{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:MXLQTHMNTIGGXFPH7PFVXCUM5G","short_pith_number":"pith:MXLQTHMN","schema_version":"1.0","canonical_sha256":"65d7099d8d9a0c6b95e7fbcb5b8a8ce99180dfc14634c339139166af3cabfac2","source":{"kind":"arxiv","id":"2606.26286","version":1},"attestation_state":"computed","paper":{"title":"Analogues of Gr\\\"un's lemma and Baer's theorem for skew left braces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.GR","authors_text":"A. Ballester-Bolinches, L. A. Kurdachenko, P. P\\'erez-Altarriba, R. Esteban-Romero","submitted_at":"2026-06-24T18:31:20Z","abstract_excerpt":"We prove in this paper some analogues of the well-known group-theoretical Gr\\\"un's lemma, stating that in a perfect group the first and the second centre coincide, and Baer's theorem, stating that if the quotient by the nth centre of a group is finite, then so is the $(n + 1)$th term of the lower central series, in the scope of nfinite slew left braces. These results represent significant improvements over previous work. The trifactorised group associated with a skew left brace will be crucial for our proofs."},"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":"2606.26286","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-06-24T18:31:20Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"2109a13fa3c707f8b1cd2e5128cc4dca0f8e58cc8a269250ac033e93e9aa566a","abstract_canon_sha256":"561082db4d04712871286f179817354e8ce3f82ae0eabbdd0d1316769580a7d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-26T00:15:35.479825Z","signature_b64":"8bxYq7aCn23iUZo/BSJCOryKsX6zfSPqI1+04ccvUHzjwBm7k3I6v8Rtl1ir72E0Wvns59ncD2CjC5KBzQvyCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65d7099d8d9a0c6b95e7fbcb5b8a8ce99180dfc14634c339139166af3cabfac2","last_reissued_at":"2026-06-26T00:15:35.479435Z","signature_status":"signed_v1","first_computed_at":"2026-06-26T00:15:35.479435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analogues of Gr\\\"un's lemma and Baer's theorem for skew left braces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.GR","authors_text":"A. Ballester-Bolinches, L. A. Kurdachenko, P. P\\'erez-Altarriba, R. Esteban-Romero","submitted_at":"2026-06-24T18:31:20Z","abstract_excerpt":"We prove in this paper some analogues of the well-known group-theoretical Gr\\\"un's lemma, stating that in a perfect group the first and the second centre coincide, and Baer's theorem, stating that if the quotient by the nth centre of a group is finite, then so is the $(n + 1)$th term of the lower central series, in the scope of nfinite slew left braces. These results represent significant improvements over previous work. The trifactorised group associated with a skew left brace will be crucial for our proofs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26286","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.26286/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.26286","created_at":"2026-06-26T00:15:35.479491+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.26286v1","created_at":"2026-06-26T00:15:35.479491+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.26286","created_at":"2026-06-26T00:15:35.479491+00:00"},{"alias_kind":"pith_short_12","alias_value":"MXLQTHMNTIGG","created_at":"2026-06-26T00:15:35.479491+00:00"},{"alias_kind":"pith_short_16","alias_value":"MXLQTHMNTIGGXFPH","created_at":"2026-06-26T00:15:35.479491+00:00"},{"alias_kind":"pith_short_8","alias_value":"MXLQTHMN","created_at":"2026-06-26T00:15:35.479491+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/MXLQTHMNTIGGXFPH7PFVXCUM5G","json":"https://pith.science/pith/MXLQTHMNTIGGXFPH7PFVXCUM5G.json","graph_json":"https://pith.science/api/pith-number/MXLQTHMNTIGGXFPH7PFVXCUM5G/graph.json","events_json":"https://pith.science/api/pith-number/MXLQTHMNTIGGXFPH7PFVXCUM5G/events.json","paper":"https://pith.science/paper/MXLQTHMN"},"agent_actions":{"view_html":"https://pith.science/pith/MXLQTHMNTIGGXFPH7PFVXCUM5G","download_json":"https://pith.science/pith/MXLQTHMNTIGGXFPH7PFVXCUM5G.json","view_paper":"https://pith.science/paper/MXLQTHMN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.26286&json=true","fetch_graph":"https://pith.science/api/pith-number/MXLQTHMNTIGGXFPH7PFVXCUM5G/graph.json","fetch_events":"https://pith.science/api/pith-number/MXLQTHMNTIGGXFPH7PFVXCUM5G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MXLQTHMNTIGGXFPH7PFVXCUM5G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MXLQTHMNTIGGXFPH7PFVXCUM5G/action/storage_attestation","attest_author":"https://pith.science/pith/MXLQTHMNTIGGXFPH7PFVXCUM5G/action/author_attestation","sign_citation":"https://pith.science/pith/MXLQTHMNTIGGXFPH7PFVXCUM5G/action/citation_signature","submit_replication":"https://pith.science/pith/MXLQTHMNTIGGXFPH7PFVXCUM5G/action/replication_record"}},"created_at":"2026-06-26T00:15:35.479491+00:00","updated_at":"2026-06-26T00:15:35.479491+00:00"}