{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NFSUXH3HIE6LGINSPBHITTJJ6K","short_pith_number":"pith:NFSUXH3H","canonical_record":{"source":{"id":"1201.0476","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-01-02T14:55:24Z","cross_cats_sorted":[],"title_canon_sha256":"d1db69fd290dc513a4730e4bca1ccc5fe924437f89df73a8117f55e677c35bc7","abstract_canon_sha256":"0dc50581a85e641fa38d9af7952a622ad568512577b5e7b91b6082f2c29f4438"},"schema_version":"1.0"},"canonical_sha256":"69654b9f67413cb321b2784e89cd29f2be2b9ddbdf62d44873fd71f2bc755b24","source":{"kind":"arxiv","id":"1201.0476","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0476","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0476v1","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0476","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"pith_short_12","alias_value":"NFSUXH3HIE6L","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NFSUXH3HIE6LGINS","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NFSUXH3H","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NFSUXH3HIE6LGINSPBHITTJJ6K","target":"record","payload":{"canonical_record":{"source":{"id":"1201.0476","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-01-02T14:55:24Z","cross_cats_sorted":[],"title_canon_sha256":"d1db69fd290dc513a4730e4bca1ccc5fe924437f89df73a8117f55e677c35bc7","abstract_canon_sha256":"0dc50581a85e641fa38d9af7952a622ad568512577b5e7b91b6082f2c29f4438"},"schema_version":"1.0"},"canonical_sha256":"69654b9f67413cb321b2784e89cd29f2be2b9ddbdf62d44873fd71f2bc755b24","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:17.431665Z","signature_b64":"cAe78jGAZWuZeWKwbs6Gq7Ekf1K2JFR7BOYCfDxD5zOMwkeCxl/6PI/YqTVQl9o0coM7jrZtiz7FQYsTSfHpBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69654b9f67413cb321b2784e89cd29f2be2b9ddbdf62d44873fd71f2bc755b24","last_reissued_at":"2026-05-18T04:05:17.431032Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:17.431032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.0476","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":"2026-05-18T04:05:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"doOFMdvrSNyicreEDCBiO/W01xKnhsFxmGJLfrek+MD8ZHH2oFYn9JwSN65xXNsFqYuZUBuRkmOyYTOF7I9CBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:27:43.047595Z"},"content_sha256":"587e24eeb873d12a0a4044f99048ed24743e5fcd0d7ac76d5f72124ba95168c9","schema_version":"1.0","event_id":"sha256:587e24eeb873d12a0a4044f99048ed24743e5fcd0d7ac76d5f72124ba95168c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NFSUXH3HIE6LGINSPBHITTJJ6K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global and Local: Synchronization and Emergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Leo P. Kadanoff, Mogens H. Jensen","submitted_at":"2012-01-02T14:55:24Z","abstract_excerpt":"When a dynamical system contains several different modes of oscillations it may behave in a variety of ways: If the modes oscillate at their own individual frequencies, it exhibits quasiperiodic behavior; when the modes lock to one another it becomes synchronized, or, as a third possibility, complex chaotic behavior may emerge. With two modes present, like an internal oscillation coupled to a periodic external signal, one obtains a highly structured phase diagram that exhibits these possibilities. In essence, the details are related to the difference between rational and irrational numbers. Na"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0476","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":"2026-05-18T04:05:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ITbU4DJz2J3Nm6eemc+5IajcSoGrKT2uwi/niYTZv+J+G+RrgO/q8CM0HS99o1aTsBO2ejc2uRkxV3LSr4P8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:27:43.047950Z"},"content_sha256":"38b879343fc433a9ab868284e5d4bdca56ae82d3acea99199a749c3391e88c8a","schema_version":"1.0","event_id":"sha256:38b879343fc433a9ab868284e5d4bdca56ae82d3acea99199a749c3391e88c8a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NFSUXH3HIE6LGINSPBHITTJJ6K/bundle.json","state_url":"https://pith.science/pith