{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BO734L2GN3L4DRCBK36YCMQA5J","short_pith_number":"pith:BO734L2G","canonical_record":{"source":{"id":"1210.2821","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-10-10T07:54:13Z","cross_cats_sorted":[],"title_canon_sha256":"4ea682ed9aff59e899a0d829f2c03f20dc4fc7652c108d5812e37a248fbfd76a","abstract_canon_sha256":"a02f30119c43e22837a5b1de980218cee42977e3eed284926558c81b25829917"},"schema_version":"1.0"},"canonical_sha256":"0bbfbe2f466ed7c1c44156fd813200ea7a3bc726a829080975a44e82384706d3","source":{"kind":"arxiv","id":"1210.2821","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.2821","created_at":"2026-05-18T01:54:03Z"},{"alias_kind":"arxiv_version","alias_value":"1210.2821v1","created_at":"2026-05-18T01:54:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2821","created_at":"2026-05-18T01:54:03Z"},{"alias_kind":"pith_short_12","alias_value":"BO734L2GN3L4","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BO734L2GN3L4DRCB","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BO734L2G","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BO734L2GN3L4DRCBK36YCMQA5J","target":"record","payload":{"canonical_record":{"source":{"id":"1210.2821","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-10-10T07:54:13Z","cross_cats_sorted":[],"title_canon_sha256":"4ea682ed9aff59e899a0d829f2c03f20dc4fc7652c108d5812e37a248fbfd76a","abstract_canon_sha256":"a02f30119c43e22837a5b1de980218cee42977e3eed284926558c81b25829917"},"schema_version":"1.0"},"canonical_sha256":"0bbfbe2f466ed7c1c44156fd813200ea7a3bc726a829080975a44e82384706d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:54:03.612490Z","signature_b64":"41ZUyjFEtgdLnHFnQtM7s7WIHCns5tRyRHBgt9duf8ogRyf70dAiSf3dvIuFpNRKSaEiSgrJK5KXKYCtpeFrBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bbfbe2f466ed7c1c44156fd813200ea7a3bc726a829080975a44e82384706d3","last_reissued_at":"2026-05-18T01:54:03.611971Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:54:03.611971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.2821","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":"2026-05-18T01:54:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hxm/6xAO1W79q8l/E5/LVXKFFogj3HkIPoc7p/M/Byq18kZYIKRWcX265l4L+lT47pEBT+jtiS4kt+Zwsy4DAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:31:45.617283Z"},"content_sha256":"79ea137fcbc95ee511f44292401e5cd519f41fa5855242443d3f45bd0fbccdfa","schema_version":"1.0","event_id":"sha256:79ea137fcbc95ee511f44292401e5cd519f41fa5855242443d3f45bd0fbccdfa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BO734L2GN3L4DRCBK36YCMQA5J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discontinuous Attractor Dimension at the Synchronization Transition of Time-Delayed Chaotic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Eckehard Sch\\\"oll, Ido Kanter, Steffen Zeeb, Thomas Dahms, Valentin Flunkert, Wolfgang Kinzel","submitted_at":"2012-10-10T07:54:13Z","abstract_excerpt":"The attractor dimension at the transition to complete synchronization in a network of chaotic units with time-delayed couplings is investigated. In particular, we determine the Kaplan-Yorke dimension from the spectrum of Lyapunov exponents for iterated maps and for two coupled semiconductor lasers. We argue that the Kaplan-Yorke dimension must be discontinuous at the transition and compare it to the correlation dimension. For a system of Bernoulli maps we indeed find a jump in the correlation dimension. The magnitude of the discontinuity in the Kaplan-Yorke dimension is calculated for networks"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2821","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":"2026-05-18T01:54:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rJEkIIwR4ZCfgfEbE8tf4ivlDcBSeZgtIPXhsIvNBGxO9L1E4Yw5UwTCIL3zVURLOYWHrTNlMnCtI4+4UJPEAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:31:45.617647Z"},"content_sha256":"39ad8a0d69de0d1fa23627d48211bff2e677e5898821999aa96b4ec4fe7a9722","schema_version":"1.0","event_id":"sha256:39ad8a0d69de0d1fa23627d48211bff2e677e5898821999aa96b4ec4fe7a9722"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BO734L2GN3L4DRCBK36YCMQA5J/bundle.json","state_url":"https://pith.science/pith