{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:QGURWVHOJD3IKYK3UAEXD5K2PZ","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":"c773bbb2fbb71c33406e3c1b6762b6c116be08dc57dc5dbf3791b1dc84ff0a2e","cross_cats_sorted":["nlin.AO"],"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2004-06-24T02:34:44Z","title_canon_sha256":"cdfc2ae64d043b32659359cacc708f13df92cf4178a71f6df68115df64a295f9"},"schema_version":"1.0","source":{"id":"cond-mat/0406580","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0406580","created_at":"2026-05-18T01:06:53Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0406580v1","created_at":"2026-05-18T01:06:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0406580","created_at":"2026-05-18T01:06:53Z"},{"alias_kind":"pith_short_12","alias_value":"QGURWVHOJD3I","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"QGURWVHOJD3IKYK3","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"QGURWVHO","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:7eb10259bb34275cde7278d5f624dc95dbfa8a9ec113c3aa20e07732976acd38","target":"graph","created_at":"2026-05-18T01:06:53Z","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 the frequency-synchronization of randomly coupled oscillators. By analyzing the continuum limit, we obtain the sufficient condition for the mean-field type synchronization. We especially find that the critical coupling constant $K$ becomes 0 in the random scale free network,\n $P(k)\\propto k^{-\\gamma}$, if $2 < \\gamma \\le 3$. Numerical simulations in finite networks are consistent with these analysis.","authors_text":"Takashi Ichinomiya","cross_cats":["nlin.AO"],"headline":"","license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2004-06-24T02:34:44Z","title":"Frequency synchronization in random oscillator network"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0406580","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":"sha256:7d416f71afa9b5070ffe335505a8d0d0d02b9c2a993535be507ee61b0cf2a07f","target":"record","created_at":"2026-05-18T01:06:53Z","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":"c773bbb2fbb71c33406e3c1b6762b6c116be08dc57dc5dbf3791b1dc84ff0a2e","cross_cats_sorted":["nlin.AO"],"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2004-06-24T02:34:44Z","title_canon_sha256":"cdfc2ae64d043b32659359cacc708f13df92cf4178a71f6df68115df64a295f9"},"schema_version":"1.0","source":{"id":"cond-mat/0406580","kind":"arxiv","version":1}},"canonical_sha256":"81a91b54ee48f685615ba00971f55a7e63ae871aa398dd5df3de0dc00bb25d22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81a91b54ee48f685615ba00971f55a7e63ae871aa398dd5df3de0dc00bb25d22","first_computed_at":"2026-05-18T01:06:53.922843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:53.922843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JhbxZ8RDCZS/TVSl2lOSCH+XcAewD9wuj7M03yDGHl1AamP4KIKoBN+3RH46C4GNvVCPXxPK4mvXMYxwt+X6Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:53.923264Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0406580","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d416f71afa9b5070ffe335505a8d0d0d02b9c2a993535be507ee61b0cf2a07f","sha256:7eb10259bb34275cde7278d5f624dc95dbfa8a9ec113c3aa20e07732976acd38"],"state_sha256":"980a262524a715fd0f363cbc50018ed2a343ec9e09a2d4b2878964bee6ee5dff"}