{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:SKXZPDMAB6UXTMZFMMUF6UGDFT","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":"bf875a6b423c6b9a9f26bc51bb6cf5fe6065753df626b38d9bc1ff24fcdd3888","cross_cats_sorted":["cond-mat.other"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-07-28T12:47:22Z","title_canon_sha256":"56ff82ff872bc8db123093d085156d43b12ab809960e5ed8c7064fc0b4233d5f"},"schema_version":"1.0","source":{"id":"cond-mat/0507670","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0507670","created_at":"2026-05-18T01:39:50Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0507670v1","created_at":"2026-05-18T01:39:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0507670","created_at":"2026-05-18T01:39:50Z"},{"alias_kind":"pith_short_12","alias_value":"SKXZPDMAB6UX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"SKXZPDMAB6UXTMZF","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"SKXZPDMA","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:67cbb48c76d01d37321c24f6464699f3c6930d7378dd38a6246a302ad1a88c7b","target":"graph","created_at":"2026-05-18T01:39:50Z","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":"Based on a rigorous extension of classical statistical mechanics to networks, we study a specific microscopic network Hamiltonian. The form of this Hamiltonian is derived from the assumption that individual nodes increase/decrease their utility by linking to nodes with a higher/lower degree than their own. We interpret utility as an equivalent to energy in physical systems and discuss the temperature dependence of the emerging networks. We observe the existence of a critical temperature $T_c$ where total energy (utility) and network-architecture undergo radical changes. Along this topological ","authors_text":"Christoly Biely, Stefan Thurner","cross_cats":["cond-mat.other"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-07-28T12:47:22Z","title":"Statistical mechanics of scale-free networks at a critical point: Complexity without irreversibility?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0507670","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":"sha256:0a8d1fdab3c53f5f3f3a3959f478aacf5db9e44bd5e7abc477369d2444cb79f3","target":"record","created_at":"2026-05-18T01:39:50Z","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":"bf875a6b423c6b9a9f26bc51bb6cf5fe6065753df626b38d9bc1ff24fcdd3888","cross_cats_sorted":["cond-mat.other"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-07-28T12:47:22Z","title_canon_sha256":"56ff82ff872bc8db123093d085156d43b12ab809960e5ed8c7064fc0b4233d5f"},"schema_version":"1.0","source":{"id":"cond-mat/0507670","kind":"arxiv","version":1}},"canonical_sha256":"92af978d800fa979b32563285f50c32cc15f02984a192e5d75169b8c65cc55bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92af978d800fa979b32563285f50c32cc15f02984a192e5d75169b8c65cc55bc","first_computed_at":"2026-05-18T01:39:50.643744Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:50.643744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zhmNrVxWoZPmEGfqSzehljoh8+7zGSiynHBetcxRvV5wnxP6yHOHPYt2jBUirc2nK6AswpFntAiTiKhdHgtTAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:50.644426Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0507670","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a8d1fdab3c53f5f3f3a3959f478aacf5db9e44bd5e7abc477369d2444cb79f3","sha256:67cbb48c76d01d37321c24f6464699f3c6930d7378dd38a6246a302ad1a88c7b"],"state_sha256":"5f9ba75af622c00da2e264940ad4beae8835e366aecabb0c34348ab555bbbeba"}