{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:L6UCPUDHKIULTG5BVMQGSAHPK7","short_pith_number":"pith:L6UCPUDH","canonical_record":{"source":{"id":"1806.06083","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-15T18:16:32Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"35ecca32b1b5be7af5787d037fa39a39596c74b48ca32dd2d1f6cc9c79a5cc10","abstract_canon_sha256":"4810bf9be3bde993b294f1dc1ebc526f594d569281a8a96b9464ab4c8c905c20"},"schema_version":"1.0"},"canonical_sha256":"5fa827d0675228b99ba1ab206900ef57d521f4aafd9dec16d02e6c47cd84cff1","source":{"kind":"arxiv","id":"1806.06083","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.06083","created_at":"2026-06-04T19:11:59Z"},{"alias_kind":"arxiv_version","alias_value":"1806.06083v2","created_at":"2026-06-04T19:11:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06083","created_at":"2026-06-04T19:11:59Z"},{"alias_kind":"pith_short_12","alias_value":"L6UCPUDHKIUL","created_at":"2026-06-04T19:11:59Z"},{"alias_kind":"pith_short_16","alias_value":"L6UCPUDHKIULTG5B","created_at":"2026-06-04T19:11:59Z"},{"alias_kind":"pith_short_8","alias_value":"L6UCPUDH","created_at":"2026-06-04T19:11:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:L6UCPUDHKIULTG5BVMQGSAHPK7","target":"record","payload":{"canonical_record":{"source":{"id":"1806.06083","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-15T18:16:32Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"35ecca32b1b5be7af5787d037fa39a39596c74b48ca32dd2d1f6cc9c79a5cc10","abstract_canon_sha256":"4810bf9be3bde993b294f1dc1ebc526f594d569281a8a96b9464ab4c8c905c20"},"schema_version":"1.0"},"canonical_sha256":"5fa827d0675228b99ba1ab206900ef57d521f4aafd9dec16d02e6c47cd84cff1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T19:11:59.167932Z","signature_b64":"OJe2BS/+xkn6bhmMzpsy55BZAgT9eeBSJemTXOuCarvVpnXM1BWri6eRX5ZtldIGqCqdh81+PpqZfAhKXGcOAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fa827d0675228b99ba1ab206900ef57d521f4aafd9dec16d02e6c47cd84cff1","last_reissued_at":"2026-06-04T19:11:59.167446Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T19:11:59.167446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.06083","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T19:11:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LbnH+gx4vJlelbKLH6TnvW8KEMX4Z2K6LSIDS+JSrFm/jyDDDPG6iX4Ip+sOu+A1tYpFTOSROArzsB6EpHPbBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:24:56.137130Z"},"content_sha256":"50ad68a976cb387a3471cd7fe33bcd5156ff274ec6b95113cce4b09c60362d0a","schema_version":"1.0","event_id":"sha256:50ad68a976cb387a3471cd7fe33bcd5156ff274ec6b95113cce4b09c60362d0a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:L6UCPUDHKIULTG5BVMQGSAHPK7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability Conditions for Cluster Synchronization in Networks of Heterogeneous Kuramoto Oscillators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","eess.SY"],"primary_cat":"math.OC","authors_text":"Danielle S. Bassett, Fabio Pasqualetti, Giacomo Baggio, Tommaso Menara","submitted_at":"2018-06-15T18:16:32Z","abstract_excerpt":"In this paper we study cluster synchronization in networks of oscillators with heterogenous Kuramoto dynamics, where multiple groups of oscillators with identical phases coexist in a connected network. Cluster synchronization is at the basis of several biological and technological processes; yet the underlying mechanisms to enable cluster synchronization of Kuramoto oscillators have remained elusive. In this paper we derive quantitative conditions on the network weights, cluster configuration, and oscillators' natural frequency that ensure asymptotic stability of the cluster synchronization ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06083","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1806.06083/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T19:11:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hFkHKXJ5PNRl5P3Ir36Gx1aG8hXZ3psT7ub2nEzKBzIa6RdWQ0+nV2jUZ6Wde8LvOLTHC9Tel8wl1V46S8GwDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:24:56.137843Z"},"content_sha256":"59ffba608eb4e57bf16bfded17c578f6d25a37aab8d71a329a27212e345a8a49","schema_version":"1.0","event_id":"sha256:59ffba608eb4e57bf16bfded17c578f6d25a37aab8d71a329a27212e345a8a49"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L6UCPUDHKIULTG5BVMQGSAHPK7/bundle.json","state_url":