{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Q5NJT7TYCLPJGVNKGAARZLTFLY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a7d6449f646426c3385948a715d067fcc1223b0532227e4f0890138ef55cd03a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-04-20T14:08:13Z","title_canon_sha256":"9f0f5ab022b65b286189ca71095f51372e1ebc8a0f07b14d1ed2e81b1f8b11c8"},"schema_version":"1.0","source":{"id":"1104.4030","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.4030","created_at":"2026-05-18T04:23:47Z"},{"alias_kind":"arxiv_version","alias_value":"1104.4030v1","created_at":"2026-05-18T04:23:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4030","created_at":"2026-05-18T04:23:47Z"},{"alias_kind":"pith_short_12","alias_value":"Q5NJT7TYCLPJ","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q5NJT7TYCLPJGVNK","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q5NJT7TY","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:5369be26055adbabadaccd99e38ebd81657db4e7b79e8a0be7d39733426ed3f7","target":"graph","created_at":"2026-05-18T04:23:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We investigate analytically and numerically an Ising spin model with ferromagnetic coupling defined on random graphs corresponding to Feynman diagrams of a $\\phi^q$ field theory, which exhibits a mean field phase transition. We explicitly calculate the correlation functions both in the symmetric and in the broken symmetry phase in the large volume limit. They agree with the results for finite size systems obtained from Monte Carlo simulations.","authors_text":"Andrzej K. Ole\\'s, Piotr Bialas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-04-20T14:08:13Z","title":"Correlation functions of Ising spins on thin graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4030","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f4c3fe1eb135a71bcad3fc1dffd6cdfaf726a316ac0265a78029edc2f9ce7347","target":"record","created_at":"2026-05-18T04:23:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a7d6449f646426c3385948a715d067fcc1223b0532227e4f0890138ef55cd03a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-04-20T14:08:13Z","title_canon_sha256":"9f0f5ab022b65b286189ca71095f51372e1ebc8a0f07b14d1ed2e81b1f8b11c8"},"schema_version":"1.0","source":{"id":"1104.4030","kind":"arxiv","version":1}},"canonical_sha256":"875a99fe7812de9355aa30011cae655e23c6131a8da1a9001ba22ec5440408cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"875a99fe7812de9355aa30011cae655e23c6131a8da1a9001ba22ec5440408cb","first_computed_at":"2026-05-18T04:23:47.191553Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:47.191553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9u5oa5ycJFFDq+gcHP46Pv9RAFHlB6qOGDSZd9GNIty3vU7hnwbCPS/CLASzWEKAjwjvFI3QX0H3pUbJ2+bgBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:47.192102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.4030","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4c3fe1eb135a71bcad3fc1dffd6cdfaf726a316ac0265a78029edc2f9ce7347","sha256:5369be26055adbabadaccd99e38ebd81657db4e7b79e8a0be7d39733426ed3f7"],"state_sha256":"54d65ee9c0d9a9158b3685420567f40db6cc371b886d1f2793fd32f80d37397e"}