{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:T2SQZX4655B6E6YYUWMQRDJZXU","short_pith_number":"pith:T2SQZX46","schema_version":"1.0","canonical_sha256":"9ea50cdf9eef43e27b18a599088d39bd1202d68dce0a2db385eafc253cb98654","source":{"kind":"arxiv","id":"1407.5224","version":1},"attestation_state":"computed","paper":{"title":"Classification of braces of order $p^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GR","authors_text":"David Bachiller","submitted_at":"2014-07-19T22:08:51Z","abstract_excerpt":"A classification up to isomorphism of all left braces of order $p^3$, where $p$ is any prime number, is given. To this end, we first classify all the left braces of order $p$ and $p^2$, and then we construct explicitly the hypothesis required in Corollary D of N. Ben David's Ph.D. thesis to build multiplications of left braces."},"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":"1407.5224","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-07-19T22:08:51Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"ccc8fa7f8e66b12d08119a672188ec227a9ae270343dfdfc87708c0390b263dc","abstract_canon_sha256":"77fa348cd165879abfd68004cd000267f823391a9490c2f1570f459d5fa6d397"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:14.645226Z","signature_b64":"P+88vI/i0DAJBZWKTM+wF21CGR5zYn6jh6Jc/LcZ9imjOUQiRfB6JWAYfLVRpkwtdLIgKgBhouVNxmY0ikbKDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ea50cdf9eef43e27b18a599088d39bd1202d68dce0a2db385eafc253cb98654","last_reissued_at":"2026-05-18T02:47:14.644512Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:14.644512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification of braces of order $p^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GR","authors_text":"David Bachiller","submitted_at":"2014-07-19T22:08:51Z","abstract_excerpt":"A classification up to isomorphism of all left braces of order $p^3$, where $p$ is any prime number, is given. To this end, we first classify all the left braces of order $p$ and $p^2$, and then we construct explicitly the hypothesis required in Corollary D of N. Ben David's Ph.D. thesis to build multiplications of left braces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5224","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":"1407.5224","created_at":"2026-05-18T02:47:14.644594+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.5224v1","created_at":"2026-05-18T02:47:14.644594+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5224","created_at":"2026-05-18T02:47:14.644594+00:00"},{"alias_kind":"pith_short_12","alias_value":"T2SQZX4655B6","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"T2SQZX4655B6E6YY","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"T2SQZX46","created_at":"2026-05-18T12:28:49.207871+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/T2SQZX4655B6E6YYUWMQRDJZXU","json":"https://pith.science/pith/T2SQZX4655B6E6YYUWMQRDJZXU.json","graph_json":"https://pith.science/api/pith-number/T2SQZX4655B6E6YYUWMQRDJZXU/graph.json","events_json":"https://pith.science/api/pith-number/T2SQZX4655B6E6YYUWMQRDJZXU/events.json","paper":"https://pith.science/paper/T2SQZX46"},"agent_actions":{"view_html":"https://pith.science/pith/T2SQZX4655B6E6YYUWMQRDJZXU","download_json":"https://pith.science/pith/T2SQZX4655B6E6YYUWMQRDJZXU.json","view_paper":"https://pith.science/paper/T2SQZX46","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.5224&json=true","fetch_graph":"https://pith.science/api/pith-number/T2SQZX4655B6E6YYUWMQRDJZXU/graph.json","fetch_events":"https://pith.science/api/pith-number/T2SQZX4655B6E6YYUWMQRDJZXU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T2SQZX4655B6E6YYUWMQRDJZXU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T2SQZX4655B6E6YYUWMQRDJZXU/action/storage_attestation","attest_author":"https://pith.science/pith/T2SQZX4655B6E6YYUWMQRDJZXU/action/author_attestation","sign_citation":"https://pith.science/pith/T2SQZX4655B6E6YYUWMQRDJZXU/action/citation_signature","submit_replication":"https://pith.science/pith/T2SQZX4655B6E6YYUWMQRDJZXU/action/replication_record"}},"created_at":"2026-05-18T02:47:14.644594+00:00","updated_at":"2026-05-18T02:47:14.644594+00:00"}