{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:CRQGQZPPWP7YCU52YA7UFNZRV7","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":"594a3ad97f103275d22fa6da10d7b564d04ad9e2989f8ac4c909dfb530b890e9","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2002-04-26T10:56:50Z","title_canon_sha256":"12aa3d63c5f64ecaa81529e762091f9a83f46bdd9d30f29e12ed6983be3800eb"},"schema_version":"1.0","source":{"id":"cond-mat/0204573","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0204573","created_at":"2026-05-18T01:09:03Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0204573v1","created_at":"2026-05-18T01:09:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0204573","created_at":"2026-05-18T01:09:03Z"},{"alias_kind":"pith_short_12","alias_value":"CRQGQZPPWP7Y","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"CRQGQZPPWP7YCU52","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"CRQGQZPP","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:e8e61c7291c71ae5f701d5f8d0176172fc378635862c289da0d93816484b6ddb","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":"Small-world (SW) networks have been identified in many different fields. Topological coefficients like the clustering coefficient and the characteristic path length have been used in the past for a qualitative characterization of these networks. Here a dynamical approach is used to characterize the small-world phenomenon. Using the $\\beta -$model, a coupled map dynamical system is defined on the network. Entrance to and exit from the SW phase are related to the behavior of the ergodic invariants of the dynamics.","authors_text":"Jo\\~ao Seixas, R. Vilela Mendes, Tanya Araujo","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2002-04-26T10:56:50Z","title":"A dynamical characterization of the small world phase"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0204573","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":"sha256:27deaf8646463baa7459289cfc1b982d82d034bf0934d66ff2cab8054ce6e8bb","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":"594a3ad97f103275d22fa6da10d7b564d04ad9e2989f8ac4c909dfb530b890e9","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2002-04-26T10:56:50Z","title_canon_sha256":"12aa3d63c5f64ecaa81529e762091f9a83f46bdd9d30f29e12ed6983be3800eb"},"schema_version":"1.0","source":{"id":"cond-mat/0204573","kind":"arxiv","version":1}},"canonical_sha256":"14606865efb3ff8153bac03f42b731affd1eb424fe71cecc9289216d28e242fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14606865efb3ff8153bac03f42b731affd1eb424fe71cecc9289216d28e242fc","first_computed_at":"2026-05-18T01:09:03.101807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:03.101807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p+7CImkVVYOY+QqIyVBwlKX4GDqWlVjbruyLbtibIfG6vHGasaE/xi4i1VeDM+nEoeWcE7TXrbkQ21KkkqYGCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:03.102244Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0204573","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27deaf8646463baa7459289cfc1b982d82d034bf0934d66ff2cab8054ce6e8bb","sha256:e8e61c7291c71ae5f701d5f8d0176172fc378635862c289da0d93816484b6ddb"],"state_sha256":"7186c98062229d27e25a9a936361baff27fcd41661d6e8d6a2875a99c0979c80"}