{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:CASXV7HCMWQTBIKHLBBOCZX7ON","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":"67c23dd213cedaa97b69e3575a2195ed27af46b90bb592d55cee29968b6548b7","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-01-09T19:42:29Z","title_canon_sha256":"094ad40f384784bffc549d730797b5f0e1d7927adf1dc73cb37c3f32ac19c883"},"schema_version":"1.0","source":{"id":"1001.1439","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.1439","created_at":"2026-05-18T03:21:45Z"},{"alias_kind":"arxiv_version","alias_value":"1001.1439v1","created_at":"2026-05-18T03:21:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.1439","created_at":"2026-05-18T03:21:45Z"},{"alias_kind":"pith_short_12","alias_value":"CASXV7HCMWQT","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"CASXV7HCMWQTBIKH","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"CASXV7HC","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:8fa2fe2d9ecc83f8e81a312d4136e46904a1f9127ab6dd54d0a6aee1da8d61b0","target":"graph","created_at":"2026-05-18T03:21:45Z","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 demonstrate that a tree-based theory for various dynamical processes yields extremely accurate results for several networks with high levels of clustering. We find that such a theory works well as long as the mean intervertex distance $\\ell$ is sufficiently small - i.e., as long as it is close to the value of $\\ell$ in a random network with negligible clustering and the same degree-degree correlations. We confirm this hypothesis numerically using real-world networks from various domains and on several classes of synthetic clustered networks. We present analytical calculations that further s","authors_text":"Adam Hackett, James P. Gleeson, Mason A. Porter, Peter J. Mucha, Sergey Melnik","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-01-09T19:42:29Z","title":"The unreasonable effectiveness of tree-based theory for networks with clustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.1439","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":"sha256:21e4ec634c631f8a3b6567312430cfa9fdb1af09ce04093f3ce11aa2793982cc","target":"record","created_at":"2026-05-18T03:21:45Z","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":"67c23dd213cedaa97b69e3575a2195ed27af46b90bb592d55cee29968b6548b7","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-01-09T19:42:29Z","title_canon_sha256":"094ad40f384784bffc549d730797b5f0e1d7927adf1dc73cb37c3f32ac19c883"},"schema_version":"1.0","source":{"id":"1001.1439","kind":"arxiv","version":1}},"canonical_sha256":"10257afce265a130a1475842e166ff73585512579972718cfa81e6a5f1e0db11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10257afce265a130a1475842e166ff73585512579972718cfa81e6a5f1e0db11","first_computed_at":"2026-05-18T03:21:45.953062Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:45.953062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/ADYp7XZwX+ODaCE+Wx/FlTKTsn5+64YboKW0QHLzLOi3AKgHdQAQdp4TXAZA9sTa7iOa2BiIZ6Q98ILrURWBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:45.953556Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.1439","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21e4ec634c631f8a3b6567312430cfa9fdb1af09ce04093f3ce11aa2793982cc","sha256:8fa2fe2d9ecc83f8e81a312d4136e46904a1f9127ab6dd54d0a6aee1da8d61b0"],"state_sha256":"923c5ab35553c0a3275f3f9e13517a527d36a321468ec52dd9edcc170f19454d"}