{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MYQ6C6KT36T2C4SQQQHOJRPVYD","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":"b950a37b12331356229539152194846bbc6cb1ebdc8b75bfafee2b40ebabb558","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-09-12T11:28:07Z","title_canon_sha256":"c7a21be6a7a05fe34865bebdde7eefac704197222f44bce40329f9754190049c"},"schema_version":"1.0","source":{"id":"1209.2568","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2568","created_at":"2026-05-18T03:45:41Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2568v1","created_at":"2026-05-18T03:45:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2568","created_at":"2026-05-18T03:45:41Z"},{"alias_kind":"pith_short_12","alias_value":"MYQ6C6KT36T2","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MYQ6C6KT36T2C4SQ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MYQ6C6KT","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:3b6d4c466e95bccd95ce587214d836878387401c03a77981ab3855d31b11c23f","target":"graph","created_at":"2026-05-18T03:45:41Z","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 numerically investigate the heterogeneity in cluster sizes in the two-dimensional Ising model and verify its scaling form recently proposed in the context of percolation problems [Phys. Rev. E 84, 010101(R) (2011)]. The scaling exponents obtained via the finite-size scaling analysis are shown to be consistent with theoretical values of the fractal dimension $d_f$ and the Fisher exponent $\\tau$ for the cluster distribution. We also point out that strong finite-size effects exist due to the geometric nature of the cluster-size heterogeneity.","authors_text":"Beom Jun Kim, Seung Ki Baek, Su Do Yi, Woo Seong Jo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-09-12T11:28:07Z","title":"Cluster-size heterogeneity in the two-dimensional Ising model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2568","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":"sha256:0f65d9f4db81d804902ff2591df90feb8c0ac8164b7e7caa2598f64e42ed902d","target":"record","created_at":"2026-05-18T03:45:41Z","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":"b950a37b12331356229539152194846bbc6cb1ebdc8b75bfafee2b40ebabb558","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-09-12T11:28:07Z","title_canon_sha256":"c7a21be6a7a05fe34865bebdde7eefac704197222f44bce40329f9754190049c"},"schema_version":"1.0","source":{"id":"1209.2568","kind":"arxiv","version":1}},"canonical_sha256":"6621e17953dfa7a17250840ee4c5f5c0e09c4b0f3872d6e6ef88cda199c3c52d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6621e17953dfa7a17250840ee4c5f5c0e09c4b0f3872d6e6ef88cda199c3c52d","first_computed_at":"2026-05-18T03:45:41.232031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:41.232031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cndKT3VB/SxLEYgDOZpZ7jlj2iqHihc8Nc9zzq5qw0lYvENtriZkzUrS0boHLCuG9ZV12bhKaImA2KZ0CN9AAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:41.232835Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.2568","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f65d9f4db81d804902ff2591df90feb8c0ac8164b7e7caa2598f64e42ed902d","sha256:3b6d4c466e95bccd95ce587214d836878387401c03a77981ab3855d31b11c23f"],"state_sha256":"8f30586bf9ca2d93a37df6e4ef44a77a3fbd3e8f1132c2cd30d537f7fc828025"}