{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XRGUVLJIVIYKCYJCHJOIC52IQV","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":"d6592d61a7e7ef5ad902d81c1beb0775c833c833e2ce375829301d3a9dbcb36a","cross_cats_sorted":["math.MP","math.PR","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-26T21:28:35Z","title_canon_sha256":"19960bb1f703a8e07d6214c2ed7311b894f285e94f387dc450e2cf6696dcdf4a"},"schema_version":"1.0","source":{"id":"1203.5823","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.5823","created_at":"2026-05-18T00:26:58Z"},{"alias_kind":"arxiv_version","alias_value":"1203.5823v2","created_at":"2026-05-18T00:26:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.5823","created_at":"2026-05-18T00:26:58Z"},{"alias_kind":"pith_short_12","alias_value":"XRGUVLJIVIYK","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XRGUVLJIVIYKCYJC","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XRGUVLJI","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:123ace360e9fbc3d499d88aacb64fa461fe25f580239eced25a96e8cc0c36e2a","target":"graph","created_at":"2026-05-18T00:26:58Z","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":"For a finite random graph, we defined a simple model of statistical mechanics. We obtain an annealed asymptotic result for the random partition function for this model on finite random graphs as n; the size of the graph is very large. To obtain this result, we define the empirical bond distribution, which enumerates the number of bonds between a given couple of spins, and empirical spin distribution, which enumerates the number of sites having a given spin on the spinned random graphs. For these empirical distributions we extend the large deviation principle(LDP) to cover random graphs with co","authors_text":"Kwabena Doku-Amponsah","cross_cats":["math.MP","math.PR","physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-26T21:28:35Z","title":"Asymptotics of the partition function of Ising model on inhomogeneous random graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5823","kind":"arxiv","version":2},"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:cb2310f6484432640be3cd5e3aa0c898caf9f79d6fa8c4750a786cee443b7626","target":"record","created_at":"2026-05-18T00:26:58Z","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":"d6592d61a7e7ef5ad902d81c1beb0775c833c833e2ce375829301d3a9dbcb36a","cross_cats_sorted":["math.MP","math.PR","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-26T21:28:35Z","title_canon_sha256":"19960bb1f703a8e07d6214c2ed7311b894f285e94f387dc450e2cf6696dcdf4a"},"schema_version":"1.0","source":{"id":"1203.5823","kind":"arxiv","version":2}},"canonical_sha256":"bc4d4aad28aa30a161223a5c8177488575e3c3a8457f8ff1e9c8d7636f38c507","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc4d4aad28aa30a161223a5c8177488575e3c3a8457f8ff1e9c8d7636f38c507","first_computed_at":"2026-05-18T00:26:58.103903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:58.103903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lg0/iAfKFA8oVXbkDUIDFmrIRbpzLCg0Gy88NcMYuMq8L1Iup7k5LCtI3zgkt0iUuWPiX3hUnZGBMmo7zmr+AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:58.104441Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.5823","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb2310f6484432640be3cd5e3aa0c898caf9f79d6fa8c4750a786cee443b7626","sha256:123ace360e9fbc3d499d88aacb64fa461fe25f580239eced25a96e8cc0c36e2a"],"state_sha256":"0d2f4dba55af623bd72588d13063486bc5a4f7ddb9733f0865653a3bf57d8e03"}