{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:5Q3PFI7HLELNTGBEUJAMX6YEJE","short_pith_number":"pith:5Q3PFI7H","canonical_record":{"source":{"id":"1804.01143","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2018-03-29T16:25:20Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"2929e2c5b817449dbaa4660f1c500c196a068a942beaedc693d27750a1d546d0","abstract_canon_sha256":"a49f56b7bdd7da10c7130f64d0eef0fc0f0ffe57343b7d7611bd69f3aaf1174d"},"schema_version":"1.0"},"canonical_sha256":"ec36f2a3e75916d99824a240cbfb04491e158881fcf0967c0030edb5de0424d5","source":{"kind":"arxiv","id":"1804.01143","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.01143","created_at":"2026-05-18T00:11:34Z"},{"alias_kind":"arxiv_version","alias_value":"1804.01143v1","created_at":"2026-05-18T00:11:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01143","created_at":"2026-05-18T00:11:34Z"},{"alias_kind":"pith_short_12","alias_value":"5Q3PFI7HLELN","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5Q3PFI7HLELNTGBE","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5Q3PFI7H","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:5Q3PFI7HLELNTGBEUJAMX6YEJE","target":"record","payload":{"canonical_record":{"source":{"id":"1804.01143","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2018-03-29T16:25:20Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"2929e2c5b817449dbaa4660f1c500c196a068a942beaedc693d27750a1d546d0","abstract_canon_sha256":"a49f56b7bdd7da10c7130f64d0eef0fc0f0ffe57343b7d7611bd69f3aaf1174d"},"schema_version":"1.0"},"canonical_sha256":"ec36f2a3e75916d99824a240cbfb04491e158881fcf0967c0030edb5de0424d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:34.903166Z","signature_b64":"ZlaHe9j8zflU3WoFSjII4bANvHcyzj1NbXo5TPnCZLxIi9DvCNp2NBUCBfYOFk9QolSF4JjeQWUtaSzcwUb9Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec36f2a3e75916d99824a240cbfb04491e158881fcf0967c0030edb5de0424d5","last_reissued_at":"2026-05-18T00:11:34.902550Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:34.902550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.01143","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":"2026-05-18T00:11:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UVlR95KMylBpSahptyaT1FxwL7tSYug0DUMWH3YYRAG8JH1b6F2z03RMi8IB7Q6mjkFytw9DJu3wzLE2062mCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:10:32.123937Z"},"content_sha256":"6d3c9b9df8942bbbfd0163397b4b6884b7e8641fcf2061224de70b0fd48e877b","schema_version":"1.0","event_id":"sha256:6d3c9b9df8942bbbfd0163397b4b6884b7e8641fcf2061224de70b0fd48e877b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:5Q3PFI7HLELNTGBEUJAMX6YEJE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matlab code for Lyapunov exponents of fractional order systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"physics.comp-ph","authors_text":"Marius-F. Danca, Nikolay Kuznetsov","submitted_at":"2018-03-29T16:25:20Z","abstract_excerpt":"In this paper the Benettin-Wolf algorithm to determine all Lyapunov exponents for a class of fractional-order systems modeled by Caputo's derivative and the corresponding Matlab code are presented. First it is proved that the considered class of fractional-order systems admits the necessary variational system necessary to find the Lyapunov exponents. The underlying numerical method to solve the extended system of fractional order, composed of the initial value problem and the variational system, is the predictor-corrector Adams-Bashforth-Moulton for fractional differential equations. The Matla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01143","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":"2026-05-18T00:11:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Iqm5vZpFtUQhEGAnrMvpwVZ/DvCsSx59AgndUwWFfZ/d4/KsexZjyZFYrElOJ9LjtUkQ2J6mU9MpK6tR4ptcAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:10:32.124613Z"},"content_sha256":"e7b7d5d08e724df20c4b21c79c14db9aa2d7af52780286154407bb36f2630c6b","schema_version":"1.0","event_id":"sha256:e7b7d5d08e724df20c4b21c79c14db9aa2d7af52780286154407bb36f2630c6b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5Q3PFI7HLELNTGBEUJAMX6YEJE/bundle.json","state_url":"https://pith