{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:C3J6GQVHV3JNX4FO5HSB5T3G2E","short_pith_number":"pith:C3J6GQVH","schema_version":"1.0","canonical_sha256":"16d3e342a7aed2dbf0aee9e41ecf66d108215db80607e28563b6bf55f24202d5","source":{"kind":"arxiv","id":"1306.2689","version":1},"attestation_state":"computed","paper":{"title":"Groups in which some primary subgroups are weakly s-supplemented?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Baojun LI","submitted_at":"2013-06-12T01:40:39Z","abstract_excerpt":"A subgroup $H$ of a group $G$ is called weakly s-supplemented in $G$ if there is a subgroup $T$ such that $G=HT$ and $H\\cap T\\le H_{sG}$, where $H_{sG}$ is the subgroup of $H$ generated by all those subgroups of $H$ which are s-permutable in $G$. The influence of primary weakly s-supplemented subgroups on the structure of finite groups is investigated. An open question promoted by Skiba is studied and some known results are generalized."},"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":"1306.2689","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-06-12T01:40:39Z","cross_cats_sorted":[],"title_canon_sha256":"77e15b6377ae8518b68439a1ddef5505fd17f0b53c9f86168b6b76f04be26fae","abstract_canon_sha256":"81b02648442de85de3de81b0c4c984e327eabde126689fc03684181d2353c104"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:09.753335Z","signature_b64":"cAtI4txr/knHEvUTpEXzjrPOvedPEsJayjduTg8+9oGfRgKKfIMMwyDb5SJ83fdQjNYI/PesQ5mzSudAy4o8Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16d3e342a7aed2dbf0aee9e41ecf66d108215db80607e28563b6bf55f24202d5","last_reissued_at":"2026-05-18T03:21:09.752536Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:09.752536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Groups in which some primary subgroups are weakly s-supplemented?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Baojun LI","submitted_at":"2013-06-12T01:40:39Z","abstract_excerpt":"A subgroup $H$ of a group $G$ is called weakly s-supplemented in $G$ if there is a subgroup $T$ such that $G=HT$ and $H\\cap T\\le H_{sG}$, where $H_{sG}$ is the subgroup of $H$ generated by all those subgroups of $H$ which are s-permutable in $G$. The influence of primary weakly s-supplemented subgroups on the structure of finite groups is investigated. An open question promoted by Skiba is studied and some known results are generalized."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2689","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":"1306.2689","created_at":"2026-05-18T03:21:09.752663+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.2689v1","created_at":"2026-05-18T03:21:09.752663+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2689","created_at":"2026-05-18T03:21:09.752663+00:00"},{"alias_kind":"pith_short_12","alias_value":"C3J6GQVHV3JN","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"C3J6GQVHV3JNX4FO","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"C3J6GQVH","created_at":"2026-05-18T12:27:40.988391+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/C3J6GQVHV3JNX4FO5HSB5T3G2E","json":"https://pith.science/pith/C3J6GQVHV3JNX4FO5HSB5T3G2E.json","graph_json":"https://pith.science/api/pith-number/C3J6GQVHV3JNX4FO5HSB5T3G2E/graph.json","events_json":"https://pith.science/api/pith-number/C3J6GQVHV3JNX4FO5HSB5T3G2E/events.json","paper":"https://pith.science/paper/C3J6GQVH"},"agent_actions":{"view_html":"https://pith.science/pith/C3J6GQVHV3JNX4FO5HSB5T3G2E","download_json":"https://pith.science/pith/C3J6GQVHV3JNX4FO5HSB5T3G2E.json","view_paper":"https://pith.science/paper/C3J6GQVH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.2689&json=true","fetch_graph":"https://pith.science/api/pith-number/C3J6GQVHV3JNX4FO5HSB5T3G2E/graph.json","fetch_events":"https://pith.science/api/pith-number/C3J6GQVHV3JNX4FO5HSB5T3G2E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C3J6GQVHV3JNX4FO5HSB5T3G2E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C3J6GQVHV3JNX4FO5HSB5T3G2E/action/storage_attestation","attest_author":"https://pith.science/pith/C3J6GQVHV3JNX4FO5HSB5T3G2E/action/author_attestation","sign_citation":"https://pith.science/pith/C3J6GQVHV3JNX4FO5HSB5T3G2E/action/citation_signature","submit_replication":"https://pith.science/pith/C3J6GQVHV3JNX4FO5HSB5T3G2E/action/replication_record"}},"created_at":"2026-05-18T03:21:09.752663+00:00","updated_at":"2026-05-18T03:21:09.752663+00:00"}