{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:RCFRFKT6I57AAI66RK6KSYCKHM","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":"453c2474234fb4c6773c07dcb940c4b92b43bfc28643365946a0ef44e32132ae","cross_cats_sorted":["nlin.AO"],"license":"","primary_cat":"nlin.CD","submitted_at":"2006-12-26T23:39:56Z","title_canon_sha256":"b17a7ae703480782eca36c4175a62ca87f2a1a2d8669c0bdb7f190d219a3503f"},"schema_version":"1.0","source":{"id":"nlin/0612057","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0612057","created_at":"2026-05-18T01:38:17Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0612057v2","created_at":"2026-05-18T01:38:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0612057","created_at":"2026-05-18T01:38:17Z"},{"alias_kind":"pith_short_12","alias_value":"RCFRFKT6I57A","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"RCFRFKT6I57AAI66","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"RCFRFKT6","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:2895d1986b888fa4bb4fdd4c2b88dce5d01f0856057f3142796d9c12f3db299d","target":"graph","created_at":"2026-05-18T01:38:17Z","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 complex clustered networks with a gradient structure, where sizes of the clusters are distributed unevenly. Such networks describe more closely actual networks in biophysical systems and in technological applications than previous models. Theoretical analysis predicts that the network synchronizability can be optimized by the strength of the gradient field but only when the gradient field points from large to small clusters. A remarkable finding is that, if the gradient field is sufficiently strong, synchronizability of the network is mainly determined by the properties of the subn","authors_text":"Choy Heng Lai, Liang Huang, Xingang Wang, Ying-Cheng Lai","cross_cats":["nlin.AO"],"headline":"","license":"","primary_cat":"nlin.CD","submitted_at":"2006-12-26T23:39:56Z","title":"Optimization of synchronization in gradient clustered networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0612057","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:ff13016081e0e8659a73d5bbb3a88b3dcd79e5871b2b2a3a7b1e9144f19cc7d7","target":"record","created_at":"2026-05-18T01:38:17Z","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":"453c2474234fb4c6773c07dcb940c4b92b43bfc28643365946a0ef44e32132ae","cross_cats_sorted":["nlin.AO"],"license":"","primary_cat":"nlin.CD","submitted_at":"2006-12-26T23:39:56Z","title_canon_sha256":"b17a7ae703480782eca36c4175a62ca87f2a1a2d8669c0bdb7f190d219a3503f"},"schema_version":"1.0","source":{"id":"nlin/0612057","kind":"arxiv","version":2}},"canonical_sha256":"888b12aa7e477e0023de8abca9604a3b1805ee725c76e0cbc6d7d1a74ebe58bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"888b12aa7e477e0023de8abca9604a3b1805ee725c76e0cbc6d7d1a74ebe58bf","first_computed_at":"2026-05-18T01:38:17.662578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:17.662578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aRVpX45xw54Gc93c4askwXUOpDveCp1QZHslKyjd7bQm5ToRgeNwx6SNfzXhu8tItAAwS47gcRW7nWsVJ9otBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:17.663200Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0612057","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff13016081e0e8659a73d5bbb3a88b3dcd79e5871b2b2a3a7b1e9144f19cc7d7","sha256:2895d1986b888fa4bb4fdd4c2b88dce5d01f0856057f3142796d9c12f3db299d"],"state_sha256":"96c3cb69ac6591defd90ed528e6085642fcddb877dadc39d81e567d48f801f22"}