{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:UM3A4UXVQNHC5M7TF5FSM2EUQE","short_pith_number":"pith:UM3A4UXV","schema_version":"1.0","canonical_sha256":"a3360e52f5834e2eb3f32f4b26689481342db8c3a67d7850d7f004d60a6aa1c0","source":{"kind":"arxiv","id":"1106.3594","version":1},"attestation_state":"computed","paper":{"title":"Odd cutsets and the hard-core model on Z^d","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.PR","authors_text":"Ron Peled, Wojciech Samotij","submitted_at":"2011-06-17T23:27:44Z","abstract_excerpt":"We consider the hard-core lattice gas model on Z^d and investigate its phase structure in high dimensions. We prove that when the intensity parameter exceeds Cd^{-1/3}(log d)^2, the model exhibits multiple hard-core measures, thus improving the previous bound of Cd^{-1/4}(log d)^{3/4} given by Galvin and Kahn. At the heart of our approach lies the study of a certain class of edge cutsets in Z^d, the so-called odd cutsets, that appear naturally as the boundary between different phases in the hard-core model. We provide a refined combinatorial analysis of the structure of these cutsets yielding "},"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":"1106.3594","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-17T23:27:44Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"9a0855669e97324dac3d6ae84bf9874233b65e125874edb7b1039f14a1c459c0","abstract_canon_sha256":"ae0b57b4320a3c6343b0866fa2937651a735eb0c74d5ee2b2dcdd674691c07bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:55.589918Z","signature_b64":"PJPVdGsVi2kj7/RzdC7aAYIrtJ6KAkXWR+9QlEsXIE27lpUlVQD3I9LMhdFozMAWwHiKsqJPS3n7xPYqZRb/Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3360e52f5834e2eb3f32f4b26689481342db8c3a67d7850d7f004d60a6aa1c0","last_reissued_at":"2026-05-18T00:48:55.589146Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:55.589146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Odd cutsets and the hard-core model on Z^d","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.PR","authors_text":"Ron Peled, Wojciech Samotij","submitted_at":"2011-06-17T23:27:44Z","abstract_excerpt":"We consider the hard-core lattice gas model on Z^d and investigate its phase structure in high dimensions. We prove that when the intensity parameter exceeds Cd^{-1/3}(log d)^2, the model exhibits multiple hard-core measures, thus improving the previous bound of Cd^{-1/4}(log d)^{3/4} given by Galvin and Kahn. At the heart of our approach lies the study of a certain class of edge cutsets in Z^d, the so-called odd cutsets, that appear naturally as the boundary between different phases in the hard-core model. We provide a refined combinatorial analysis of the structure of these cutsets yielding "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3594","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":"1106.3594","created_at":"2026-05-18T00:48:55.589261+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.3594v1","created_at":"2026-05-18T00:48:55.589261+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3594","created_at":"2026-05-18T00:48:55.589261+00:00"},{"alias_kind":"pith_short_12","alias_value":"UM3A4UXVQNHC","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"UM3A4UXVQNHC5M7T","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"UM3A4UXV","created_at":"2026-05-18T12:26:42.757692+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/UM3A4UXVQNHC5M7TF5FSM2EUQE","json":"https://pith.science/pith/UM3A4UXVQNHC5M7TF5FSM2EUQE.json","graph_json":"https://pith.science/api/pith-number/UM3A4UXVQNHC5M7TF5FSM2EUQE/graph.json","events_json":"https://pith.science/api/pith-number/UM3A4UXVQNHC5M7TF5FSM2EUQE/events.json","paper":"https://pith.science/paper/UM3A4UXV"},"agent_actions":{"view_html":"https://pith.science/pith/UM3A4UXVQNHC5M7TF5FSM2EUQE","download_json":"https://pith.science/pith/UM3A4UXVQNHC5M7TF5FSM2EUQE.json","view_paper":"https://pith.science/paper/UM3A4UXV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.3594&json=true","fetch_graph":"https://pith.science/api/pith-number/UM3A4UXVQNHC5M7TF5FSM2EUQE/graph.json","fetch_events":"https://pith.science/api/pith-number/UM3A4UXVQNHC5M7TF5FSM2EUQE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UM3A4UXVQNHC5M7TF5FSM2EUQE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UM3A4UXVQNHC5M7TF5FSM2EUQE/action/storage_attestation","attest_author":"https://pith.science/pith/UM3A4UXVQNHC5M7TF5FSM2EUQE/action/author_attestation","sign_citation":"https://pith.science/pith/UM3A4UXVQNHC5M7TF5FSM2EUQE/action/citation_signature","submit_replication":"https://pith.science/pith/UM3A4UXVQNHC5M7TF5FSM2EUQE/action/replication_record"}},"created_at":"2026-05-18T00:48:55.589261+00:00","updated_at":"2026-05-18T00:48:55.589261+00:00"}