{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:KX5ZU4IS44HMLDNVEHDQ72ZDIK","short_pith_number":"pith:KX5ZU4IS","schema_version":"1.0","canonical_sha256":"55fb9a7112e70ec58db521c70feb234297b6eaac5092aadb1a20a1c7f92a58f2","source":{"kind":"arxiv","id":"1810.00590","version":1},"attestation_state":"computed","paper":{"title":"An infinite family of axial algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RA","authors_text":"Madeleine Whybrow","submitted_at":"2018-10-01T09:18:12Z","abstract_excerpt":"Axial algebras are non-associative algebras generated by semisimple idempotents, known as axes, that all obey a fusion rule. Axial algebras were introduced by Hall, Rehren and Shpectorov as a generalisation of the axioms of Majorana theory, which was in turn introduced by Ivanov as an axiomatisation of certain properties of the 2A-axes of the Griess algebra. Axial algebras of Monster type are axial algebras whose axes obey the Monster, or Majorana, fusion rule.\n  We construct an axial algebra of Monster type $M_{4A}$ over the polynomial ring $\\mathbb{R}[t]$ that is generated by six axes whose "},"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":"1810.00590","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-10-01T09:18:12Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"ab39e89334eb6ce84b089d842f578a372c046e36b8c1728616a1b800e4d7217a","abstract_canon_sha256":"4e245cc5768185fb6c2694d9b5a67913e760c48e44dfae84dc61241cd16b44e7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:25.325332Z","signature_b64":"KuOImnsxzmy2WWjD1IqGWjqtx85C7vIuBx7wJ/hqSdP9tqShN/0dh4U3QDpViosz/RbT9WDRbl1PeRi5l6AmCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55fb9a7112e70ec58db521c70feb234297b6eaac5092aadb1a20a1c7f92a58f2","last_reissued_at":"2026-05-18T00:04:25.324779Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:25.324779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An infinite family of axial algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RA","authors_text":"Madeleine Whybrow","submitted_at":"2018-10-01T09:18:12Z","abstract_excerpt":"Axial algebras are non-associative algebras generated by semisimple idempotents, known as axes, that all obey a fusion rule. Axial algebras were introduced by Hall, Rehren and Shpectorov as a generalisation of the axioms of Majorana theory, which was in turn introduced by Ivanov as an axiomatisation of certain properties of the 2A-axes of the Griess algebra. Axial algebras of Monster type are axial algebras whose axes obey the Monster, or Majorana, fusion rule.\n  We construct an axial algebra of Monster type $M_{4A}$ over the polynomial ring $\\mathbb{R}[t]$ that is generated by six axes whose "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00590","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":"1810.00590","created_at":"2026-05-18T00:04:25.324876+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.00590v1","created_at":"2026-05-18T00:04:25.324876+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00590","created_at":"2026-05-18T00:04:25.324876+00:00"},{"alias_kind":"pith_short_12","alias_value":"KX5ZU4IS44HM","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_16","alias_value":"KX5ZU4IS44HMLDNV","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_8","alias_value":"KX5ZU4IS","created_at":"2026-05-18T12:32:33.847187+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/KX5ZU4IS44HMLDNVEHDQ72ZDIK","json":"https://pith.science/pith/KX5ZU4IS44HMLDNVEHDQ72ZDIK.json","graph_json":"https://pith.science/api/pith-number/KX5ZU4IS44HMLDNVEHDQ72ZDIK/graph.json","events_json":"https://pith.science/api/pith-number/KX5ZU4IS44HMLDNVEHDQ72ZDIK/events.json","paper":"https://pith.science/paper/KX5ZU4IS"},"agent_actions":{"view_html":"https://pith.science/pith/KX5ZU4IS44HMLDNVEHDQ72ZDIK","download_json":"https://pith.science/pith/KX5ZU4IS44HMLDNVEHDQ72ZDIK.json","view_paper":"https://pith.science/paper/KX5ZU4IS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.00590&json=true","fetch_graph":"https://pith.science/api/pith-number/KX5ZU4IS44HMLDNVEHDQ72ZDIK/graph.json","fetch_events":"https://pith.science/api/pith-number/KX5ZU4IS44HMLDNVEHDQ72ZDIK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KX5ZU4IS44HMLDNVEHDQ72ZDIK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KX5ZU4IS44HMLDNVEHDQ72ZDIK/action/storage_attestation","attest_author":"https://pith.science/pith/KX5ZU4IS44HMLDNVEHDQ72ZDIK/action/author_attestation","sign_citation":"https://pith.science/pith/KX5ZU4IS44HMLDNVEHDQ72ZDIK/action/citation_signature","submit_replication":"https://pith.science/pith/KX5ZU4IS44HMLDNVEHDQ72ZDIK/action/replication_record"}},"created_at":"2026-05-18T00:04:25.324876+00:00","updated_at":"2026-05-18T00:04:25.324876+00:00"}