{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:M7Q3VMJICQNGL3HFILXIYPGESF","short_pith_number":"pith:M7Q3VMJI","schema_version":"1.0","canonical_sha256":"67e1bab128141a65ece542ee8c3cc4916daf0e20da033d0f613f40172488993c","source":{"kind":"arxiv","id":"1105.5742","version":5},"attestation_state":"computed","paper":{"title":"Subset currents on free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Ilya Kapovich, Tatiana Nagnibeda","submitted_at":"2011-05-28T22:23:02Z","abstract_excerpt":"We introduce and study the space of \\emph{subset currents} on the free group $F_N$. A subset current on $F_N$ is a positive $F_N$-invariant locally finite Borel measure on the space $\\mathfrak C_N$ of all closed subsets of $\\partial F_N$ consisting of at least two points. While ordinary geodesic currents generalize conjugacy classes of nontrivial group elements, a subset current is a measure-theoretic generalization of the conjugacy class of a nontrivial finitely generated subgroup in $F_N$, and, more generally, in a word-hyperbolic group. The concept of a subset current is related to the noti"},"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":"1105.5742","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-28T22:23:02Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"1c1ea50fb9659235cf48f47d2b7d3cd956b0889a27089fb25a0bf3a53c03193a","abstract_canon_sha256":"4c676e1184348bd75e6509d4a9c63d0bdf3668d1a7774ed9433553429b2cbea5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:32.282151Z","signature_b64":"J0KeZoXJO8hHGmslStuulbnA6n0EN8vEl09SwUxXDar/k/RRl2hu/HXJpPF1BEBLPgCeRQp6d5LJFKZxYTK7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67e1bab128141a65ece542ee8c3cc4916daf0e20da033d0f613f40172488993c","last_reissued_at":"2026-05-18T03:13:32.281563Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:32.281563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subset currents on free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Ilya Kapovich, Tatiana Nagnibeda","submitted_at":"2011-05-28T22:23:02Z","abstract_excerpt":"We introduce and study the space of \\emph{subset currents} on the free group $F_N$. A subset current on $F_N$ is a positive $F_N$-invariant locally finite Borel measure on the space $\\mathfrak C_N$ of all closed subsets of $\\partial F_N$ consisting of at least two points. While ordinary geodesic currents generalize conjugacy classes of nontrivial group elements, a subset current is a measure-theoretic generalization of the conjugacy class of a nontrivial finitely generated subgroup in $F_N$, and, more generally, in a word-hyperbolic group. The concept of a subset current is related to the noti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5742","kind":"arxiv","version":5},"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":"1105.5742","created_at":"2026-05-18T03:13:32.281657+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.5742v5","created_at":"2026-05-18T03:13:32.281657+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5742","created_at":"2026-05-18T03:13:32.281657+00:00"},{"alias_kind":"pith_short_12","alias_value":"M7Q3VMJICQNG","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"M7Q3VMJICQNGL3HF","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"M7Q3VMJI","created_at":"2026-05-18T12:26:34.985390+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/M7Q3VMJICQNGL3HFILXIYPGESF","json":"https://pith.science/pith/M7Q3VMJICQNGL3HFILXIYPGESF.json","graph_json":"https://pith.science/api/pith-number/M7Q3VMJICQNGL3HFILXIYPGESF/graph.json","events_json":"https://pith.science/api/pith-number/M7Q3VMJICQNGL3HFILXIYPGESF/events.json","paper":"https://pith.science/paper/M7Q3VMJI"},"agent_actions":{"view_html":"https://pith.science/pith/M7Q3VMJICQNGL3HFILXIYPGESF","download_json":"https://pith.science/pith/M7Q3VMJICQNGL3HFILXIYPGESF.json","view_paper":"https://pith.science/paper/M7Q3VMJI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.5742&json=true","fetch_graph":"https://pith.science/api/pith-number/M7Q3VMJICQNGL3HFILXIYPGESF/graph.json","fetch_events":"https://pith.science/api/pith-number/M7Q3VMJICQNGL3HFILXIYPGESF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M7Q3VMJICQNGL3HFILXIYPGESF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M7Q3VMJICQNGL3HFILXIYPGESF/action/storage_attestation","attest_author":"https://pith.science/pith/M7Q3VMJICQNGL3HFILXIYPGESF/action/author_attestation","sign_citation":"https://pith.science/pith/M7Q3VMJICQNGL3HFILXIYPGESF/action/citation_signature","submit_replication":"https://pith.science/pith/M7Q3VMJICQNGL3HFILXIYPGESF/action/replication_record"}},"created_at":"2026-05-18T03:13:32.281657+00:00","updated_at":"2026-05-18T03:13:32.281657+00:00"}