/BO734L2GN3L4DRCBK36YCMQA5J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BO734L2GN3L4DRCBK36YCMQA5J/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":"2026-06-04T06:31:45Z","links":{"resolver":"https://pith.science/pith/BO734L2GN3L4DRCBK36YCMQA5J","bundle":"https://pith.science/pith/BO734L2GN3L4DRCBK36YCMQA5J/bundle.json","state":"https://pith.science/pith/BO734L2GN3L4DRCBK36YCMQA5J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BO734L2GN3L4DRCBK36YCMQA5J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BO734L2GN3L4DRCBK36YCMQA5J","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":"a02f30119c43e22837a5b1de980218cee42977e3eed284926558c81b25829917","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-10-10T07:54:13Z","title_canon_sha256":"4ea682ed9aff59e899a0d829f2c03f20dc4fc7652c108d5812e37a248fbfd76a"},"schema_version":"1.0","source":{"id":"1210.2821","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.2821","created_at":"2026-05-18T01:54:03Z"},{"alias_kind":"arxiv_version","alias_value":"1210.2821v1","created_at":"2026-05-18T01:54:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2821","created_at":"2026-05-18T01:54:03Z"},{"alias_kind":"pith_short_12","alias_value":"BO734L2GN3L4","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BO734L2GN3L4DRCB","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BO734L2G","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:39ad8a0d69de0d1fa23627d48211bff2e677e5898821999aa96b4ec4fe7a9722","target":"graph","created_at":"2026-05-18T01:54:03Z","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":"The attractor dimension at the transition to complete synchronization in a network of chaotic units with time-delayed couplings is investigated. In particular, we determine the Kaplan-Yorke dimension from the spectrum of Lyapunov exponents for iterated maps and for two coupled semiconductor lasers. We argue that the Kaplan-Yorke dimension must be discontinuous at the transition and compare it to the correlation dimension. For a system of Bernoulli maps we indeed find a jump in the correlation dimension. The magnitude of the discontinuity in the Kaplan-Yorke dimension is calculated for networks","authors_text":"Eckehard Sch\\\"oll, Ido Kanter, Steffen Zeeb, Thomas Dahms, Valentin Flunkert, Wolfgang Kinzel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-10-10T07:54:13Z","title":"Discontinuous Attractor Dimension at the Synchronization Transition of Time-Delayed Chaotic Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2821","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":"sha256:79ea137fcbc95ee511f44292401e5cd519f41fa5855242443d3f45bd0fbccdfa","target":"record","created_at":"2026-05-18T01:54:03Z","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":"a02f30119c43e22837a5b1de980218cee42977e3eed284926558c81b25829917","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-10-10T07:54:13Z","title_canon_sha256":"4ea682ed9aff59e899a0d829f2c03f20dc4fc7652c108d5812e37a248fbfd76a"},"schema_version":"1.0","source":{"id":"1210.2821","kind":"arxiv","version":1}},"canonical_sha256":"0bbfbe2f466ed7c1c44156fd813200ea7a3bc726a829080975a44e82384706d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bbfbe2f466ed7c1c44156fd813200ea7a3bc726a829080975a44e82384706d3","first_computed_at":"2026-05-18T01:54:03.611971Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:54:03.611971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"41ZUyjFEtgdLnHFnQtM7s7WIHCns5tRyRHBgt9duf8ogRyf70dAiSf3dvIuFpNRKSaEiSgrJK5KXKYCtpeFrBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:54:03.612490Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.2821","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79ea137fcbc95ee511f44292401e5cd519f41fa5855242443d3f45bd0fbccdfa","sha256:39ad8a0d69de0d1fa23627d48211bff2e677e5898821999aa96b4ec4fe7a9722"],"state_sha256":"8ca48aae84417435ce5453fe5c73491bdfa9b99f920111ea092f8bee1d0c2fdb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x1Vgtn34fYOiBRDmkMPMVLHKQJSlwPYlMGTgB0BJOsBBd4EpO8clxrB9eDIhOyPUoSKXSwxACf22TLb0FL1uDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T06:31:45.619626Z","bundle_sha256":"bbbe8b6520e08e4913332ab3af563eccd3087df3e8f08420e0f55e86c7e20dc5"}}