{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:RLORBX2YAGWIMCIBHYRDOQ36KO","short_pith_number":"pith:RLORBX2Y","canonical_record":{"source":{"id":"1205.3029","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-05-14T13:57:46Z","cross_cats_sorted":["cond-mat.stat-mech","nlin.AO"],"title_canon_sha256":"07f6d0dc69891f99046da4daee5d120aeb17ee5a8b1b623abf785746194f9a2f","abstract_canon_sha256":"471fd5e7e6e5fe59588565fb62b782c28dea753d9500457b83c38fd5e7bb182c"},"schema_version":"1.0"},"canonical_sha256":"8add10df5801ac8609013e2237437e53bb172a49748688c1e09d86636f88584a","source":{"kind":"arxiv","id":"1205.3029","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3029","created_at":"2026-05-18T03:26:08Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3029v1","created_at":"2026-05-18T03:26:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3029","created_at":"2026-05-18T03:26:08Z"},{"alias_kind":"pith_short_12","alias_value":"RLORBX2YAGWI","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RLORBX2YAGWIMCIB","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RLORBX2Y","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:RLORBX2YAGWIMCIBHYRDOQ36KO","target":"record","payload":{"canonical_record":{"source":{"id":"1205.3029","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-05-14T13:57:46Z","cross_cats_sorted":["cond-mat.stat-mech","nlin.AO"],"title_canon_sha256":"07f6d0dc69891f99046da4daee5d120aeb17ee5a8b1b623abf785746194f9a2f","abstract_canon_sha256":"471fd5e7e6e5fe59588565fb62b782c28dea753d9500457b83c38fd5e7bb182c"},"schema_version":"1.0"},"canonical_sha256":"8add10df5801ac8609013e2237437e53bb172a49748688c1e09d86636f88584a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:08.866018Z","signature_b64":"pdqjuZYudavmY1HXEYy/Zu39CcCWmmdmSCHvukSYDg9VzOWWRMxxbvuvDgMTqYqSEkraosvlwlrQRKnP4jM4CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8add10df5801ac8609013e2237437e53bb172a49748688c1e09d86636f88584a","last_reissued_at":"2026-05-18T03:26:08.865374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:08.865374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.3029","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":"2026-05-18T03:26:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"czG5Y5mnBSUoiYGcQ5LTer/Ooh9CJi8+9VOTe7Zfa55te+bOaZHJ4e19hYTMy2uVW3QXRw4wLOYo0ABkPiYsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T17:41:54.980606Z"},"content_sha256":"cfd34f5a873b78f41c1472e6e350a641b99536e36bc0d000764f722a40f0d3a3","schema_version":"1.0","event_id":"sha256:cfd34f5a873b78f41c1472e6e350a641b99536e36bc0d000764f722a40f0d3a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:RLORBX2YAGWIMCIBHYRDOQ36KO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global dynamics of oscillator populations under common noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","nlin.AO"],"primary_cat":"nlin.CD","authors_text":"A. Pikovsky, M. A. Matias, P. Colet, W. Braun","submitted_at":"2012-05-14T13:57:46Z","abstract_excerpt":"Common noise acting on a population of identical oscillators can synchronize them. We develop a description of this process which is not limited to the states close to synchrony, but provides a global picture of the evolution of the ensembles. The theory is based on the Watanabe-Strogatz transformation, allowing us to obtain closed stochastic equations for the global variables. We show that on the initial stage, the order parameter grows linearly in time, while on the late stages the convergence to synchrony is exponentially fast. Furthermore, we extend the theory to nonidentical ensembles wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3029","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":"2026-05-18T03:26:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mhdKw0OKkWeFDkAezEnkoWxSme1Am5TnPzuz10KvHbAzKg0r76ZKkDeznVV23BCRGdwMDqRCs0MtyykHwTPhAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T17:41:54.981376Z"},"content_sha256":"a7b062c96f363a24655eed6c976e39c0b3a05e46002ca387f1c71ec61a24b944","schema_version":"1.0","event_id":"sha256:a7b062c96f363a24655eed6c976e39c0b3a05e46002ca387f1c71ec61a24b944"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RLORBX2YAGWIMCIBHYRDOQ36KO/bundle.json","state_url":"https://pith.science/pith/RLORBX2YAGWIMCIBHYRDOQ36KO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RLORBX2YAGWIMCIBHYRDOQ36KO/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":"2026-05-26T17:41:54Z","links":{"resolver":"https://pith.science/pith/RLORBX2YAGWIMCIBHYRDOQ36KO","bundle":"https://pith.science/pith/RLORBX2YAGWIMCIBHYRDOQ36KO/bundle.json","state":"https://pith.science/pith/RLORBX2YAGWIMCIBHYRDOQ36KO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RLORBX2YAGWIMCIBHYRDOQ36KO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RLORBX2YAGWIMCIBHYRDOQ36KO","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":"471fd5e7e6e5fe59588565fb62b782c28dea753d9500457b83c38fd5e7bb182c","cross_cats_sorted":["cond-mat.stat-mech","nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-05-14T13:57:46Z","title_canon_sha256":"07f6d0dc69891f99046da4daee5d120aeb17ee5a8b1b623abf785746194f9a2f"},"schema_version":"1.0","source":{"id":"1205.3029","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3029","created_at":"2026-05-18T03:26:08Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3029v1","created_at":"2026-05-18T03:26:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3029","created_at":"2026-05-18T03:26:08Z"},{"alias_kind":"pith_short_12","alias_value":"RLORBX2YAGWI","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RLORBX2YAGWIMCIB","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RLORBX2Y","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:a7b062c96f363a24655eed6c976e39c0b3a05e46002ca387f1c71ec61a24b944","target":"graph","created_at":"2026-05-18T03:26:08Z","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":"Common noise acting on a population of identical oscillators can synchronize them. We develop a description of this process which is not limited to the states close to synchrony, but provides a global picture of the evolution of the ensembles. The theory is based on the Watanabe-Strogatz transformation, allowing us to obtain closed stochastic equations for the global variables. We show that on the initial stage, the order parameter grows linearly in time, while on the late stages the convergence to synchrony is exponentially fast. Furthermore, we extend the theory to nonidentical ensembles wit","authors_text":"A. Pikovsky, M. A. Matias, P. Colet, W. Braun","cross_cats":["cond-mat.stat-mech","nlin.AO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-05-14T13:57:46Z","title":"Global dynamics of oscillator populations under common noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3029","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:cfd34f5a873b78f41c1472e6e350a641b99536e36bc0d000764f722a40f0d3a3","target":"record","created_at":"2026-05-18T03:26:08Z","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":"471fd5e7e6e5fe59588565fb62b782c28dea753d9500457b83c38fd5e7bb182c","cross_cats_sorted":["cond-mat.stat-mech","nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-05-14T13:57:46Z","title_canon_sha256":"07f6d0dc69891f99046da4daee5d120aeb17ee5a8b1b623abf785746194f9a2f"},"schema_version":"1.0","source":{"id":"1205.3029","kind":"arxiv","version":1}},"canonical_sha256":"8add10df5801ac8609013e2237437e53bb172a49748688c1e09d86636f88584a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8add10df5801ac8609013e2237437e53bb172a49748688c1e09d86636f88584a","first_computed_at":"2026-05-18T03:26:08.865374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:08.865374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pdqjuZYudavmY1HXEYy/Zu39CcCWmmdmSCHvukSYDg9VzOWWRMxxbvuvDgMTqYqSEkraosvlwlrQRKnP4jM4CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:08.866018Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.3029","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfd34f5a873b78f41c1472e6e350a641b99536e36bc0d000764f722a40f0d3a3","sha256:a7b062c96f363a24655eed6c976e39c0b3a05e46002ca387f1c71ec61a24b944"],"state_sha256":"2f0ff3b0551f339ce9dd00d5e73b5cefa76839e071ad3e7cab2e8c685b182f33"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QnuA6aQWgqaSKU75YcSO8QENWhaagX7N5InVUShUqCIV/PIMXQf4dx2glLgxny+TfPLS7BdxMBKeajcVJC6pAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T17:41:54.985693Z","bundle_sha256":"a3d2b0d70f5b9b446d9ce71f47d1ee9cf5ffd1d3ffba6db5a83d821a3eb344a2"}}