{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:6NYIJR45FIWOT2Z6TF2QEGFJO3","short_pith_number":"pith:6NYIJR45","schema_version":"1.0","canonical_sha256":"f37084c79d2a2ce9eb3e99750218a976c283374b0c4d44bd3e9f8a059a3a42eb","source":{"kind":"arxiv","id":"1611.01115","version":2},"attestation_state":"computed","paper":{"title":"Phase Coexistence for the Hard-Core Model on ${\\mathbb Z}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math-ph","math.CO","math.MP"],"primary_cat":"math.PR","authors_text":"Antonio Blanca, Dana Randall, David Galvin, Prasad Tetali, Yuxuan Chen","submitted_at":"2016-11-03T18:07:34Z","abstract_excerpt":"The hard-core model has attracted much attention across several disciplines, representing lattice gases in statistical physics and independent sets in discrete mathematics and computer science. On finite graphs, we are given a parameter $\\lambda$, and an independent set $I$ arises with probability proportional to $\\lambda^{|I|}$. On infinite graphs a Gibbs measure is defined as a suitable limit with the correct conditional probabilities, and we are interested in determining when this limit is unique and when there is phase coexistence, i.e., existence of multiple Gibbs measures.\n  It has long "},"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":"1611.01115","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-03T18:07:34Z","cross_cats_sorted":["cs.DM","math-ph","math.CO","math.MP"],"title_canon_sha256":"0fcdd80b7a7363b346dd6a98509d595f0aacaa5c0cd8caa5dcd76e138c8c13fa","abstract_canon_sha256":"1db834c538237408fa119572bb0857f242bb032bc5f8f720018e5a8abbb969f5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:42.585142Z","signature_b64":"FzsVRoMdandkCXRcSarVTRCsB9RNOPbwIWY9M4LF3unk79+D3KxVs+XEkKkO0kWzoYwIcLeof+PKeSCE6a0RAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f37084c79d2a2ce9eb3e99750218a976c283374b0c4d44bd3e9f8a059a3a42eb","last_reissued_at":"2026-05-18T00:19:42.584482Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:42.584482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phase Coexistence for the Hard-Core Model on ${\\mathbb Z}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math-ph","math.CO","math.MP"],"primary_cat":"math.PR","authors_text":"Antonio Blanca, Dana Randall, David Galvin, Prasad Tetali, Yuxuan Chen","submitted_at":"2016-11-03T18:07:34Z","abstract_excerpt":"The hard-core model has attracted much attention across several disciplines, representing lattice gases in statistical physics and independent sets in discrete mathematics and computer science. On finite graphs, we are given a parameter $\\lambda$, and an independent set $I$ arises with probability proportional to $\\lambda^{|I|}$. On infinite graphs a Gibbs measure is defined as a suitable limit with the correct conditional probabilities, and we are interested in determining when this limit is unique and when there is phase coexistence, i.e., existence of multiple Gibbs measures.\n  It has long "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01115","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":"1611.01115","created_at":"2026-05-18T00:19:42.584595+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.01115v2","created_at":"2026-05-18T00:19:42.584595+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01115","created_at":"2026-05-18T00:19:42.584595+00:00"},{"alias_kind":"pith_short_12","alias_value":"6NYIJR45FIWO","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"6NYIJR45FIWOT2Z6","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"6NYIJR45","created_at":"2026-05-18T12:30:01.593930+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/6NYIJR45FIWOT2Z6TF2QEGFJO3","json":"https://pith.science/pith/6NYIJR45FIWOT2Z6TF2QEGFJO3.json","graph_json":"https://pith.science/api/pith-number/6NYIJR45FIWOT2Z6TF2QEGFJO3/graph.json","events_json":"https://pith.science/api/pith-number/6NYIJR45FIWOT2Z6TF2QEGFJO3/events.json","paper":"https://pith.science/paper/6NYIJR45"},"agent_actions":{"view_html":"https://pith.science/pith/6NYIJR45FIWOT2Z6TF2QEGFJO3","download_json":"https://pith.science/pith/6NYIJR45FIWOT2Z6TF2QEGFJO3.json","view_paper":"https://pith.science/paper/6NYIJR45","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.01115&json=true","fetch_graph":"https://pith.science/api/pith-number/6NYIJR45FIWOT2Z6TF2QEGFJO3/graph.json","fetch_events":"https://pith.science/api/pith-number/6NYIJR45FIWOT2Z6TF2QEGFJO3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6NYIJR45FIWOT2Z6TF2QEGFJO3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6NYIJR45FIWOT2Z6TF2QEGFJO3/action/storage_attestation","attest_author":"https://pith.science/pith/6NYIJR45FIWOT2Z6TF2QEGFJO3/action/author_attestation","sign_citation":"https://pith.science/pith/6NYIJR45FIWOT2Z6TF2QEGFJO3/action/citation_signature","submit_replication":"https://pith.science/pith/6NYIJR45FIWOT2Z6TF2QEGFJO3/action/replication_record"}},"created_at":"2026-05-18T00:19:42.584595+00:00","updated_at":"2026-05-18T00:19:42.584595+00:00"}