{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PHFOFKJU4UU4JDR4YIDLAZ4CBQ","short_pith_number":"pith:PHFOFKJU","canonical_record":{"source":{"id":"1501.07264","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-01-28T20:45:02Z","cross_cats_sorted":["astro-ph.EP"],"title_canon_sha256":"9db94c8d3a2050fb2aa522564f534e0f6516a5a43010c3145ee982df7b3b5b7a","abstract_canon_sha256":"7c65ba9caf35ff7d4dfe2299ab1491a38b858888f3e45385efa93974f0dc2fc9"},"schema_version":"1.0"},"canonical_sha256":"79cae2a934e529c48e3cc206b067820c147adc4ab859e13f1830c4741a5cc34e","source":{"kind":"arxiv","id":"1501.07264","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.07264","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"arxiv_version","alias_value":"1501.07264v2","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07264","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"pith_short_12","alias_value":"PHFOFKJU4UU4","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PHFOFKJU4UU4JDR4","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PHFOFKJU","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PHFOFKJU4UU4JDR4YIDLAZ4CBQ","target":"record","payload":{"canonical_record":{"source":{"id":"1501.07264","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-01-28T20:45:02Z","cross_cats_sorted":["astro-ph.EP"],"title_canon_sha256":"9db94c8d3a2050fb2aa522564f534e0f6516a5a43010c3145ee982df7b3b5b7a","abstract_canon_sha256":"7c65ba9caf35ff7d4dfe2299ab1491a38b858888f3e45385efa93974f0dc2fc9"},"schema_version":"1.0"},"canonical_sha256":"79cae2a934e529c48e3cc206b067820c147adc4ab859e13f1830c4741a5cc34e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:53.218737Z","signature_b64":"2HM88sd1YCcZezUNm9h9KzluFd1owNTqptjAl7BI7FfZU6dCRqqhLpHa1xDxeRbRgaFPzvzRfiokNufzJdCnDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79cae2a934e529c48e3cc206b067820c147adc4ab859e13f1830c4741a5cc34e","last_reissued_at":"2026-05-18T01:31:53.218292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:53.218292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.07264","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:31:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BUV6CnQ2UIqerW4yrggAbdmiqvA8dj+urVdenzkfY70XP4aJeQJJ/gR1e5F/kg9+/OBDVHrKBdIasCUSrOUyBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:16:43.888653Z"},"content_sha256":"0a87dd5041276c836f9d44bfb098c70fe5025c3386e7b064945980834e048d68","schema_version":"1.0","event_id":"sha256:0a87dd5041276c836f9d44bfb098c70fe5025c3386e7b064945980834e048d68"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PHFOFKJU4UU4JDR4YIDLAZ4CBQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Relative Lyapunov Indicators: Theory and Application to Dynamical Astronomy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.EP"],"primary_cat":"nlin.CD","authors_text":"Nicol\\'as Maffione, Zsolt S\\'andor","submitted_at":"2015-01-28T20:45:02Z","abstract_excerpt":"A recently introduced chaos detection method, the Relative Lyapunov Indicator (RLI) is investigated in the cases of symplectic mappings and continuous Hamiltonian systems. It is shown that the RLI is an efficient numerical tool in determining the true nature of individual orbits, and in separating ordered and chaotic regions of the phase space of dynamical systems. A comparison between the RLI and some other variational indicators are presented, as well as the recent applications of the RLI to various problems of dynamical astronomy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07264","kind":"arxiv","version":2},"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":"2026-05-18T01:31:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w/4mlEvBefuUB45hUYB+AM60UwF9WLOJKe8lYHSVokAePoSHZiiwbtPnoan4gQEEaMsGRrZMyPTa87LHXveUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:16:43.888998Z"},"content_sha256":"c1c751bb26a16540a0e4e1e1edc5463f2d1498a41181f827168d6b81377a3abb","schema_version":"1.0","event_id":"sha256:c1c751bb26a16540a0e4e1e1edc5463f2d1498a41181f827168d6b81377a3abb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PHFOFKJU4UU4JDR4YIDLAZ4CBQ/bundle.json","state_url":"https://pith.science/pith/PHFOFKJU4UU4JDR4YIDLAZ4CBQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PHFOFKJU4UU4JDR4YIDLAZ4CBQ/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":"2026-06-04T18:16:43Z","links":{"resolver":"https://pith.science/pith/PHFOFKJU4UU4JDR4YIDLAZ4CBQ","bundle":"https://pith.science/pith/PHFOFKJU4UU4JDR4YIDLAZ4CBQ/bundle.json","state":"https://pith.science/pith/PHFOFKJU4UU4JDR4YIDLAZ4CBQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PHFOFKJU4UU4JDR4YIDLAZ4CBQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PHFOFKJU4UU4JDR4YIDLAZ4CBQ","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":"7c65ba9caf35ff7d4dfe2299ab1491a38b858888f3e45385efa93974f0dc2fc9","cross_cats_sorted":["astro-ph.EP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-01-28T20:45:02Z","title_canon_sha256":"9db94c8d3a2050fb2aa522564f534e0f6516a5a43010c3145ee982df7b3b5b7a"},"schema_version":"1.0","source":{"id":"1501.07264","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.07264","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"arxiv_version","alias_value":"1501.07264v2","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07264","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"pith_short_12","alias_value":"PHFOFKJU4UU4","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PHFOFKJU4UU4JDR4","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PHFOFKJU","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:c1c751bb26a16540a0e4e1e1edc5463f2d1498a41181f827168d6b81377a3abb","target":"graph","created_at":"2026-05-18T01:31:53Z","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":"A recently introduced chaos detection method, the Relative Lyapunov Indicator (RLI) is investigated in the cases of symplectic mappings and continuous Hamiltonian systems. It is shown that the RLI is an efficient numerical tool in determining the true nature of individual orbits, and in separating ordered and chaotic regions of the phase space of dynamical systems. A comparison between the RLI and some other variational indicators are presented, as well as the recent applications of the RLI to various problems of dynamical astronomy.","authors_text":"Nicol\\'as Maffione, Zsolt S\\'andor","cross_cats":["astro-ph.EP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-01-28T20:45:02Z","title":"The Relative Lyapunov Indicators: Theory and Application to Dynamical Astronomy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07264","kind":"arxiv","version":2},"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":"sha256:0a87dd5041276c836f9d44bfb098c70fe5025c3386e7b064945980834e048d68","target":"record","created_at":"2026-05-18T01:31:53Z","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":"7c65ba9caf35ff7d4dfe2299ab1491a38b858888f3e45385efa93974f0dc2fc9","cross_cats_sorted":["astro-ph.EP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-01-28T20:45:02Z","title_canon_sha256":"9db94c8d3a2050fb2aa522564f534e0f6516a5a43010c3145ee982df7b3b5b7a"},"schema_version":"1.0","source":{"id":"1501.07264","kind":"arxiv","version":2}},"canonical_sha256":"79cae2a934e529c48e3cc206b067820c147adc4ab859e13f1830c4741a5cc34e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79cae2a934e529c48e3cc206b067820c147adc4ab859e13f1830c4741a5cc34e","first_computed_at":"2026-05-18T01:31:53.218292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:53.218292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2HM88sd1YCcZezUNm9h9KzluFd1owNTqptjAl7BI7FfZU6dCRqqhLpHa1xDxeRbRgaFPzvzRfiokNufzJdCnDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:53.218737Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.07264","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a87dd5041276c836f9d44bfb098c70fe5025c3386e7b064945980834e048d68","sha256:c1c751bb26a16540a0e4e1e1edc5463f2d1498a41181f827168d6b81377a3abb"],"state_sha256":"44ddecdf31fbdd71e9094d014748e6452419301a57a1ef9bc3381839cf5c668c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xAARcSW5N7xzoIGjJLhz/cg00+/lkq9h8LdQCMWvFLE35NhQ/13IFajOVM4RFN2oaExQApuu9IO3lWpRtyS2CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T18:16:43.890981Z","bundle_sha256":"191a821e20e5b9b2cf6e27327b619f701713f007e2947254f561b3b7a7c8830a"}}