{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6HXVJQAHRMS5VVL5QSSADXHIMV","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":"91fa0567dc58ddb4d6d4d89d36ddbeb90a25750f3bb31a6236963410f00f5725","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2016-02-19T19:47:15Z","title_canon_sha256":"88f0aa2615a576c6d924868a0b56caf6edb5da43407fc635b1a0de74b0667f4d"},"schema_version":"1.0","source":{"id":"1602.06262","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.06262","created_at":"2026-05-18T01:11:59Z"},{"alias_kind":"arxiv_version","alias_value":"1602.06262v2","created_at":"2026-05-18T01:11:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06262","created_at":"2026-05-18T01:11:59Z"},{"alias_kind":"pith_short_12","alias_value":"6HXVJQAHRMS5","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6HXVJQAHRMS5VVL5","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6HXVJQAH","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:8f82d3fccca81b4a70901a7b4f47e2ea2ddd849d4f5bd19bb352319ae30d42da","target":"graph","created_at":"2026-05-18T01:11:59Z","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 study optimal synchronization of networks of coupled phase oscillators. We extend previous theory for optimizing the synchronization properties of undirected networks to the important case of directed networks. We derive a generalized synchrony alignment function that encodes the interplay between network structure and the oscillators' natural frequencies and serves as an objective measure for the network's degree of synchronization. Using the generalized synchrony alignment function, we show that a network's synchronization properties can be systematically optimized. This framework also al","authors_text":"Dane Taylor, Jie Sun, Per Sebastian Skardal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2016-02-19T19:47:15Z","title":"Optimal synchronization of directed complex networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06262","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":"sha256:14039c9c2acdb98afefc1b8a3b21a353ad3f4dd354453e05fc319b232e859885","target":"record","created_at":"2026-05-18T01:11:59Z","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":"91fa0567dc58ddb4d6d4d89d36ddbeb90a25750f3bb31a6236963410f00f5725","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2016-02-19T19:47:15Z","title_canon_sha256":"88f0aa2615a576c6d924868a0b56caf6edb5da43407fc635b1a0de74b0667f4d"},"schema_version":"1.0","source":{"id":"1602.06262","kind":"arxiv","version":2}},"canonical_sha256":"f1ef54c0078b25dad57d84a401dce8654450cd8d6f032504509271e71b694c17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1ef54c0078b25dad57d84a401dce8654450cd8d6f032504509271e71b694c17","first_computed_at":"2026-05-18T01:11:59.015580Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:59.015580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gc+RpjdoeygbeQCBFRXyVyRfdBUqzCAjdxM4lfXhsmgVwTiUfKsv4RwTHuGIz6e+fdQMAiLKnRS8FdGyutmCCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:59.015946Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.06262","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14039c9c2acdb98afefc1b8a3b21a353ad3f4dd354453e05fc319b232e859885","sha256:8f82d3fccca81b4a70901a7b4f47e2ea2ddd849d4f5bd19bb352319ae30d42da"],"state_sha256":"24ffbc65ae5645ead828503d53607013a825e9050110c3c325ad051e1ed30a9e"}