"https://pith.science/pith/L6UCPUDHKIULTG5BVMQGSAHPK7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L6UCPUDHKIULTG5BVMQGSAHPK7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T16:24:56Z","links":{"resolver":"https://pith.science/pith/L6UCPUDHKIULTG5BVMQGSAHPK7","bundle":"https://pith.science/pith/L6UCPUDHKIULTG5BVMQGSAHPK7/bundle.json","state":"https://pith.science/pith/L6UCPUDHKIULTG5BVMQGSAHPK7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L6UCPUDHKIULTG5BVMQGSAHPK7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:L6UCPUDHKIULTG5BVMQGSAHPK7","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":"4810bf9be3bde993b294f1dc1ebc526f594d569281a8a96b9464ab4c8c905c20","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-15T18:16:32Z","title_canon_sha256":"35ecca32b1b5be7af5787d037fa39a39596c74b48ca32dd2d1f6cc9c79a5cc10"},"schema_version":"1.0","source":{"id":"1806.06083","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.06083","created_at":"2026-06-04T19:11:59Z"},{"alias_kind":"arxiv_version","alias_value":"1806.06083v2","created_at":"2026-06-04T19:11:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06083","created_at":"2026-06-04T19:11:59Z"},{"alias_kind":"pith_short_12","alias_value":"L6UCPUDHKIUL","created_at":"2026-06-04T19:11:59Z"},{"alias_kind":"pith_short_16","alias_value":"L6UCPUDHKIULTG5B","created_at":"2026-06-04T19:11:59Z"},{"alias_kind":"pith_short_8","alias_value":"L6UCPUDH","created_at":"2026-06-04T19:11:59Z"}],"graph_snapshots":[{"event_id":"sha256:59ffba608eb4e57bf16bfded17c578f6d25a37aab8d71a329a27212e345a8a49","target":"graph","created_at":"2026-06-04T19:11:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1806.06083/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we study cluster synchronization in networks of oscillators with heterogenous Kuramoto dynamics, where multiple groups of oscillators with identical phases coexist in a connected network. Cluster synchronization is at the basis of several biological and technological processes; yet the underlying mechanisms to enable cluster synchronization of Kuramoto oscillators have remained elusive. In this paper we derive quantitative conditions on the network weights, cluster configuration, and oscillators' natural frequency that ensure asymptotic stability of the cluster synchronization ma","authors_text":"Danielle S. Bassett, Fabio Pasqualetti, Giacomo Baggio, Tommaso Menara","cross_cats":["cs.SY","eess.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-15T18:16:32Z","title":"Stability Conditions for Cluster Synchronization in Networks of Heterogeneous Kuramoto Oscillators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06083","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":"sha256:50ad68a976cb387a3471cd7fe33bcd5156ff274ec6b95113cce4b09c60362d0a","target":"record","created_at":"2026-06-04T19:11:59Z","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":"4810bf9be3bde993b294f1dc1ebc526f594d569281a8a96b9464ab4c8c905c20","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-15T18:16:32Z","title_canon_sha256":"35ecca32b1b5be7af5787d037fa39a39596c74b48ca32dd2d1f6cc9c79a5cc10"},"schema_version":"1.0","source":{"id":"1806.06083","kind":"arxiv","version":2}},"canonical_sha256":"5fa827d0675228b99ba1ab206900ef57d521f4aafd9dec16d02e6c47cd84cff1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fa827d0675228b99ba1ab206900ef57d521f4aafd9dec16d02e6c47cd84cff1","first_computed_at":"2026-06-04T19:11:59.167446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T19:11:59.167446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OJe2BS/+xkn6bhmMzpsy55BZAgT9eeBSJemTXOuCarvVpnXM1BWri6eRX5ZtldIGqCqdh81+PpqZfAhKXGcOAQ==","signature_status":"signed_v1","signed_at":"2026-06-04T19:11:59.167932Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.06083","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50ad68a976cb387a3471cd7fe33bcd5156ff274ec6b95113cce4b09c60362d0a","sha256:59ffba608eb4e57bf16bfded17c578f6d25a37aab8d71a329a27212e345a8a49"],"state_sha256":"9e8a4854833e712539e369400c69d0f654601e837022ecc185487c8890615d2a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q9YeZ576AbfbYP9TO2LYr1dLHz57BWsx8mly72NQCivvnSM917vpBuyoUUujkM8qAXfetQAtqKO7k3MVC9d4Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:24:56.141328Z","bundle_sha256":"e94f96064345ad5e29aa96215e02b89331e288a3d2f9b7dac9bd13b8743bc9d1"}}