-18T12:26:26.731475+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CRO5G7VGSYYFEDGOFJTKHCH6WS","json":"https://pith.science/pith/CRO5G7VGSYYFEDGOFJTKHCH6WS.json","graph_json":"https://pith.science/api/pith-number/CRO5G7VGSYYFEDGOFJTKHCH6WS/graph.json","events_json":"https://pith.science/api/pith-number/CRO5G7VGSYYFEDGOFJTKHCH6WS/events.json","paper":"https://pith.science/paper/CRO5G7VG"},"agent_actions":{"view_html":"https://pith.science/pith/CRO5G7VGSYYFEDGOFJTKHCH6WS","download_json":"https://pith.science/pith/CRO5G7VGSYYFEDGOFJTKHCH6WS.json","view_paper":"https://pith.science/paper/CRO5G7VG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.3824&json=true","fetch_graph":"https://pith.science/api/pith-number/CRO5G7VGSYYFEDGOFJTKHCH6WS/graph.json","fetch_events":"https://pith.science/api/pith-number/CRO5G7VGSYYFEDGOFJTKHCH6WS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CRO5G7VGSYYFEDGOFJTKHCH6WS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CRO5G7VGSYYFEDGOFJTKHCH6WS/action/storage_attestation","attest_author":"https://pith.science/pith/CRO5G7VGSYYFEDGOFJTKHCH6WS/action/author_attestation","sign_citation":"https://pith.science/pith/CRO5G7VGSYYFEDGOFJTKHCH6WS/action/citation_signature","submit_replication":"https://pith.science/pith/CRO5G7VGSYYFEDGOFJTKHCH6WS/action/replication_record"}},"created_at":"2026-05-18T04:23:55.634159+00:00","updated_at":"2026-05-18T04:23:55.634159+00:00"}