{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:73F2ORM7FFC2LO75ODZXQEGEZE","short_pith_number":"pith:73F2ORM7","schema_version":"1.0","canonical_sha256":"fecba7459f2945a5bbfd70f37810c4c9056646a4a9c062ee3029c967bb2de4e0","source":{"kind":"arxiv","id":"math/0701514","version":5},"attestation_state":"computed","paper":{"title":"Operator algebras for multivariable dynamics","license":"","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Elias G. Katsoulis, Kenneth R. Davidson","submitted_at":"2007-01-18T18:39:46Z","abstract_excerpt":"Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $\\tau_i:X \\to X$ for $1 \\le i \\le n$. To this we associate two topological conjugacy algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra $\\A(X, \\tau)$ and the semicrossed product $\\rC_0(X)\\times_\\tau\\Fn$.\n  We introduce a concept of conjugacy for multidimensional systems, which we coin piecewise conjugacy. We prove that the piecewise conjugacy class of the system can be recovered from either the algebraic structure of $\\A(X, \\tau)$ or $\\rC_0(X)\\times_\\tau\\Fn"},"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":"math/0701514","kind":"arxiv","version":5},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2007-01-18T18:39:46Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"425f7e0e5822b5b453884dcc1a17cab6cb4a63cb4ca0e189146c0b10f1649a36","abstract_canon_sha256":"019b8b8a89cb3725c01d6b5eab99a2db854641054404ac8ec8227d346c9faad9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:52.956910Z","signature_b64":"Qxhr2xG0zowBOvecZmHZ8y6iwMvekJPJSK2ao0IgDmIywpRgfBmNQijyeEjNyiMILaK/fLr3pfo3gdq4KLVuAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fecba7459f2945a5bbfd70f37810c4c9056646a4a9c062ee3029c967bb2de4e0","last_reissued_at":"2026-05-18T04:08:52.956390Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:52.956390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Operator algebras for multivariable dynamics","license":"","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Elias G. Katsoulis, Kenneth R. Davidson","submitted_at":"2007-01-18T18:39:46Z","abstract_excerpt":"Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $\\tau_i:X \\to X$ for $1 \\le i \\le n$. To this we associate two topological conjugacy algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra $\\A(X, \\tau)$ and the semicrossed product $\\rC_0(X)\\times_\\tau\\Fn$.\n  We introduce a concept of conjugacy for multidimensional systems, which we coin piecewise conjugacy. We prove that the piecewise conjugacy class of the system can be recovered from either the algebraic structure of $\\A(X, \\tau)$ or $\\rC_0(X)\\times_\\tau\\Fn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701514","kind":"arxiv","version":5},"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":"math/0701514","created_at":"2026-05-18T04:08:52.956489+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0701514v5","created_at":"2026-05-18T04:08:52.956489+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701514","created_at":"2026-05-18T04:08:52.956489+00:00"},{"alias_kind":"pith_short_12","alias_value":"73F2ORM7FFC2","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"73F2ORM7FFC2LO75","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"73F2ORM7","created_at":"2026-05-18T12:25:55.427421+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/73F2ORM7FFC2LO75ODZXQEGEZE","json":"https://pith.science/pith/73F2ORM7FFC2LO75ODZXQEGEZE.json","graph_json":"https://pith.science/api/pith-number/73F2ORM7FFC2LO75ODZXQEGEZE/graph.json","events_json":"https://pith.science/api/pith-number/73F2ORM7FFC2LO75ODZXQEGEZE/events.json","paper":"https://pith.science/paper/73F2ORM7"},"agent_actions":{"view_html":"https://pith.science/pith/73F2ORM7FFC2LO75ODZXQEGEZE","download_json":"https://pith.science/pith/73F2ORM7FFC2LO75ODZXQEGEZE.json","view_paper":"https://pith.science/paper/73F2ORM7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0701514&json=true","fetch_graph":"https://pith.science/api/pith-number/73F2ORM7FFC2LO75ODZXQEGEZE/graph.json","fetch_events":"https://pith.science/api/pith-number/73F2ORM7FFC2LO75ODZXQEGEZE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/73F2ORM7FFC2LO75ODZXQEGEZE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/73F2ORM7FFC2LO75ODZXQEGEZE/action/storage_attestation","attest_author":"https://pith.science/pith/73F2ORM7FFC2LO75ODZXQEGEZE/action/author_attestation","sign_citation":"https://pith.science/pith/73F2ORM7FFC2LO75ODZXQEGEZE/action/citation_signature","submit_replication":"https://pith.science/pith/73F2ORM7FFC2LO75ODZXQEGEZE/action/replication_record"}},"created_at":"2026-05-18T04:08:52.956489+00:00","updated_at":"2026-05-18T04:08:52.956489+00:00"}