{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:AXKXUBHU64X44GF4HMD5Y5IHEU","short_pith_number":"pith:AXKXUBHU","schema_version":"1.0","canonical_sha256":"05d57a04f4f72fce18bc3b07dc75072534d39ebccaa6b53df0213c9dc0a35d4a","source":{"kind":"arxiv","id":"1402.3705","version":3},"attestation_state":"computed","paper":{"title":"Characteristic random subgroups of geometric groups and free abelian groups of infinite rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GR","authors_text":"Lewis Bowen, Rostislav Grigorchuk, Rostyslav Kravchenko","submitted_at":"2014-02-15T17:01:10Z","abstract_excerpt":"We show that if $G$ is a non-elementary word hyperbolic group, mapping class group of a hyperbolic surface or the outer automorphism group of a nonabelian free group then $G$ has $2^{\\aleph_0}$ many continuous ergodic invariant random subgroups. If $G$ is a nonabelian free group then $G$ has $2^{\\aleph_0}$ many continuous $G$-ergodic characteristic random subgroups. We also provide a complete classification of characteristic random subgroups of free abelian groups of countably infinite rank and elementary $p$-groups of countably infinite rank."},"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":"1402.3705","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-02-15T17:01:10Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"bcba3c16ff63133bf26ecf5744333e84a9ccb556b34d62b56aad8696f86caabe","abstract_canon_sha256":"cd06ef720c021f8bd7ff8cfdd383d0eaa7c087755961ac9eaac4b475ba75dd22"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:58.797483Z","signature_b64":"P/RX7LW5kdrUdyXUagRHPCoypHYfPFYbgp9NKSiFW9flXhPgbnP+lsFEyP5wggvWx0dqkH7L2GBs5YwC4rDzAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05d57a04f4f72fce18bc3b07dc75072534d39ebccaa6b53df0213c9dc0a35d4a","last_reissued_at":"2026-05-18T01:59:58.796953Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:58.796953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characteristic random subgroups of geometric groups and free abelian groups of infinite rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GR","authors_text":"Lewis Bowen, Rostislav Grigorchuk, Rostyslav Kravchenko","submitted_at":"2014-02-15T17:01:10Z","abstract_excerpt":"We show that if $G$ is a non-elementary word hyperbolic group, mapping class group of a hyperbolic surface or the outer automorphism group of a nonabelian free group then $G$ has $2^{\\aleph_0}$ many continuous ergodic invariant random subgroups. If $G$ is a nonabelian free group then $G$ has $2^{\\aleph_0}$ many continuous $G$-ergodic characteristic random subgroups. We also provide a complete classification of characteristic random subgroups of free abelian groups of countably infinite rank and elementary $p$-groups of countably infinite rank."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3705","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1402.3705","created_at":"2026-05-18T01:59:58.797059+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.3705v3","created_at":"2026-05-18T01:59:58.797059+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3705","created_at":"2026-05-18T01:59:58.797059+00:00"},{"alias_kind":"pith_short_12","alias_value":"AXKXUBHU64X4","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"AXKXUBHU64X44GF4","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"AXKXUBHU","created_at":"2026-05-18T12:28:19.803747+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/AXKXUBHU64X44GF4HMD5Y5IHEU","json":"https://pith.science/pith/AXKXUBHU64X44GF4HMD5Y5IHEU.json","graph_json":"https://pith.science/api/pith-number/AXKXUBHU64X44GF4HMD5Y5IHEU/graph.json","events_json":"https://pith.science/api/pith-number/AXKXUBHU64X44GF4HMD5Y5IHEU/events.json","paper":"https://pith.science/paper/AXKXUBHU"},"agent_actions":{"view_html":"https://pith.science/pith/AXKXUBHU64X44GF4HMD5Y5IHEU","download_json":"https://pith.science/pith/AXKXUBHU64X44GF4HMD5Y5IHEU.json","view_paper":"https://pith.science/paper/AXKXUBHU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.3705&json=true","fetch_graph":"https://pith.science/api/pith-number/AXKXUBHU64X44GF4HMD5Y5IHEU/graph.json","fetch_events":"https://pith.science/api/pith-number/AXKXUBHU64X44GF4HMD5Y5IHEU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AXKXUBHU64X44GF4HMD5Y5IHEU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AXKXUBHU64X44GF4HMD5Y5IHEU/action/storage_attestation","attest_author":"https://pith.science/pith/AXKXUBHU64X44GF4HMD5Y5IHEU/action/author_attestation","sign_citation":"https://pith.science/pith/AXKXUBHU64X44GF4HMD5Y5IHEU/action/citation_signature","submit_replication":"https://pith.science/pith/AXKXUBHU64X44GF4HMD5Y5IHEU/action/replication_record"}},"created_at":"2026-05-18T01:59:58.797059+00:00","updated_at":"2026-05-18T01:59:58.797059+00:00"}