{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:G75HZ3KR2S4DARLAUEZRQABPEZ","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":"29b087518ab85d01f11ed3946e5d5b7a41d68c06fed7d11e7acdc61f5137d08d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2015-09-11T15:10:50Z","title_canon_sha256":"8582dbc3199b32051b556da605925c7520952f3c1407299aedc52503f1447777"},"schema_version":"1.0","source":{"id":"1509.04244","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.04244","created_at":"2026-05-18T01:33:07Z"},{"alias_kind":"arxiv_version","alias_value":"1509.04244v1","created_at":"2026-05-18T01:33:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04244","created_at":"2026-05-18T01:33:07Z"},{"alias_kind":"pith_short_12","alias_value":"G75HZ3KR2S4D","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"G75HZ3KR2S4DARLA","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"G75HZ3KR","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:f3b37f157e55747b04c98fa5bed80b2425100ac44ef0713a025dd0d6e07157ec","target":"graph","created_at":"2026-05-18T01:33:07Z","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":"Scientists have been considering the Kuramoto model to understand the mechanism behind the appearance of collective behaviour, such as frequency synchronisation (FS) as a paradigm, in real-world networks with a finite number of oscillators. A major current challenge is to obtain an analytical solution for the phase-angles. Here, we provide an approximate analytical solution for this problem by deriving a master solution for the finite-size Kuramoto model, without imposing any restriction on the distribution of the natural frequencies of the oscillators. The master solution embodies all particu","authors_text":"Celso Grebogi, Chengwei Wang, Murilo S. Baptista, Nicolas Rubido","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2015-09-11T15:10:50Z","title":"Approximate solution for frequency synchronisation in a finite-size Kuramoto model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04244","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:ff2ae6c5d15b66f897507a73858411aef2d015c88924f04e0f55f404afd75675","target":"record","created_at":"2026-05-18T01:33:07Z","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":"29b087518ab85d01f11ed3946e5d5b7a41d68c06fed7d11e7acdc61f5137d08d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2015-09-11T15:10:50Z","title_canon_sha256":"8582dbc3199b32051b556da605925c7520952f3c1407299aedc52503f1447777"},"schema_version":"1.0","source":{"id":"1509.04244","kind":"arxiv","version":1}},"canonical_sha256":"37fa7ced51d4b8304560a13318002f267dab54d9d75b824f7a1fce06d6e9fb74","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37fa7ced51d4b8304560a13318002f267dab54d9d75b824f7a1fce06d6e9fb74","first_computed_at":"2026-05-18T01:33:07.941558Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:07.941558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F5MxQSq3he0PABfNQKwy0jmVwazzMFWlTbdAMirIQpEKWuhh7Sn8KWQEV6+1gH7xvCZqMfTtzxaOGuNpD64RDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:07.941919Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.04244","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff2ae6c5d15b66f897507a73858411aef2d015c88924f04e0f55f404afd75675","sha256:f3b37f157e55747b04c98fa5bed80b2425100ac44ef0713a025dd0d6e07157ec"],"state_sha256":"559f1ad414f45900fb1bd132e5eaad730dea731a6dc67d708ba3d42c93ab55a8"}