{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:5FAPVACPWW6STC4NXQU2V7PK4C","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":"9832d79d21ac85816a4753fe10a462af577f05c56378a34bfa08870f2c118099","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-01-29T17:51:02Z","title_canon_sha256":"b9735bfbe81d6fe9c93ddcfebb57b234e31ca2c4776eb74af9743c13e36c2c25"},"schema_version":"1.0","source":{"id":"0901.4734","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.4734","created_at":"2026-05-18T02:39:32Z"},{"alias_kind":"arxiv_version","alias_value":"0901.4734v3","created_at":"2026-05-18T02:39:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.4734","created_at":"2026-05-18T02:39:32Z"},{"alias_kind":"pith_short_12","alias_value":"5FAPVACPWW6S","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"5FAPVACPWW6STC4N","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"5FAPVACP","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:098939c70cbcf4a60468ef11b33715fcf5cbc10e6ed2e65d008fa3f69760426c","target":"graph","created_at":"2026-05-18T02:39:32Z","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 basic ergodic properties (ergodicity and conservativity) of the action of an arbitrary subgroup $H$ of a free group $F$ on the boundary $\\partial F$ with respect to the uniform measure. Our approach is geometrical and combinatorial, and it is based on choosing a system of Nielsen--Schreier generators in $H$ associated with a geodesic spanning tree in the Schreier graph $X=H\\backslash F$. We give several (mod 0) equivalent descriptions of the Hopf decomposition of the boundary into the conservative and the dissipative parts. Further we relate conservativity and dissipativity of the","authors_text":"Rostislav Grigorchuk, Tatiana Nagnibeda, Vadim A. Kaimanovich","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-01-29T17:51:02Z","title":"Ergodic properties of boundary actions and Nielsen--Schreier theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.4734","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:c4d4f275ec9bbb5223603dedce1b1a787f9d700724ccb992b1ded3ba5054ee1a","target":"record","created_at":"2026-05-18T02:39:32Z","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":"9832d79d21ac85816a4753fe10a462af577f05c56378a34bfa08870f2c118099","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-01-29T17:51:02Z","title_canon_sha256":"b9735bfbe81d6fe9c93ddcfebb57b234e31ca2c4776eb74af9743c13e36c2c25"},"schema_version":"1.0","source":{"id":"0901.4734","kind":"arxiv","version":3}},"canonical_sha256":"e940fa804fb5bd298b8dbc29aafdeae0a8b139961d5258ca9d916139789f1506","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e940fa804fb5bd298b8dbc29aafdeae0a8b139961d5258ca9d916139789f1506","first_computed_at":"2026-05-18T02:39:32.513499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:32.513499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tgx02Pf+MHpgdnNqPYLDky0QVvoZgY/LRLrPKK5F7DHPAPmiZ3etgNCPt17s1hVdFmS9CtRjbi/DLUjTxHsSBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:32.513992Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.4734","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4d4f275ec9bbb5223603dedce1b1a787f9d700724ccb992b1ded3ba5054ee1a","sha256:098939c70cbcf4a60468ef11b33715fcf5cbc10e6ed2e65d008fa3f69760426c"],"state_sha256":"f59f90d2c4447e7022bb6b8741bf835f52211d41a4f032b18f7f3f42a7b157b3"}