{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:DOZ7GVVRH5RVQ4QJ4DHGRLZUQZ","short_pith_number":"pith:DOZ7GVVR","schema_version":"1.0","canonical_sha256":"1bb3f356b13f63587209e0ce68af348663001ec20e4aea8fb51fc45a8a73d0f4","source":{"kind":"arxiv","id":"1709.07606","version":1},"attestation_state":"computed","paper":{"title":"Equilibrium states and growth of quasi-lattice ordered monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Aidan Sims, Chris Bruce, Jacqui Ramagge, Marcelo Laca","submitted_at":"2017-09-22T06:15:07Z","abstract_excerpt":"Each multiplicative real-valued homomorphism on a quasi-lattice ordered monoid gives rise to a quasi-periodic dynamics on the associated Toeplitz C*-algebra; here we study the KMS equilibrium states of the resulting C*-dynamical system. We show that, under a nondegeneracy assumption on the homomorphism, there is a critical inverse temperature $\\beta_c$ such that at each inverse temperature $\\beta \\geq \\beta_c$ there exists a unique KMS state. Strictly above $\\beta_c$, the KMS states are generalised Gibbs states with density operators determined by analytic extension to the upper half-plane of "},"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":"1709.07606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-09-22T06:15:07Z","cross_cats_sorted":[],"title_canon_sha256":"a6b5a4eda7f85df807590f28632270d8228d33848dbe4ae3a6326ae0c9e28fa8","abstract_canon_sha256":"b83699607a2b1dcf5cbec087a805463c744c024deb101d72885d006fa65486af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:09.830151Z","signature_b64":"XeYaR4H4TiuDTeJb7Ht59jZ3YWS2cz/iSouKRPrDy7MXZ/0nekQq+MR2hqkVAMxbQUA3ETxurTmvYGXl+21SAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bb3f356b13f63587209e0ce68af348663001ec20e4aea8fb51fc45a8a73d0f4","last_reissued_at":"2026-05-17T23:51:09.829675Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:09.829675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equilibrium states and growth of quasi-lattice ordered monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Aidan Sims, Chris Bruce, Jacqui Ramagge, Marcelo Laca","submitted_at":"2017-09-22T06:15:07Z","abstract_excerpt":"Each multiplicative real-valued homomorphism on a quasi-lattice ordered monoid gives rise to a quasi-periodic dynamics on the associated Toeplitz C*-algebra; here we study the KMS equilibrium states of the resulting C*-dynamical system. We show that, under a nondegeneracy assumption on the homomorphism, there is a critical inverse temperature $\\beta_c$ such that at each inverse temperature $\\beta \\geq \\beta_c$ there exists a unique KMS state. Strictly above $\\beta_c$, the KMS states are generalised Gibbs states with density operators determined by analytic extension to the upper half-plane of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07606","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":"1709.07606","created_at":"2026-05-17T23:51:09.829746+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.07606v1","created_at":"2026-05-17T23:51:09.829746+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.07606","created_at":"2026-05-17T23:51:09.829746+00:00"},{"alias_kind":"pith_short_12","alias_value":"DOZ7GVVRH5RV","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"DOZ7GVVRH5RVQ4QJ","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"DOZ7GVVR","created_at":"2026-05-18T12:31:12.930513+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/DOZ7GVVRH5RVQ4QJ4DHGRLZUQZ","json":"https://pith.science/pith/DOZ7GVVRH5RVQ4QJ4DHGRLZUQZ.json","graph_json":"https://pith.science/api/pith-number/DOZ7GVVRH5RVQ4QJ4DHGRLZUQZ/graph.json","events_json":"https://pith.science/api/pith-number/DOZ7GVVRH5RVQ4QJ4DHGRLZUQZ/events.json","paper":"https://pith.science/paper/DOZ7GVVR"},"agent_actions":{"view_html":"https://pith.science/pith/DOZ7GVVRH5RVQ4QJ4DHGRLZUQZ","download_json":"https://pith.science/pith/DOZ7GVVRH5RVQ4QJ4DHGRLZUQZ.json","view_paper":"https://pith.science/paper/DOZ7GVVR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.07606&json=true","fetch_graph":"https://pith.science/api/pith-number/DOZ7GVVRH5RVQ4QJ4DHGRLZUQZ/graph.json","fetch_events":"https://pith.science/api/pith-number/DOZ7GVVRH5RVQ4QJ4DHGRLZUQZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DOZ7GVVRH5RVQ4QJ4DHGRLZUQZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DOZ7GVVRH5RVQ4QJ4DHGRLZUQZ/action/storage_attestation","attest_author":"https://pith.science/pith/DOZ7GVVRH5RVQ4QJ4DHGRLZUQZ/action/author_attestation","sign_citation":"https://pith.science/pith/DOZ7GVVRH5RVQ4QJ4DHGRLZUQZ/action/citation_signature","submit_replication":"https://pith.science/pith/DOZ7GVVRH5RVQ4QJ4DHGRLZUQZ/action/replication_record"}},"created_at":"2026-05-17T23:51:09.829746+00:00","updated_at":"2026-05-17T23:51:09.829746+00:00"}