{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:3WDMFV63H37IKQC4TYPF4W5XRT","short_pith_number":"pith:3WDMFV63","schema_version":"1.0","canonical_sha256":"dd86c2d7db3efe85405c9e1e5e5bb78cc526b5e4ee0fa7f983c19c938d44eeaa","source":{"kind":"arxiv","id":"math/0702874","version":1},"attestation_state":"computed","paper":{"title":"Primary decompositions in varieties of commutative diassociative loops","license":"","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Michael K. Kinyon, Petr Vojtechovsky","submitted_at":"2007-02-28T11:43:56Z","abstract_excerpt":"The decomposition theorem for torsion abelian groups holds analogously for torsion commutative diassociative loops. With this theorem in mind, we investigate commutative diassociative loops satisfying the additional condition (trivially satisfied in the abelian group case) that all $n$th powers are central, for a fixed $n$. For $n=2$, we get precisely commutative $C$ loops. For $n=3$, a prominent variety is that of commutative Moufang loops.\n  Many analogies between commutative C and Moufang loops have been noted in the literature, often obtained by interchanging the role of the primes 2 and 3"},"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":"math/0702874","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2007-02-28T11:43:56Z","cross_cats_sorted":[],"title_canon_sha256":"366e4e2bc318ca951a4fe61a32e7de36247f36cba515646f92115b01b2896e04","abstract_canon_sha256":"46fa2df7e35767b214bef1841ab71a081219166d3623b992bbaf02de07e0efd2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:07.284679Z","signature_b64":"m5tu0JIbenmURffurP4bm+sWgBSwOts5/4E7JhYOKqEHwBbVWJDgj732rsrOWslvu1DoG/Q8R48m3F/jHeFKCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd86c2d7db3efe85405c9e1e5e5bb78cc526b5e4ee0fa7f983c19c938d44eeaa","last_reissued_at":"2026-05-18T04:15:07.283982Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:07.283982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Primary decompositions in varieties of commutative diassociative loops","license":"","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Michael K. Kinyon, Petr Vojtechovsky","submitted_at":"2007-02-28T11:43:56Z","abstract_excerpt":"The decomposition theorem for torsion abelian groups holds analogously for torsion commutative diassociative loops. With this theorem in mind, we investigate commutative diassociative loops satisfying the additional condition (trivially satisfied in the abelian group case) that all $n$th powers are central, for a fixed $n$. For $n=2$, we get precisely commutative $C$ loops. For $n=3$, a prominent variety is that of commutative Moufang loops.\n  Many analogies between commutative C and Moufang loops have been noted in the literature, often obtained by interchanging the role of the primes 2 and 3"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702874","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":"math/0702874","created_at":"2026-05-18T04:15:07.284084+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0702874v1","created_at":"2026-05-18T04:15:07.284084+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702874","created_at":"2026-05-18T04:15:07.284084+00:00"},{"alias_kind":"pith_short_12","alias_value":"3WDMFV63H37I","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"3WDMFV63H37IKQC4","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"3WDMFV63","created_at":"2026-05-18T12:25:54.717736+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/3WDMFV63H37IKQC4TYPF4W5XRT","json":"https://pith.science/pith/3WDMFV63H37IKQC4TYPF4W5XRT.json","graph_json":"https://pith.science/api/pith-number/3WDMFV63H37IKQC4TYPF4W5XRT/graph.json","events_json":"https://pith.science/api/pith-number/3WDMFV63H37IKQC4TYPF4W5XRT/events.json","paper":"https://pith.science/paper/3WDMFV63"},"agent_actions":{"view_html":"https://pith.science/pith/3WDMFV63H37IKQC4TYPF4W5XRT","download_json":"https://pith.science/pith/3WDMFV63H37IKQC4TYPF4W5XRT.json","view_paper":"https://pith.science/paper/3WDMFV63","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0702874&json=true","fetch_graph":"https://pith.science/api/pith-number/3WDMFV63H37IKQC4TYPF4W5XRT/graph.json","fetch_events":"https://pith.science/api/pith-number/3WDMFV63H37IKQC4TYPF4W5XRT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3WDMFV63H37IKQC4TYPF4W5XRT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3WDMFV63H37IKQC4TYPF4W5XRT/action/storage_attestation","attest_author":"https://pith.science/pith/3WDMFV63H37IKQC4TYPF4W5XRT/action/author_attestation","sign_citation":"https://pith.science/pith/3WDMFV63H37IKQC4TYPF4W5XRT/action/citation_signature","submit_replication":"https://pith.science/pith/3WDMFV63H37IKQC4TYPF4W5XRT/action/replication_record"}},"created_at":"2026-05-18T04:15:07.284084+00:00","updated_at":"2026-05-18T04:15:07.284084+00:00"}