{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VQB7S6INZ53EPFP6ZE34RSMQED","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":"51208642e2cffb276f88a94d2db4763c036251c3f2eb5843d7e1699f1fcef841","cross_cats_sorted":["math.GR","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-02T19:02:49Z","title_canon_sha256":"30788ace9fa09218839b41c7160fd81a2be2015938de69a37fd91bc20c642d41"},"schema_version":"1.0","source":{"id":"1201.0513","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0513","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0513v1","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0513","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"pith_short_12","alias_value":"VQB7S6INZ53E","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VQB7S6INZ53EPFP6","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VQB7S6IN","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:000734adc8c792037982bbd49a16825d85d7323a036903615603766ffc32fdfe","target":"graph","created_at":"2026-05-18T04:05:17Z","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":"In this paper we study the dynamics of Bernoulli flows and their subflows over general countable groups from the symbolic and topological perspectives. We study free subflows (subflows in which every point has trivial stabilizer), minimal subflows, disjointness of subflows, the problem of classifying subflows up to topological conjugacy, and the differences in dynamical behavior between pairs of points which disagree on finitely many coordinates. We call a point hyper aperiodic if the closure of its orbit is a free subflow and we call it minimal if the closure of its orbit is a minimal subflow","authors_text":"Brandon Seward, Steve Jackson, Su Gao","cross_cats":["math.GR","math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-02T19:02:49Z","title":"Group Colorings and Bernoulli Subflows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0513","kind":"arxiv","version":1},"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":"sha256:66828a2a41a5cfcc8729ee299498b7de462b3aefdecd3f846597c27f70bb6430","target":"record","created_at":"2026-05-18T04:05:17Z","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":"51208642e2cffb276f88a94d2db4763c036251c3f2eb5843d7e1699f1fcef841","cross_cats_sorted":["math.GR","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-02T19:02:49Z","title_canon_sha256":"30788ace9fa09218839b41c7160fd81a2be2015938de69a37fd91bc20c642d41"},"schema_version":"1.0","source":{"id":"1201.0513","kind":"arxiv","version":1}},"canonical_sha256":"ac03f9790dcf764795fec937c8c99020ec5368ee42c94dcdb53cd65ffc8bd23a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac03f9790dcf764795fec937c8c99020ec5368ee42c94dcdb53cd65ffc8bd23a","first_computed_at":"2026-05-18T04:05:17.365780Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:17.365780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RgYZS84q+Lw4I4XcsY6OZLQXnlTuMfl3GNFSxbULo3yJUnVREvxhUnnKy4m6+/i39gPZvGRg9EBew0p9iPLYAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:17.366277Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.0513","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66828a2a41a5cfcc8729ee299498b7de462b3aefdecd3f846597c27f70bb6430","sha256:000734adc8c792037982bbd49a16825d85d7323a036903615603766ffc32fdfe"],"state_sha256":"3283e1732c3cf1ea2957a891e4718d324d5647a314f2aee216fd308c3a4ca14c"}