{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KQVIU54WQPO75OM534I6MWN5EW","short_pith_number":"pith:KQVIU54W","canonical_record":{"source":{"id":"1610.02834","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-10T10:16:01Z","cross_cats_sorted":[],"title_canon_sha256":"55023f664707432f5254d61a0327000edfbc13b19a2bb2260cf67989d08d75a9","abstract_canon_sha256":"8e2fa4c17a146a2fd7ea86b6131dd6895646894ff00ba660ef2f59da5274bbe7"},"schema_version":"1.0"},"canonical_sha256":"542a8a779683ddfeb99ddf11e659bd25a38d9891aff4904728f99a014c491f78","source":{"kind":"arxiv","id":"1610.02834","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02834","created_at":"2026-05-18T01:02:50Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02834v1","created_at":"2026-05-18T01:02:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02834","created_at":"2026-05-18T01:02:50Z"},{"alias_kind":"pith_short_12","alias_value":"KQVIU54WQPO7","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KQVIU54WQPO75OM5","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KQVIU54W","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KQVIU54WQPO75OM534I6MWN5EW","target":"record","payload":{"canonical_record":{"source":{"id":"1610.02834","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-10T10:16:01Z","cross_cats_sorted":[],"title_canon_sha256":"55023f664707432f5254d61a0327000edfbc13b19a2bb2260cf67989d08d75a9","abstract_canon_sha256":"8e2fa4c17a146a2fd7ea86b6131dd6895646894ff00ba660ef2f59da5274bbe7"},"schema_version":"1.0"},"canonical_sha256":"542a8a779683ddfeb99ddf11e659bd25a38d9891aff4904728f99a014c491f78","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:50.600811Z","signature_b64":"OP38L7kD3JTHO8VMdt+Q1bGCKT2kVU8XQ+d+LIxLYjgTp+FsvB7NcCPqufHms3V1z/Oidlt01OO65KPYwPXWAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"542a8a779683ddfeb99ddf11e659bd25a38d9891aff4904728f99a014c491f78","last_reissued_at":"2026-05-18T01:02:50.600446Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:50.600446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.02834","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:02:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pFLxtAQnZRBihDMtoza/QgsW3mlebaoS/w7QNywb83pxca+mReBNk2msALKwrgNN3CH4Nhu05+fcLYtz0ix7DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:22:02.649005Z"},"content_sha256":"39f27f2124721d68593f26c0d4464b9bda5eccbdc23930ed0879bfe5a4072b92","schema_version":"1.0","event_id":"sha256:39f27f2124721d68593f26c0d4464b9bda5eccbdc23930ed0879bfe5a4072b92"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KQVIU54WQPO75OM534I6MWN5EW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Hopf bifurcation in the Kuramoto-Daido model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hayato Chiba","submitted_at":"2016-10-10T10:16:01Z","abstract_excerpt":"A Hopf bifurcation in the Kuramoto-Daido model is investigated based on the generalized spectral theory and the center manifold reduction for a certain class of frequency distributions. The dynamical system of the order parameter on a four-dimensional center manifold is derived. It is shown that the dynamical system undergoes a Hopf bifurcation as the coupling strength increases, which proves the existence of a periodic two-cluster state of oscillators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02834","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T01:02:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lwap4r5nvO0B62MRKXM+5PqwaS3clkRjEt6vQsiJ+YFetQRDDkAFd5ubHaekMSjpbopsLo/JvxFc0vHtPyKrCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:22:02.649356Z"},"content_sha256":"51d6946751997796d29ad154c9d04ba2d72836d62fc1b20d3df11930b92d3b31","schema_version":"1.0","event_id":"sha256:51d6946751997796d29ad154c9d04ba2d72836d62fc1b20d3df11930b92d3b31"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KQVIU54WQPO75OM534I6MWN5EW/bundle.json","state_url":"https://pith.science/pith/KQVIU54WQPO75OM534I6MWN5EW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KQVIU54WQPO75OM534I6MWN5EW/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":"2026-06-23T21:22:02Z","links":{"resolver":"https://pith.science/pith/KQVIU54WQPO75OM534I6MWN5EW","bundle":"https://pith.science/pith/KQVIU54WQPO75OM534I6MWN5EW/bundle.json","state":"https://pith.science/pith/KQVIU54WQPO75OM534I6MWN5EW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KQVIU54WQPO75OM534I6MWN5EW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KQVIU54WQPO75OM534I6MWN5EW","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":"8e2fa4c17a146a2fd7ea86b6131dd6895646894ff00ba660ef2f59da5274bbe7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-10T10:16:01Z","title_canon_sha256":"55023f664707432f5254d61a0327000edfbc13b19a2bb2260cf67989d08d75a9"},"schema_version":"1.0","source":{"id":"1610.02834","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02834","created_at":"2026-05-18T01:02:50Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02834v1","created_at":"2026-05-18T01:02:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02834","created_at":"2026-05-18T01:02:50Z"},{"alias_kind":"pith_short_12","alias_value":"KQVIU54WQPO7","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KQVIU54WQPO75OM5","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KQVIU54W","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:51d6946751997796d29ad154c9d04ba2d72836d62fc1b20d3df11930b92d3b31","target":"graph","created_at":"2026-05-18T01:02:50Z","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":"A Hopf bifurcation in the Kuramoto-Daido model is investigated based on the generalized spectral theory and the center manifold reduction for a certain class of frequency distributions. The dynamical system of the order parameter on a four-dimensional center manifold is derived. It is shown that the dynamical system undergoes a Hopf bifurcation as the coupling strength increases, which proves the existence of a periodic two-cluster state of oscillators.","authors_text":"Hayato Chiba","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-10T10:16:01Z","title":"A Hopf bifurcation in the Kuramoto-Daido model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02834","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":"sha256:39f27f2124721d68593f26c0d4464b9bda5eccbdc23930ed0879bfe5a4072b92","target":"record","created_at":"2026-05-18T01:02:50Z","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":"8e2fa4c17a146a2fd7ea86b6131dd6895646894ff00ba660ef2f59da5274bbe7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-10T10:16:01Z","title_canon_sha256":"55023f664707432f5254d61a0327000edfbc13b19a2bb2260cf67989d08d75a9"},"schema_version":"1.0","source":{"id":"1610.02834","kind":"arxiv","version":1}},"canonical_sha256":"542a8a779683ddfeb99ddf11e659bd25a38d9891aff4904728f99a014c491f78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"542a8a779683ddfeb99ddf11e659bd25a38d9891aff4904728f99a014c491f78","first_computed_at":"2026-05-18T01:02:50.600446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:50.600446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OP38L7kD3JTHO8VMdt+Q1bGCKT2kVU8XQ+d+LIxLYjgTp+FsvB7NcCPqufHms3V1z/Oidlt01OO65KPYwPXWAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:50.600811Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.02834","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39f27f2124721d68593f26c0d4464b9bda5eccbdc23930ed0879bfe5a4072b92","sha256:51d6946751997796d29ad154c9d04ba2d72836d62fc1b20d3df11930b92d3b31"],"state_sha256":"13e8b625dc0298f41f6b941ea058fa5adbc270c54c2220c40c713f0f2d112fe4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2rlv4oH6ex9txB+my6zwMML25OJo8z6BQs5Mf/pin5umXX+f5Yiv25UDvuc9nM1u6yRfiWgwf32IzTI0D6uyCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T21:22:02.651891Z","bundle_sha256":"908f0d1bafa29e6e8390d92630f9f6cd4fe5f561baeefc36e8a4782ca43a81e7"}}