{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:6XYBZJHMAW5I524JWEMV6R7RWV","short_pith_number":"pith:6XYBZJHM","schema_version":"1.0","canonical_sha256":"f5f01ca4ec05ba8eeb89b1195f47f1b5518b381ad136ec212e8d4e8f04ba7008","source":{"kind":"arxiv","id":"1101.4713","version":1},"attestation_state":"computed","paper":{"title":"Phase transition on Exel crossed products assocaited to dilation matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Iain Raeburn, Jacqui Ramagge, Marcelo Laca","submitted_at":"2011-01-25T03:52:11Z","abstract_excerpt":"An integer matrix $A\\in M_d(\\Z)$ induces a covering $\\sigma_A$ of $\\T^d$ and an endomorphism $\\alpha_A:f\\mapsto f\\circ \\sigma_A$ of $C(\\T^d)$ for which there is a natural transfer operator $L$. In this paper, we compute the KMS states on the Exel crossed product $C(\\T^d)\\rtimes_{\\alpha_A,L}\\N$ and its Toeplitz extension. We find that $C(\\T^d)\\rtimes_{\\alpha_A,L}\\N$ has a unique KMS state, which has inverse temperature $\\beta=\\log|\\det A|$. Its Toeplitz extension, on the other hand, exhibits a phase transition at $\\beta=\\log|\\det A|$, and for larger $\\beta$ the simplex of KMS$_\\beta$ states is "},"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":"1101.4713","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-01-25T03:52:11Z","cross_cats_sorted":[],"title_canon_sha256":"f6d58cfee97241edc5cac797be844266f7fb8dad7bd889fc2a206d9169e33c0b","abstract_canon_sha256":"8024b936972d908f6c7137585fbd8bebd1b5e3a53c937b9466aeb7acd5420ee2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:59.132188Z","signature_b64":"S2ULOQG44CBRTevGDOoFt1GRxh38eQ11DNxTcLc/3r0+8jbCEt9QOKwBOKRFeTLF8GT1Pqeq7AfULXIvrgxKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5f01ca4ec05ba8eeb89b1195f47f1b5518b381ad136ec212e8d4e8f04ba7008","last_reissued_at":"2026-05-18T04:30:59.131363Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:59.131363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phase transition on Exel crossed products assocaited to dilation matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Iain Raeburn, Jacqui Ramagge, Marcelo Laca","submitted_at":"2011-01-25T03:52:11Z","abstract_excerpt":"An integer matrix $A\\in M_d(\\Z)$ induces a covering $\\sigma_A$ of $\\T^d$ and an endomorphism $\\alpha_A:f\\mapsto f\\circ \\sigma_A$ of $C(\\T^d)$ for which there is a natural transfer operator $L$. In this paper, we compute the KMS states on the Exel crossed product $C(\\T^d)\\rtimes_{\\alpha_A,L}\\N$ and its Toeplitz extension. We find that $C(\\T^d)\\rtimes_{\\alpha_A,L}\\N$ has a unique KMS state, which has inverse temperature $\\beta=\\log|\\det A|$. Its Toeplitz extension, on the other hand, exhibits a phase transition at $\\beta=\\log|\\det A|$, and for larger $\\beta$ the simplex of KMS$_\\beta$ states is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4713","kind":"arxiv","version":1},"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":"1101.4713","created_at":"2026-05-18T04:30:59.131508+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.4713v1","created_at":"2026-05-18T04:30:59.131508+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4713","created_at":"2026-05-18T04:30:59.131508+00:00"},{"alias_kind":"pith_short_12","alias_value":"6XYBZJHMAW5I","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"6XYBZJHMAW5I524J","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"6XYBZJHM","created_at":"2026-05-18T12:26:22.705136+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/6XYBZJHMAW5I524JWEMV6R7RWV","json":"https://pith.science/pith/6XYBZJHMAW5I524JWEMV6R7RWV.json","graph_json":"https://pith.science/api/pith-number/6XYBZJHMAW5I524JWEMV6R7RWV/graph.json","events_json":"https://pith.science/api/pith-number/6XYBZJHMAW5I524JWEMV6R7RWV/events.json","paper":"https://pith.science/paper/6XYBZJHM"},"agent_actions":{"view_html":"https://pith.science/pith/6XYBZJHMAW5I524JWEMV6R7RWV","download_json":"https://pith.science/pith/6XYBZJHMAW5I524JWEMV6R7RWV.json","view_paper":"https://pith.science/paper/6XYBZJHM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.4713&json=true","fetch_graph":"https://pith.science/api/pith-number/6XYBZJHMAW5I524JWEMV6R7RWV/graph.json","fetch_events":"https://pith.science/api/pith-number/6XYBZJHMAW5I524JWEMV6R7RWV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6XYBZJHMAW5I524JWEMV6R7RWV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6XYBZJHMAW5I524JWEMV6R7RWV/action/storage_attestation","attest_author":"https://pith.science/pith/6XYBZJHMAW5I524JWEMV6R7RWV/action/author_attestation","sign_citation":"https://pith.science/pith/6XYBZJHMAW5I524JWEMV6R7RWV/action/citation_signature","submit_replication":"https://pith.science/pith/6XYBZJHMAW5I524JWEMV6R7RWV/action/replication_record"}},"created_at":"2026-05-18T04:30:59.131508+00:00","updated_at":"2026-05-18T04:30:59.131508+00:00"}