{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:GPFVRDSEQ6CNDOB5H3LRYE3IHT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a2d2314635d960b4531adfa6801b4428e2007403d118052cc29eacbce04f25e1","cross_cats_sorted":[],"license":"","primary_cat":"math.GR","submitted_at":"2002-10-13T18:16:44Z","title_canon_sha256":"b3796a67abdd26c67bffad1d8b755d9709f38b9406d918ac0fe1266392c3e336"},"schema_version":"1.0","source":{"id":"math/0210191","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0210191","created_at":"2026-07-04T14:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"math/0210191v1","created_at":"2026-07-04T14:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0210191","created_at":"2026-07-04T14:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"GPFVRDSEQ6CN","created_at":"2026-07-04T14:36:37Z"},{"alias_kind":"pith_short_16","alias_value":"GPFVRDSEQ6CNDOB5","created_at":"2026-07-04T14:36:37Z"},{"alias_kind":"pith_short_8","alias_value":"GPFVRDSE","created_at":"2026-07-04T14:36:37Z"}],"graph_snapshots":[{"event_id":"sha256:01e044523ec6ce330c5dfd2921b82ccc6c559006ce9623fa5daec5a838ea171b","target":"graph","created_at":"2026-07-04T14:36:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0210191/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that every noncyclic subgroup of a free $m$-generator Burnside group $B(m,n)$ of odd exponent $n \\gg 1$ contains a subgroup $H$ isomorphic to a free Burnside group $B(\\infty,n)$ of exponent $n$ and countably infinite rank such that for every normal subgroup $K$ of $H$ the normal closure $<K >^{B(m,n)}$ of $K$ in $B(m,n)$ meets $H$ in $K$. This implies that every noncyclic subgroup of $B(m,n)$ is SQ-universal in the class of groups of exponent $n$.","authors_text":"S.V. Ivanov","cross_cats":[],"headline":"","license":"","primary_cat":"math.GR","submitted_at":"2002-10-13T18:16:44Z","title":"On subgroups of free Burnside groups of large odd exponent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0210191","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:62519e10f4ad51d757be5ae8c52cab44c460bddb4859c41728fe7454fb7a2db0","target":"record","created_at":"2026-07-04T14:36:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a2d2314635d960b4531adfa6801b4428e2007403d118052cc29eacbce04f25e1","cross_cats_sorted":[],"license":"","primary_cat":"math.GR","submitted_at":"2002-10-13T18:16:44Z","title_canon_sha256":"b3796a67abdd26c67bffad1d8b755d9709f38b9406d918ac0fe1266392c3e336"},"schema_version":"1.0","source":{"id":"math/0210191","kind":"arxiv","version":1}},"canonical_sha256":"33cb588e448784d1b83d3ed71c13683cced276f677da0819a4b2984980ae7214","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33cb588e448784d1b83d3ed71c13683cced276f677da0819a4b2984980ae7214","first_computed_at":"2026-07-04T14:36:37.947148Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:36:37.947148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uUcbyGDwBzP8lsZMcPoYA1cnc66WvDz/EwHnHLFIu7OEidGEWCevLoPqtAWla19wXGZeGuu6aT6jTQoP4Ov7Dg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:36:37.947558Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0210191","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62519e10f4ad51d757be5ae8c52cab44c460bddb4859c41728fe7454fb7a2db0","sha256:01e044523ec6ce330c5dfd2921b82ccc6c559006ce9623fa5daec5a838ea171b"],"state_sha256":"c8b082252c7e0e7d835ee00f1cb2448cba8755750f3f01d00d5476c7de0088fd"}