{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:ZD5HRLY6R5IGNK4KBABEZVKJMZ","short_pith_number":"pith:ZD5HRLY6","schema_version":"1.0","canonical_sha256":"c8fa78af1e8f5066ab8a08024cd549664372af25bd56ea45f858db952debc204","source":{"kind":"arxiv","id":"1008.0700","version":1},"attestation_state":"computed","paper":{"title":"Powers of Elements in Jordan Loops","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Kyle Pula","submitted_at":"2010-08-04T05:23:30Z","abstract_excerpt":"A Jordan loop is a commutative loop satisfying the Jordan identity $(x^2 y) x = x^2 (y x)$. We establish several identities involving powers in Jordan loops and show that there is no nonassociative Jordan loop of order $9$."},"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":"1008.0700","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-08-04T05:23:30Z","cross_cats_sorted":[],"title_canon_sha256":"8fc1df133e05898f1a90e12b4dead61c8f64afd55135269f9f08e765779cb9bc","abstract_canon_sha256":"32195e89ffe6ed14f502d622ead013013df32d8916af9e21664e3047458da864"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:35.841185Z","signature_b64":"8pWHD0SC5T9GRQ/eqGkky5oocJEgG5RHrNlKCu3RU/DvlaLNUB9BTI2Kw3iVKSCvcDgFc2vKnP1jQp4p8wH4AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8fa78af1e8f5066ab8a08024cd549664372af25bd56ea45f858db952debc204","last_reissued_at":"2026-05-18T04:42:35.840586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:35.840586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Powers of Elements in Jordan Loops","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Kyle Pula","submitted_at":"2010-08-04T05:23:30Z","abstract_excerpt":"A Jordan loop is a commutative loop satisfying the Jordan identity $(x^2 y) x = x^2 (y x)$. We establish several identities involving powers in Jordan loops and show that there is no nonassociative Jordan loop of order $9$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0700","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":"1008.0700","created_at":"2026-05-18T04:42:35.840649+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.0700v1","created_at":"2026-05-18T04:42:35.840649+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0700","created_at":"2026-05-18T04:42:35.840649+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZD5HRLY6R5IG","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZD5HRLY6R5IGNK4K","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZD5HRLY6","created_at":"2026-05-18T12:26:17.028572+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/ZD5HRLY6R5IGNK4KBABEZVKJMZ","json":"https://pith.science/pith/ZD5HRLY6R5IGNK4KBABEZVKJMZ.json","graph_json":"https://pith.science/api/pith-number/ZD5HRLY6R5IGNK4KBABEZVKJMZ/graph.json","events_json":"https://pith.science/api/pith-number/ZD5HRLY6R5IGNK4KBABEZVKJMZ/events.json","paper":"https://pith.science/paper/ZD5HRLY6"},"agent_actions":{"view_html":"https://pith.science/pith/ZD5HRLY6R5IGNK4KBABEZVKJMZ","download_json":"https://pith.science/pith/ZD5HRLY6R5IGNK4KBABEZVKJMZ.json","view_paper":"https://pith.science/paper/ZD5HRLY6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.0700&json=true","fetch_graph":"https://pith.science/api/pith-number/ZD5HRLY6R5IGNK4KBABEZVKJMZ/graph.json","fetch_events":"https://pith.science/api/pith-number/ZD5HRLY6R5IGNK4KBABEZVKJMZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZD5HRLY6R5IGNK4KBABEZVKJMZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZD5HRLY6R5IGNK4KBABEZVKJMZ/action/storage_attestation","attest_author":"https://pith.science/pith/ZD5HRLY6R5IGNK4KBABEZVKJMZ/action/author_attestation","sign_citation":"https://pith.science/pith/ZD5HRLY6R5IGNK4KBABEZVKJMZ/action/citation_signature","submit_replication":"https://pith.science/pith/ZD5HRLY6R5IGNK4KBABEZVKJMZ/action/replication_record"}},"created_at":"2026-05-18T04:42:35.840649+00:00","updated_at":"2026-05-18T04:42:35.840649+00:00"}