{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:EIRFTFHFRM7RL5C42QC5C3MA6W","short_pith_number":"pith:EIRFTFHF","canonical_record":{"source":{"id":"1310.0493","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-01T21:18:02Z","cross_cats_sorted":[],"title_canon_sha256":"afef33ccc38a594856be0a2efd27b74c793fae5db4bdb734197708e92731b208","abstract_canon_sha256":"4d14150db01f4aec35a3bf474fc77bb4c30c14436d0a982b9075fc8c0c7c5a12"},"schema_version":"1.0"},"canonical_sha256":"22225994e58b3f15f45cd405d16d80f59818f53457b4e4e2a023b4d8a18bdd08","source":{"kind":"arxiv","id":"1310.0493","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0493","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0493v3","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0493","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"pith_short_12","alias_value":"EIRFTFHFRM7R","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EIRFTFHFRM7RL5C4","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EIRFTFHF","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:EIRFTFHFRM7RL5C42QC5C3MA6W","target":"record","payload":{"canonical_record":{"source":{"id":"1310.0493","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-01T21:18:02Z","cross_cats_sorted":[],"title_canon_sha256":"afef33ccc38a594856be0a2efd27b74c793fae5db4bdb734197708e92731b208","abstract_canon_sha256":"4d14150db01f4aec35a3bf474fc77bb4c30c14436d0a982b9075fc8c0c7c5a12"},"schema_version":"1.0"},"canonical_sha256":"22225994e58b3f15f45cd405d16d80f59818f53457b4e4e2a023b4d8a18bdd08","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:46.082251Z","signature_b64":"4gnD52YHlad9K+O/Sd8IamF4wgKQEgaer5vKsZlHgABCPSa+w24rI34MpgjErhFQPnbKb8MWoW+Ay2AhTN5XBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22225994e58b3f15f45cd405d16d80f59818f53457b4e4e2a023b4d8a18bdd08","last_reissued_at":"2026-05-18T01:04:46.081581Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:46.081581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.0493","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eFWWuKGlQE0kohKrPIgW/BzmZGK7CAt1W2/i3GzXQ6l5bR3lS2ZaXDJKka8UC1LlcE+9lHpp+CD2iQ9EWKnOCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:13:59.084269Z"},"content_sha256":"f129c302d3b24f1c5defd4d72782358fe865e077aed0f7d3e485e6e61d9202c2","schema_version":"1.0","event_id":"sha256:f129c302d3b24f1c5defd4d72782358fe865e077aed0f7d3e485e6e61d9202c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:EIRFTFHFRM7RL5C42QC5C3MA6W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Abstract commensurability and the Gupta--Sidki group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alejandra Garrido","submitted_at":"2013-10-01T21:18:02Z","abstract_excerpt":"We study the subgroup structure of the infinite torsion $p$-groups defined by Gupta and Sidki in 1983. In particular, following results of Grigorchuk and Wilson for the first Grigorchuk group, we show that all infinite finitely generated subgroups of the Gupta--Sidki 3-group $G$ are abstractly commensurable with $G$ or $G\\times G$. As a consequence, we show that $G$ is subgroup separable and from this it follows that its membership problem is soluble. Along the way, we obtain a characterization of finite subgroups of $G$ and establish an analogue for the Grigorchuk group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0493","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0jK6xLYVDkgcsU7Ha6e98871QvFYs5uZjQnxKgBwBck48AiT5352S8xK0xAAP1bnUb0HMyjNxF+sCKBYonTXDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:13:59.084753Z"},"content_sha256":"56b12216680e08b477c41cb729988b0afce320cf0388b42c6e573b73d9139016","schema_version":"1.0","event_id":"sha256:56b12216680e08b477c41cb729988b0afce320cf0388b42c6e573b73d9139016"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EIRFTFHFRM7RL5C42QC5C3MA6W/bundle.json","state_url":"https://pith.science/pith/EIRFTFHFRM7RL5C42QC5C3MA6W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EIRFTFHFRM7RL5C42QC5C3MA6W/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T20:13:59Z","links":{"resolver":"https://pith.science/pith/EIRFTFHFRM7RL5C42QC5C3MA6W","bundle":"https://pith.science/pith/EIRFTFHFRM7RL5C42QC5C3MA6W/bundle.json","state":"https://pith.science/pith/EIRFTFHFRM7RL5C42QC5C3MA6W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EIRFTFHFRM7RL5C42QC5C3MA6W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EIRFTFHFRM7RL5C42QC5C3MA6W","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":"4d14150db01f4aec35a3bf474fc77bb4c30c14436d0a982b9075fc8c0c7c5a12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-01T21:18:02Z","title_canon_sha256":"afef33ccc38a594856be0a2efd27b74c793fae5db4bdb734197708e92731b208"},"schema_version":"1.0","source":{"id":"1310.0493","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0493","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0493v3","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0493","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"pith_short_12","alias_value":"EIRFTFHFRM7R","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EIRFTFHFRM7RL5C4","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EIRFTFHF","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:56b12216680e08b477c41cb729988b0afce320cf0388b42c6e573b73d9139016","target":"graph","created_at":"2026-05-18T01:04:46Z","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"},"paper":{"abstract_excerpt":"We study the subgroup structure of the infinite torsion $p$-groups defined by Gupta and Sidki in 1983. In particular, following results of Grigorchuk and Wilson for the first Grigorchuk group, we show that all infinite finitely generated subgroups of the Gupta--Sidki 3-group $G$ are abstractly commensurable with $G$ or $G\\times G$. As a consequence, we show that $G$ is subgroup separable and from this it follows that its membership problem is soluble. Along the way, we obtain a characterization of finite subgroups of $G$ and establish an analogue for the Grigorchuk group.","authors_text":"Alejandra Garrido","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-01T21:18:02Z","title":"Abstract commensurability and the Gupta--Sidki group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0493","kind":"arxiv","version":3},"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:f129c302d3b24f1c5defd4d72782358fe865e077aed0f7d3e485e6e61d9202c2","target":"record","created_at":"2026-05-18T01:04:46Z","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":"4d14150db01f4aec35a3bf474fc77bb4c30c14436d0a982b9075fc8c0c7c5a12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-01T21:18:02Z","title_canon_sha256":"afef33ccc38a594856be0a2efd27b74c793fae5db4bdb734197708e92731b208"},"schema_version":"1.0","source":{"id":"1310.0493","kind":"arxiv","version":3}},"canonical_sha256":"22225994e58b3f15f45cd405d16d80f59818f53457b4e4e2a023b4d8a18bdd08","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22225994e58b3f15f45cd405d16d80f59818f53457b4e4e2a023b4d8a18bdd08","first_computed_at":"2026-05-18T01:04:46.081581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:46.081581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4gnD52YHlad9K+O/Sd8IamF4wgKQEgaer5vKsZlHgABCPSa+w24rI34MpgjErhFQPnbKb8MWoW+Ay2AhTN5XBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:46.082251Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.0493","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f129c302d3b24f1c5defd4d72782358fe865e077aed0f7d3e485e6e61d9202c2","sha256:56b12216680e08b477c41cb729988b0afce320cf0388b42c6e573b73d9139016"],"state_sha256":"ded2a09734f93ffbed8e04dc31f27b2daa5877dc6de275471dd9ed7e2cf8a9a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p3oNCzFdvnHy9rkCOTzLYLRAp8IUS3IUlhhv1SNMELoFSQT8Gq+7TBp4QDEwX/FO6Pcr3+vCwQ5kBEsXF9o4BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:13:59.087932Z","bundle_sha256":"851c248a4c568ce1b853b22dc047c091c1660674ca454d385c242bedb82c6867"}}