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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"},"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":"1210.6931","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-10-25T18:08:22Z","cross_cats_sorted":[],"title_canon_sha256":"f2031c258490fed784c0ef65e4e3641bdf23a9400895989fcbb9001f0e654a0a","abstract_canon_sha256":"0441c2570d3e5612cc84776613c97494a8606f620dfa85b5b326cee053589af2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:34.659642Z","signature_b64":"RrhqliniizC2/L3q0PPIUWWXKgA5aZ+btA7mdWLQMzTx/CCXpKzh0i76NKuMGzyj6qWTeIg7g0OVhOdkQC73Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfc4dff735ce3a1f8b1396a8c9ae536edfce6b0b8adb1ec4e44254d3703835ea","last_reissued_at":"2026-05-18T03:06:34.658957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:34.658957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamical systems associated to separated graphs, graph algebras, and paradoxical decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Pere Ara, Ruy Exel","submitted_at":"2012-10-25T18:08:22Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6931","kind":"arxiv","version":2},"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":"1210.6931","created_at":"2026-05-18T03:06:34.659090+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.6931v2","created_at":"2026-05-18T03:06:34.659090+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6931","created_at":"2026-05-18T03:06:34.659090+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z7CN75ZVZY5B","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z7CN75ZVZY5B7CYT","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z7CN75ZV","created_at":"2026-05-18T12:27:30.460161+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/Z7CN75ZVZY5B7CYTS2UMTLSTN3","json":"https://pith.science/pith/Z7CN75ZVZY5B7CYTS2UMTLSTN3.json","graph_json":"https://pith.science/api/pith-number/Z7CN75ZVZY5B7CYTS2UMTLSTN3/graph.json","events_json":"https://pith.science/api/pith-number/Z7CN75ZVZY5B7CYTS2UMTLSTN3/events.json","paper":"https://pith.science/paper/Z7CN75ZV"},"agent_actions":{"view_html":"https://pith.science/pith/Z7CN75ZVZY5B7CYTS2UMTLSTN3","download_json":"https://pith.science/pith/Z7CN75ZVZY5B7CYTS2UMTLSTN3.json","view_paper":"https://pith.science/paper/Z7CN75ZV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.6931&json=true","fetch_graph":"https://pith.science/api/pith-number/Z7CN75ZVZY5B7CYTS2UMTLSTN3/graph.json","fetch_events":"https://pith.science/api/pith-number/Z7CN75ZVZY5B7CYTS2UMTLSTN3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z7CN75ZVZY5B7CYTS2UMTLSTN3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z7CN75ZVZY5B7CYTS2UMTLSTN3/action/storage_attestation","attest_author":"https://pith.science/pith/Z7CN75ZVZY5B7CYTS2UMTLSTN3/action/author_attestation","sign_citation":"https://pith.science/pith/Z7CN75ZVZY5B7CYTS2UMTLSTN3/action/citation_signature","submit_replication":"https://pith.science/pith/Z7CN75ZVZY5B7CYTS2UMTLSTN3/action/replication_record"}},"created_at":"2026-05-18T03:06:34.659090+00:00","updated_at":"2026-05-18T03:06:34.659090+00:00"}