{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:BBLDGC72IP36NWQZFOZ34CYVEQ","short_pith_number":"pith:BBLDGC72","schema_version":"1.0","canonical_sha256":"0856330bfa43f7e6da192bb3be0b15242a7c1e43e59c6f163d013315c7d0c8c6","source":{"kind":"arxiv","id":"1106.4714","version":4},"attestation_state":"computed","paper":{"title":"Antiferromagnetic Potts model on the Erdos-Renyi random graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Cristian Giardina', Pierluigi Contucci, Sander Dommers, Shannon Starr","submitted_at":"2011-06-23T13:29:12Z","abstract_excerpt":"We study the antiferromagnetic Potts model on the Poissonian Erd\\\"os-R\\'enyi random graph. By identifying a suitable interpolation structure and an extended variational principle, together with a positive temperature second-moment analysis we prove the existence of a phase transition at a positive critical temperature. Upper and lower bounds on the temperature critical value are obtained from the stability analysis of the replica symmetric solution (recovered in the framework of Derrida-Ruelle probability cascades)and from a positive entropy argument."},"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":"1106.4714","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-23T13:29:12Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","math-ph","math.MP"],"title_canon_sha256":"ed7a1dfa474304e838057537d298d22e47e8633f0c85d657b7c32355822ade73","abstract_canon_sha256":"192663552b10d1d8f234ac72c68ff679eec55bfc6fe699cc3187240cf37add51"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:04.203780Z","signature_b64":"8jBq2hzSFXjuPZ3psExCmZE2GqdrwX78fe2i6QwzTyobSPUEvhwHXXS5sKEEODAHI3+s2154fE+0HwlX/iyBBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0856330bfa43f7e6da192bb3be0b15242a7c1e43e59c6f163d013315c7d0c8c6","last_reissued_at":"2026-05-18T01:31:04.203100Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:04.203100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Antiferromagnetic Potts model on the Erdos-Renyi random graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Cristian Giardina', Pierluigi Contucci, Sander Dommers, Shannon Starr","submitted_at":"2011-06-23T13:29:12Z","abstract_excerpt":"We study the antiferromagnetic Potts model on the Poissonian Erd\\\"os-R\\'enyi random graph. By identifying a suitable interpolation structure and an extended variational principle, together with a positive temperature second-moment analysis we prove the existence of a phase transition at a positive critical temperature. Upper and lower bounds on the temperature critical value are obtained from the stability analysis of the replica symmetric solution (recovered in the framework of Derrida-Ruelle probability cascades)and from a positive entropy argument."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4714","kind":"arxiv","version":4},"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":"1106.4714","created_at":"2026-05-18T01:31:04.203193+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.4714v4","created_at":"2026-05-18T01:31:04.203193+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4714","created_at":"2026-05-18T01:31:04.203193+00:00"},{"alias_kind":"pith_short_12","alias_value":"BBLDGC72IP36","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BBLDGC72IP36NWQZ","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BBLDGC72","created_at":"2026-05-18T12:26:24.575870+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/BBLDGC72IP36NWQZFOZ34CYVEQ","json":"https://pith.science/pith/BBLDGC72IP36NWQZFOZ34CYVEQ.json","graph_json":"https://pith.science/api/pith-number/BBLDGC72IP36NWQZFOZ34CYVEQ/graph.json","events_json":"https://pith.science/api/pith-number/BBLDGC72IP36NWQZFOZ34CYVEQ/events.json","paper":"https://pith.science/paper/BBLDGC72"},"agent_actions":{"view_html":"https://pith.science/pith/BBLDGC72IP36NWQZFOZ34CYVEQ","download_json":"https://pith.science/pith/BBLDGC72IP36NWQZFOZ34CYVEQ.json","view_paper":"https://pith.science/paper/BBLDGC72","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.4714&json=true","fetch_graph":"https://pith.science/api/pith-number/BBLDGC72IP36NWQZFOZ34CYVEQ/graph.json","fetch_events":"https://pith.science/api/pith-number/BBLDGC72IP36NWQZFOZ34CYVEQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BBLDGC72IP36NWQZFOZ34CYVEQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BBLDGC72IP36NWQZFOZ34CYVEQ/action/storage_attestation","attest_author":"https://pith.science/pith/BBLDGC72IP36NWQZFOZ34CYVEQ/action/author_attestation","sign_citation":"https://pith.science/pith/BBLDGC72IP36NWQZFOZ34CYVEQ/action/citation_signature","submit_replication":"https://pith.science/pith/BBLDGC72IP36NWQZFOZ34CYVEQ/action/replication_record"}},"created_at":"2026-05-18T01:31:04.203193+00:00","updated_at":"2026-05-18T01:31:04.203193+00:00"}