{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:UP5UJO7MFPT2HVQM2HRI6SVCZX","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":"85e16cd1568c433c2d057929d37510c2f12564ff65b5a74080f8435a85d0db2d","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2002-06-26T16:05:00Z","title_canon_sha256":"e045f9d05b801ffa5936d5f641851d649cb279a1356942a38fd421dac99e79d3"},"schema_version":"1.0","source":{"id":"cond-mat/0206522","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0206522","created_at":"2026-05-18T01:09:03Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0206522v2","created_at":"2026-05-18T01:09:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0206522","created_at":"2026-05-18T01:09:03Z"},{"alias_kind":"pith_short_12","alias_value":"UP5UJO7MFPT2","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"UP5UJO7MFPT2HVQM","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"UP5UJO7M","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:459cf98bfa9b9b59f72ffb8e9d456c4914827d68438fb718b205bdf639504354","target":"graph","created_at":"2026-05-18T01:09:03Z","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 study first- and second-order phase transitions of ferromagnetic lattice models on scale-free networks, with a degree exponent $\\gamma$. Using the example of the $q$-state Potts model we derive a general self-consistency relation within the frame of the Weiss molecular-field approximation, which presumably leads to exact critical singularities. Depending on the value of $\\gamma$, we have found three different regimes of the phase diagram. As a general trend first-order transitions soften with decreasing $\\gamma$ and the critical singularities at the second-order transitions are $\\gamma$-dep","authors_text":"Ferenc Igl\\'oi, Lo\\\"ic Turban","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2002-06-26T16:05:00Z","title":"First- and second-order phase transitions in scale-free networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0206522","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":"sha256:7dc9043919e9f51200afd8387191bea21da0ce76e489f515d0186632ce574bb6","target":"record","created_at":"2026-05-18T01:09:03Z","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":"85e16cd1568c433c2d057929d37510c2f12564ff65b5a74080f8435a85d0db2d","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2002-06-26T16:05:00Z","title_canon_sha256":"e045f9d05b801ffa5936d5f641851d649cb279a1356942a38fd421dac99e79d3"},"schema_version":"1.0","source":{"id":"cond-mat/0206522","kind":"arxiv","version":2}},"canonical_sha256":"a3fb44bbec2be7a3d60cd1e28f4aa2cdef7a22e7c143ebbaec016a397c97cc74","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3fb44bbec2be7a3d60cd1e28f4aa2cdef7a22e7c143ebbaec016a397c97cc74","first_computed_at":"2026-05-18T01:09:03.050765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:03.050765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KSVJV0qWj3WPsGiyrA479RJnBqOsyiz90pX/XFdRBPmgzrje+6AkBRliTy9Z+X9n65+nZi3GOHJKtujt7/VvBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:03.051098Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0206522","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7dc9043919e9f51200afd8387191bea21da0ce76e489f515d0186632ce574bb6","sha256:459cf98bfa9b9b59f72ffb8e9d456c4914827d68438fb718b205bdf639504354"],"state_sha256":"49b0ccaa5f5b4e1b70e7cd30d528bfec87f670a97c80a6d9cbb59d4066b53d2c"}