{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GH2O3MDAUICOXCA4RT6ZM5JHFE","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":"3c8a69e29a46a2b015b8731dd88bfa6930c9d2b9fbf8d1cac3c90ce02b57a4e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-31T10:26:09Z","title_canon_sha256":"95d66cbc5162402fd0720ee68ba4f75aa05839fb4575a4bf64c4f6835bd8f6c0"},"schema_version":"1.0","source":{"id":"1610.09851","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09851","created_at":"2026-05-18T00:27:22Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09851v3","created_at":"2026-05-18T00:27:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09851","created_at":"2026-05-18T00:27:22Z"},{"alias_kind":"pith_short_12","alias_value":"GH2O3MDAUICO","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GH2O3MDAUICOXCA4","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GH2O3MDA","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:845c88c2da106cbaa087cd4029205658e25583405915d2e90ed054764833a778","target":"graph","created_at":"2026-05-18T00:27:22Z","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":"Let $G$ be a discrete countable infinite group. We show that each topological $(C,F)$-action $T$ of $G$ on a locally compact non-compact Cantor set is a free minimal amenable action admitting a unique up to scaling non-zero invariant Radon measure (answer to a question by Kellerhals, Monod and R{\\o}rdam). We find necessary and sufficient conditions under which two such actions are topologically conjugate in terms of the underlying $(C,F)$-parameters. If $G$ is linearly ordered Abelian then the topological centralizer of $T$ is trivial. If $G$ is monotileable and amenable, denote by ${\\cal A}_G","authors_text":"Alexandre I. Danilenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-31T10:26:09Z","title":"Rank-one actions, their $(C,F)$-models and constructions with bounded parameters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09851","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":"sha256:689a51a9d3b3d2dda69c7bbe08865748a5f98f0f5e9b20dfeca9f57488c0a8f6","target":"record","created_at":"2026-05-18T00:27:22Z","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":"3c8a69e29a46a2b015b8731dd88bfa6930c9d2b9fbf8d1cac3c90ce02b57a4e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-31T10:26:09Z","title_canon_sha256":"95d66cbc5162402fd0720ee68ba4f75aa05839fb4575a4bf64c4f6835bd8f6c0"},"schema_version":"1.0","source":{"id":"1610.09851","kind":"arxiv","version":3}},"canonical_sha256":"31f4edb060a204eb881c8cfd967527293de99349393e725eceedbffd0c515fc3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31f4edb060a204eb881c8cfd967527293de99349393e725eceedbffd0c515fc3","first_computed_at":"2026-05-18T00:27:22.082629Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:22.082629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aLN2E1qqhLz07ntjHnNEQjzH+KyybR2Da7bqVDKlCe7dzEfLO2pQdF6/S/80I3bc44vee3PcafpcDkLzvwZoDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:22.083349Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09851","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:689a51a9d3b3d2dda69c7bbe08865748a5f98f0f5e9b20dfeca9f57488c0a8f6","sha256:845c88c2da106cbaa087cd4029205658e25583405915d2e90ed054764833a778"],"state_sha256":"b7257cd5d6751061961309abef1228f166bdf324df243d7d6e2c74d68967e6ca"}