{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:YK7KCNIZKERPLGZYBXEROTZVFK","short_pith_number":"pith:YK7KCNIZ","canonical_record":{"source":{"id":"nlin/0504015","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.CD","submitted_at":"2005-04-06T16:46:07Z","cross_cats_sorted":[],"title_canon_sha256":"be5224e4c52cbc5677c9f7cde95c2c807a607b199ecfbdfe8cc3143f9389203c","abstract_canon_sha256":"d47dd8e21f9e6906170a962fe2cbc9785bd0353fd03bfc1f4139b19444146ce6"},"schema_version":"1.0"},"canonical_sha256":"c2bea135195122f59b380dc9174f352a8c2b3336ee7dc4e393bd54eb248f36fb","source":{"kind":"arxiv","id":"nlin/0504015","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0504015","created_at":"2026-05-18T01:08:49Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0504015v1","created_at":"2026-05-18T01:08:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0504015","created_at":"2026-05-18T01:08:49Z"},{"alias_kind":"pith_short_12","alias_value":"YK7KCNIZKERP","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"YK7KCNIZKERPLGZY","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"YK7KCNIZ","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:YK7KCNIZKERPLGZYBXEROTZVFK","target":"record","payload":{"canonical_record":{"source":{"id":"nlin/0504015","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.CD","submitted_at":"2005-04-06T16:46:07Z","cross_cats_sorted":[],"title_canon_sha256":"be5224e4c52cbc5677c9f7cde95c2c807a607b199ecfbdfe8cc3143f9389203c","abstract_canon_sha256":"d47dd8e21f9e6906170a962fe2cbc9785bd0353fd03bfc1f4139b19444146ce6"},"schema_version":"1.0"},"canonical_sha256":"c2bea135195122f59b380dc9174f352a8c2b3336ee7dc4e393bd54eb248f36fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:49.167361Z","signature_b64":"5DJ6TObJTkkYwvWXaorg5Y/IP31HUqXizISs3n0SEO28El5cyfWfoP1pttrI1GU8LZbrxdtkS2KDWpL5FOPgBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2bea135195122f59b380dc9174f352a8c2b3336ee7dc4e393bd54eb248f36fb","last_reissued_at":"2026-05-18T01:08:49.166716Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:49.166716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"nlin/0504015","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":"2026-05-18T01:08:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2zCemvHbvIlyXv6VpNpoLk1nozKHOxIkwcbzgZBlLZFuEWoydRyZ4NER+QBdi8tH1mAT3gnmVA2zgbSbuOnjCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:48:09.703830Z"},"content_sha256":"e46f88b6d1923f73eb7cdeedf94b1164bad9cc4ea72de07d09777c048075b887","schema_version":"1.0","event_id":"sha256:e46f88b6d1923f73eb7cdeedf94b1164bad9cc4ea72de07d09777c048075b887"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:YK7KCNIZKERPLGZYBXEROTZVFK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some aspects of the synchronization in coupled maps","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Abdala M. Saleh, Antonio M. Batista, Jos\\'e T. Lunardi, Sandro E. de Souza Pinto","submitted_at":"2005-04-06T16:46:07Z","abstract_excerpt":"Through numerical simulations we analyze the synchronization time and the Lyapunov dimension of a coupled map lattice consisting of a chain of chaotic logistic maps exhibiting power law interactions. From the observed behaviors we find a lower bound for the size $N$ of the lattice, independent of the range and strength of the interaction, which imposes a practical lower bound in numerical simulations for the system to be considered in the thermodynamic limit. We also observe the existence of a strong correlation between the averaged synchronization time and the Lyapunov dimension. This is an i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0504015","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":"2026-05-18T01:08:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2R/54L4F6sawaX0xVGwmiTclr30YgYVmMloV7r9xDrEdWZ1bObuGRN+a9zxCAY/KeQBVZfjn6SVH1GsZStrsCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:48:09.704165Z"},"content_sha256":"f4db957609482a4a885f9254d73936306aabdc5fdfdde2afd841f2209cadf1ae","schema_version":"1.0","event_id":"sha256:f4db957609482a4a885f9254d73936306aabdc5fdfdde2afd841f2209cadf1ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YK7KCNIZKERPLGZYBXEROTZVFK/bundle.json","state_url":"https://pith.science/pith/YK7KCNIZKERPLGZYBXEROTZVFK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YK7KCNIZKERPLGZYBXEROTZVFK/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":"2026-06-08T23:48:09Z","links":{"resolver":"https://pith.science/pith/YK7KCNIZKERPLGZYBXEROTZVFK","bundle":"https://pith.science/pith/YK7KCNIZKERPLGZYBXEROTZVFK/bundle.json","state":"https://pith.science/pith/YK7KCNIZKERPLGZYBXEROTZVFK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YK7KCNIZKERPLGZYBXEROTZVFK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:YK7KCNIZKERPLGZYBXEROTZVFK","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":"d47dd8e21f9e6906170a962fe2cbc9785bd0353fd03bfc1f4139b19444146ce6","cross_cats_sorted":[],"license":"","primary_cat":"nlin.CD","submitted_at":"2005-04-06T16:46:07Z","title_canon_sha256":"be5224e4c52cbc5677c9f7cde95c2c807a607b199ecfbdfe8cc3143f9389203c"},"schema_version":"1.0","source":{"id":"nlin/0504015","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0504015","created_at":"2026-05-18T01:08:49Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0504015v1","created_at":"2026-05-18T01:08:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0504015","created_at":"2026-05-18T01:08:49Z"},{"alias_kind":"pith_short_12","alias_value":"YK7KCNIZKERP","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"YK7KCNIZKERPLGZY","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"YK7KCNIZ","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:f4db957609482a4a885f9254d73936306aabdc5fdfdde2afd841f2209cadf1ae","target":"graph","created_at":"2026-05-18T01:08:49Z","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":"Through numerical simulations we analyze the synchronization time and the Lyapunov dimension of a coupled map lattice consisting of a chain of chaotic logistic maps exhibiting power law interactions. From the observed behaviors we find a lower bound for the size $N$ of the lattice, independent of the range and strength of the interaction, which imposes a practical lower bound in numerical simulations for the system to be considered in the thermodynamic limit. We also observe the existence of a strong correlation between the averaged synchronization time and the Lyapunov dimension. This is an i","authors_text":"Abdala M. Saleh, Antonio M. Batista, Jos\\'e T. Lunardi, Sandro E. de Souza Pinto","cross_cats":[],"headline":"","license":"","primary_cat":"nlin.CD","submitted_at":"2005-04-06T16:46:07Z","title":"Some aspects of the synchronization in coupled maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0504015","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:e46f88b6d1923f73eb7cdeedf94b1164bad9cc4ea72de07d09777c048075b887","target":"record","created_at":"2026-05-18T01:08:49Z","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":"d47dd8e21f9e6906170a962fe2cbc9785bd0353fd03bfc1f4139b19444146ce6","cross_cats_sorted":[],"license":"","primary_cat":"nlin.CD","submitted_at":"2005-04-06T16:46:07Z","title_canon_sha256":"be5224e4c52cbc5677c9f7cde95c2c807a607b199ecfbdfe8cc3143f9389203c"},"schema_version":"1.0","source":{"id":"nlin/0504015","kind":"arxiv","version":1}},"canonical_sha256":"c2bea135195122f59b380dc9174f352a8c2b3336ee7dc4e393bd54eb248f36fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2bea135195122f59b380dc9174f352a8c2b3336ee7dc4e393bd54eb248f36fb","first_computed_at":"2026-05-18T01:08:49.166716Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:49.166716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5DJ6TObJTkkYwvWXaorg5Y/IP31HUqXizISs3n0SEO28El5cyfWfoP1pttrI1GU8LZbrxdtkS2KDWpL5FOPgBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:49.167361Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0504015","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e46f88b6d1923f73eb7cdeedf94b1164bad9cc4ea72de07d09777c048075b887","sha256:f4db957609482a4a885f9254d73936306aabdc5fdfdde2afd841f2209cadf1ae"],"state_sha256":"cf7cdc3678f1ce86eb68c61d72261542164ac5fc19de67e18b93a9529799d3f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XbKqFIScXRoa1rweaYLVTsFqwUihWGcVDbHIv4agAeQtKJsmrhGSlFgB7b/ZK1sMdkZZWSzx2Sv05WCG+c7BCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T23:48:09.706032Z","bundle_sha256":"8272980e8f80613a014b7ed2c2fb4e10bd1ac975010e3d22976f574c3d435a20"}}