/NFSUXH3HIE6LGINSPBHITTJJ6K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NFSUXH3HIE6LGINSPBHITTJJ6K/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":"2026-06-02T20:27:43Z","links":{"resolver":"https://pith.science/pith/NFSUXH3HIE6LGINSPBHITTJJ6K","bundle":"https://pith.science/pith/NFSUXH3HIE6LGINSPBHITTJJ6K/bundle.json","state":"https://pith.science/pith/NFSUXH3HIE6LGINSPBHITTJJ6K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NFSUXH3HIE6LGINSPBHITTJJ6K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NFSUXH3HIE6LGINSPBHITTJJ6K","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":"0dc50581a85e641fa38d9af7952a622ad568512577b5e7b91b6082f2c29f4438","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-01-02T14:55:24Z","title_canon_sha256":"d1db69fd290dc513a4730e4bca1ccc5fe924437f89df73a8117f55e677c35bc7"},"schema_version":"1.0","source":{"id":"1201.0476","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0476","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0476v1","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0476","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"pith_short_12","alias_value":"NFSUXH3HIE6L","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NFSUXH3HIE6LGINS","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NFSUXH3H","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:38b879343fc433a9ab868284e5d4bdca56ae82d3acea99199a749c3391e88c8a","target":"graph","created_at":"2026-05-18T04:05:17Z","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":"When a dynamical system contains several different modes of oscillations it may behave in a variety of ways: If the modes oscillate at their own individual frequencies, it exhibits quasiperiodic behavior; when the modes lock to one another it becomes synchronized, or, as a third possibility, complex chaotic behavior may emerge. With two modes present, like an internal oscillation coupled to a periodic external signal, one obtains a highly structured phase diagram that exhibits these possibilities. In essence, the details are related to the difference between rational and irrational numbers. Na","authors_text":"Leo P. Kadanoff, Mogens H. Jensen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-01-02T14:55:24Z","title":"Global and Local: Synchronization and Emergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0476","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":"sha256:587e24eeb873d12a0a4044f99048ed24743e5fcd0d7ac76d5f72124ba95168c9","target":"record","created_at":"2026-05-18T04:05:17Z","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":"0dc50581a85e641fa38d9af7952a622ad568512577b5e7b91b6082f2c29f4438","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-01-02T14:55:24Z","title_canon_sha256":"d1db69fd290dc513a4730e4bca1ccc5fe924437f89df73a8117f55e677c35bc7"},"schema_version":"1.0","source":{"id":"1201.0476","kind":"arxiv","version":1}},"canonical_sha256":"69654b9f67413cb321b2784e89cd29f2be2b9ddbdf62d44873fd71f2bc755b24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69654b9f67413cb321b2784e89cd29f2be2b9ddbdf62d44873fd71f2bc755b24","first_computed_at":"2026-05-18T04:05:17.431032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:17.431032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cAe78jGAZWuZeWKwbs6Gq7Ekf1K2JFR7BOYCfDxD5zOMwkeCxl/6PI/YqTVQl9o0coM7jrZtiz7FQYsTSfHpBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:17.431665Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.0476","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:587e24eeb873d12a0a4044f99048ed24743e5fcd0d7ac76d5f72124ba95168c9","sha256:38b879343fc433a9ab868284e5d4bdca56ae82d3acea99199a749c3391e88c8a"],"state_sha256":"1645b929416e375504cd9a1646d5ead41cb02d0422d09688d54c25e9a1299899"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A7CFOv6+MhbhU0o1m224Ow5dKywrbjU4U3LJzkwidcNDzKHPe8FTtdu1LCNjmc9Di67nRQK0ro+CBCOCogQvDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T20:27:43.049906Z","bundle_sha256":"911916b6b130665c595f104965da966a644e13736c122f66d6d0af1ac692d384"}}