{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:SF5DEAYGU2ULVWQXIK2XN3NKAO","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":"641dd15ae0250d75df671ec497a63cbf05774cce17652c5f5ef3c524ad5a0ff4","cross_cats_sorted":["cond-mat.dis-nn","physics.soc-ph"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-04-12T07:55:50Z","title_canon_sha256":"f50588c608bf236df2d67bf169600d61cf77d32a3a8f1eb865d02ffd6f04c388"},"schema_version":"1.0","source":{"id":"0704.1538","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.1538","created_at":"2026-05-18T04:42:34Z"},{"alias_kind":"arxiv_version","alias_value":"0704.1538v1","created_at":"2026-05-18T04:42:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.1538","created_at":"2026-05-18T04:42:34Z"},{"alias_kind":"pith_short_12","alias_value":"SF5DEAYGU2UL","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"SF5DEAYGU2ULVWQX","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"SF5DEAYG","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:8a8d90f99ccdb6ca6e75b446f879bf55a62459aad8656581d09503db68c4c74d","target":"graph","created_at":"2026-05-18T04:42:34Z","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 consider the ferromagnetic large-$q$ state Potts model in complex evolving networks, which is equivalent to an optimal cooperation problem, in which the agents try to optimize the total sum of pair cooperation benefits and the supports of independent projects. The agents are found to be typically of two kinds: a fraction of $m$ (being the magnetization of the Potts model) belongs to a large cooperating cluster, whereas the others are isolated one man's projects. It is shown rigorously that the homogeneous model has a strongly first-order phase transition, which turns to second-order for ran","authors_text":"F. Igl\\'oi, J-Ch. Angl\\`es d'Auriac, M. Karsai","cross_cats":["cond-mat.dis-nn","physics.soc-ph"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-04-12T07:55:50Z","title":"Rounding of first-order phase transitions and optimal cooperation in scale-free networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.1538","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":"sha256:7b46c61a0198b83981665c546f5d9e7e94878be74708a5ac8103c6d9cb18299c","target":"record","created_at":"2026-05-18T04:42:34Z","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":"641dd15ae0250d75df671ec497a63cbf05774cce17652c5f5ef3c524ad5a0ff4","cross_cats_sorted":["cond-mat.dis-nn","physics.soc-ph"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-04-12T07:55:50Z","title_canon_sha256":"f50588c608bf236df2d67bf169600d61cf77d32a3a8f1eb865d02ffd6f04c388"},"schema_version":"1.0","source":{"id":"0704.1538","kind":"arxiv","version":1}},"canonical_sha256":"917a320306a6a8bada1742b576edaa03ad233c31e400dcd66a07f2aab29e74b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"917a320306a6a8bada1742b576edaa03ad233c31e400dcd66a07f2aab29e74b5","first_computed_at":"2026-05-18T04:42:34.649110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:34.649110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZazCSJroi+z1fFU1kbhYmlh/jywnBDZ04VM7tQRbVcqxWcC+/XpSmW1tv34zC2SqAZYSSU+ImsGlF1H9f2EZBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:34.649608Z","signed_message":"canonical_sha256_bytes"},"source_id":"0704.1538","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b46c61a0198b83981665c546f5d9e7e94878be74708a5ac8103c6d9cb18299c","sha256:8a8d90f99ccdb6ca6e75b446f879bf55a62459aad8656581d09503db68c4c74d"],"state_sha256":"d9a360b7d2f95813ef4739819db4a5ba409512564b45455f41376145605524da"}