{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Z7CN75ZVZY5B7CYTS2UMTLSTN3","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":"0441c2570d3e5612cc84776613c97494a8606f620dfa85b5b326cee053589af2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-10-25T18:08:22Z","title_canon_sha256":"f2031c258490fed784c0ef65e4e3641bdf23a9400895989fcbb9001f0e654a0a"},"schema_version":"1.0","source":{"id":"1210.6931","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6931","created_at":"2026-05-18T03:06:34Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6931v2","created_at":"2026-05-18T03:06:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6931","created_at":"2026-05-18T03:06:34Z"},{"alias_kind":"pith_short_12","alias_value":"Z7CN75ZVZY5B","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"Z7CN75ZVZY5B7CYT","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"Z7CN75ZV","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:2a2268a56b9526703b79c8af64fabf75ed547314efed58790c29eca77fa43993","target":"graph","created_at":"2026-05-18T03:06:34Z","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 attach to each finite bipartite separated graph (E,C) a partial dynamical system (\\Omega(E,C), F, \\theta), where \\Omega(E,C) is a zero-dimensional metrizable compact space, F is a finitely generated free group, and {\\theta} is a continuous partial action of F on \\Omega(E,C). The full crossed product C*-algebra O(E,C) = C(\\Omega(E,C)) \\rtimes_{\\theta} F is shown to be a canonical quotient of the graph C*-algebra C^*(E,C) of the separated graph (E,C). Similarly, we prove that, for any *-field K, the algebraic crossed product L^{ab}_K(E,C) = C_K(\\Omega(E,C)) \\rtimes_\\theta^{alg} F is a canonic","authors_text":"Pere Ara, Ruy Exel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-10-25T18:08:22Z","title":"Dynamical systems associated to separated graphs, graph algebras, and paradoxical decompositions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6931","kind":"arxiv","version":2},"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":"sha256:694063d4f3cecfc967797c44c1b675c7fd68f3171e4b3714c6d4542ebf2d27a3","target":"record","created_at":"2026-05-18T03:06:34Z","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":"0441c2570d3e5612cc84776613c97494a8606f620dfa85b5b326cee053589af2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-10-25T18:08:22Z","title_canon_sha256":"f2031c258490fed784c0ef65e4e3641bdf23a9400895989fcbb9001f0e654a0a"},"schema_version":"1.0","source":{"id":"1210.6931","kind":"arxiv","version":2}},"canonical_sha256":"cfc4dff735ce3a1f8b1396a8c9ae536edfce6b0b8adb1ec4e44254d3703835ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfc4dff735ce3a1f8b1396a8c9ae536edfce6b0b8adb1ec4e44254d3703835ea","first_computed_at":"2026-05-18T03:06:34.658957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:34.658957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RrhqliniizC2/L3q0PPIUWWXKgA5aZ+btA7mdWLQMzTx/CCXpKzh0i76NKuMGzyj6qWTeIg7g0OVhOdkQC73Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:34.659642Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.6931","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:694063d4f3cecfc967797c44c1b675c7fd68f3171e4b3714c6d4542ebf2d27a3","sha256:2a2268a56b9526703b79c8af64fabf75ed547314efed58790c29eca77fa43993"],"state_sha256":"ddbdc75b9dd8f80f0ee245a360e333e6b2a1292afa1a1068fd866fbadfece2a0"}