.science/pith/5Q3PFI7HLELNTGBEUJAMX6YEJE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5Q3PFI7HLELNTGBEUJAMX6YEJE/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":"2026-06-04T04:10:32Z","links":{"resolver":"https://pith.science/pith/5Q3PFI7HLELNTGBEUJAMX6YEJE","bundle":"https://pith.science/pith/5Q3PFI7HLELNTGBEUJAMX6YEJE/bundle.json","state":"https://pith.science/pith/5Q3PFI7HLELNTGBEUJAMX6YEJE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5Q3PFI7HLELNTGBEUJAMX6YEJE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5Q3PFI7HLELNTGBEUJAMX6YEJE","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":"a49f56b7bdd7da10c7130f64d0eef0fc0f0ffe57343b7d7611bd69f3aaf1174d","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2018-03-29T16:25:20Z","title_canon_sha256":"2929e2c5b817449dbaa4660f1c500c196a068a942beaedc693d27750a1d546d0"},"schema_version":"1.0","source":{"id":"1804.01143","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.01143","created_at":"2026-05-18T00:11:34Z"},{"alias_kind":"arxiv_version","alias_value":"1804.01143v1","created_at":"2026-05-18T00:11:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01143","created_at":"2026-05-18T00:11:34Z"},{"alias_kind":"pith_short_12","alias_value":"5Q3PFI7HLELN","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5Q3PFI7HLELNTGBE","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5Q3PFI7H","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:e7b7d5d08e724df20c4b21c79c14db9aa2d7af52780286154407bb36f2630c6b","target":"graph","created_at":"2026-05-18T00:11:34Z","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":"In this paper the Benettin-Wolf algorithm to determine all Lyapunov exponents for a class of fractional-order systems modeled by Caputo's derivative and the corresponding Matlab code are presented. First it is proved that the considered class of fractional-order systems admits the necessary variational system necessary to find the Lyapunov exponents. The underlying numerical method to solve the extended system of fractional order, composed of the initial value problem and the variational system, is the predictor-corrector Adams-Bashforth-Moulton for fractional differential equations. The Matla","authors_text":"Marius-F. Danca, Nikolay Kuznetsov","cross_cats":["nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2018-03-29T16:25:20Z","title":"Matlab code for Lyapunov exponents of fractional order systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01143","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":"sha256:6d3c9b9df8942bbbfd0163397b4b6884b7e8641fcf2061224de70b0fd48e877b","target":"record","created_at":"2026-05-18T00:11:34Z","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":"a49f56b7bdd7da10c7130f64d0eef0fc0f0ffe57343b7d7611bd69f3aaf1174d","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2018-03-29T16:25:20Z","title_canon_sha256":"2929e2c5b817449dbaa4660f1c500c196a068a942beaedc693d27750a1d546d0"},"schema_version":"1.0","source":{"id":"1804.01143","kind":"arxiv","version":1}},"canonical_sha256":"ec36f2a3e75916d99824a240cbfb04491e158881fcf0967c0030edb5de0424d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec36f2a3e75916d99824a240cbfb04491e158881fcf0967c0030edb5de0424d5","first_computed_at":"2026-05-18T00:11:34.902550Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:34.902550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZlaHe9j8zflU3WoFSjII4bANvHcyzj1NbXo5TPnCZLxIi9DvCNp2NBUCBfYOFk9QolSF4JjeQWUtaSzcwUb9Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:34.903166Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.01143","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d3c9b9df8942bbbfd0163397b4b6884b7e8641fcf2061224de70b0fd48e877b","sha256:e7b7d5d08e724df20c4b21c79c14db9aa2d7af52780286154407bb36f2630c6b"],"state_sha256":"00ea2b7514116630ee23b147ed30e811c54799ab5fec1f07da221c5b84b35208"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SjaoJJDR1HQP+O3v4TYCzKrPfVD5d1p1zNt0T67IH3qK8gJlbUuJftXEAU83fFAVGHwAXu16zu8aS58h//cQBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T04:10:32.127569Z","bundle_sha256":"c6d2cf6d5531bc9047cc576f077d4369455086fea4e048a45e111f413745da8a"}}