{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ZSK5MLZDFJI7NY5ZEZEWMEF4HX","short_pith_number":"pith:ZSK5MLZD","schema_version":"1.0","canonical_sha256":"cc95d62f232a51f6e3b926496610bc3dcf9cca2dd83b9537a840dac38018e2a2","source":{"kind":"arxiv","id":"1404.4071","version":2},"attestation_state":"computed","paper":{"title":"Phase transition for the dilute clock model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"In\\'es Armend\\'ariz, Nahuel Soprano-Loto, Pablo Augusto Ferrari","submitted_at":"2014-04-15T20:36:10Z","abstract_excerpt":"We prove that phase transition occurs in the dilute ferromagnetic nearest-neighbour $q$-state clock model in $\\mathbb{Z}^d$, for every $q\\geq 2$ and $d\\geq 2$. This follows from the fact that the Edwards-Sokal random-cluster representation of the clock model stochastically dominates a supercritical Bernoulli bond percolation probability, a technique that has been applied to show phase transition for the low-temperature Potts model. The domination involves a combinatorial lemma which is one of the main points of this article."},"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":"1404.4071","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-15T20:36:10Z","cross_cats_sorted":[],"title_canon_sha256":"cc46d61f58b2ddd1486448a800b4e4bb7f478042487ba2f4a0026ea5e49af253","abstract_canon_sha256":"e80d2d8c63e4c298c1a787d8bf6f560213027e9ecc89595a5446ed12992fdf0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:45.545421Z","signature_b64":"DqNY4914FZJt1Cy2z4dbJru55Uwr7SxtSsiq+NCSWqQxDc8sely6zr2ic4zPQz1yt77CY/WqKugdwL0SN455DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc95d62f232a51f6e3b926496610bc3dcf9cca2dd83b9537a840dac38018e2a2","last_reissued_at":"2026-05-18T02:29:45.545038Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:45.545038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phase transition for the dilute clock model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"In\\'es Armend\\'ariz, Nahuel Soprano-Loto, Pablo Augusto Ferrari","submitted_at":"2014-04-15T20:36:10Z","abstract_excerpt":"We prove that phase transition occurs in the dilute ferromagnetic nearest-neighbour $q$-state clock model in $\\mathbb{Z}^d$, for every $q\\geq 2$ and $d\\geq 2$. This follows from the fact that the Edwards-Sokal random-cluster representation of the clock model stochastically dominates a supercritical Bernoulli bond percolation probability, a technique that has been applied to show phase transition for the low-temperature Potts model. The domination involves a combinatorial lemma which is one of the main points of this article."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4071","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":"1404.4071","created_at":"2026-05-18T02:29:45.545095+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.4071v2","created_at":"2026-05-18T02:29:45.545095+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4071","created_at":"2026-05-18T02:29:45.545095+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZSK5MLZDFJI7","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZSK5MLZDFJI7NY5Z","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZSK5MLZD","created_at":"2026-05-18T12:28:59.999130+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/ZSK5MLZDFJI7NY5ZEZEWMEF4HX","json":"https://pith.science/pith/ZSK5MLZDFJI7NY5ZEZEWMEF4HX.json","graph_json":"https://pith.science/api/pith-number/ZSK5MLZDFJI7NY5ZEZEWMEF4HX/graph.json","events_json":"https://pith.science/api/pith-number/ZSK5MLZDFJI7NY5ZEZEWMEF4HX/events.json","paper":"https://pith.science/paper/ZSK5MLZD"},"agent_actions":{"view_html":"https://pith.science/pith/ZSK5MLZDFJI7NY5ZEZEWMEF4HX","download_json":"https://pith.science/pith/ZSK5MLZDFJI7NY5ZEZEWMEF4HX.json","view_paper":"https://pith.science/paper/ZSK5MLZD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.4071&json=true","fetch_graph":"https://pith.science/api/pith-number/ZSK5MLZDFJI7NY5ZEZEWMEF4HX/graph.json","fetch_events":"https://pith.science/api/pith-number/ZSK5MLZDFJI7NY5ZEZEWMEF4HX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZSK5MLZDFJI7NY5ZEZEWMEF4HX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZSK5MLZDFJI7NY5ZEZEWMEF4HX/action/storage_attestation","attest_author":"https://pith.science/pith/ZSK5MLZDFJI7NY5ZEZEWMEF4HX/action/author_attestation","sign_citation":"https://pith.science/pith/ZSK5MLZDFJI7NY5ZEZEWMEF4HX/action/citation_signature","submit_replication":"https://pith.science/pith/ZSK5MLZDFJI7NY5ZEZEWMEF4HX/action/replication_record"}},"created_at":"2026-05-18T02:29:45.545095+00:00","updated_at":"2026-05-18T02:29:45.545095+00:00"}