{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:6WWW4IQEAW6PQHYPT52SKP3MN5","short_pith_number":"pith:6WWW4IQE","canonical_record":{"source":{"id":"1904.12923","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-04-29T19:44:46Z","cross_cats_sorted":["nlin.CD","physics.flu-dyn"],"title_canon_sha256":"2da6cee41688eccc1bf0fd2ed8ff45b3a38c975080f4285714a28c320eb6d182","abstract_canon_sha256":"2ebb6a540c935276a573c9d84781c1f78b8294a73d878fa00ad007f2d9b136f1"},"schema_version":"1.0"},"canonical_sha256":"f5ad6e220405bcf81f0f9f75253f6c6f4732c415f19867b0f303b88d0f43f3a1","source":{"kind":"arxiv","id":"1904.12923","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.12923","created_at":"2026-05-17T23:42:08Z"},{"alias_kind":"arxiv_version","alias_value":"1904.12923v2","created_at":"2026-05-17T23:42:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.12923","created_at":"2026-05-17T23:42:08Z"},{"alias_kind":"pith_short_12","alias_value":"6WWW4IQEAW6P","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"6WWW4IQEAW6PQHYP","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"6WWW4IQE","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:6WWW4IQEAW6PQHYPT52SKP3MN5","target":"record","payload":{"canonical_record":{"source":{"id":"1904.12923","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-04-29T19:44:46Z","cross_cats_sorted":["nlin.CD","physics.flu-dyn"],"title_canon_sha256":"2da6cee41688eccc1bf0fd2ed8ff45b3a38c975080f4285714a28c320eb6d182","abstract_canon_sha256":"2ebb6a540c935276a573c9d84781c1f78b8294a73d878fa00ad007f2d9b136f1"},"schema_version":"1.0"},"canonical_sha256":"f5ad6e220405bcf81f0f9f75253f6c6f4732c415f19867b0f303b88d0f43f3a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:08.016931Z","signature_b64":"vjz9MouAMZqbgFtqyGlllz5gXee64hETc61uijsEVwXL0KncYqXPQNHbKyXcf9xEuy1zSOHTUtdC3iS+etUaBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5ad6e220405bcf81f0f9f75253f6c6f4732c415f19867b0f303b88d0f43f3a1","last_reissued_at":"2026-05-17T23:42:08.016384Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:08.016384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.12923","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":"2026-05-17T23:42:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8sYX0ZZqAAdI1H6ggHKPqnac3EsCIEbuOMVL3qzR+rRiwHT05nr6WJTh+YInS5qYBI8U23BQhxtTfG6QYv2gDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:48:58.594736Z"},"content_sha256":"7f625d87d6dea3ddd2675f46f9b569f10a34ba378ce075caa279c4d9773c8d32","schema_version":"1.0","event_id":"sha256:7f625d87d6dea3ddd2675f46f9b569f10a34ba378ce075caa279c4d9773c8d32"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:6WWW4IQEAW6PQHYPT52SKP3MN5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fluctuations of separation of trajectories in chaos and correlation dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD","physics.flu-dyn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Itzhak Fouxon, Jaan Kalda, Siim Ainsaar","submitted_at":"2019-04-29T19:44:46Z","abstract_excerpt":"We consider the cumulant generating function of the logarithm of the distance between two infinitesimally close trajectories of a chaotic system. Its long-time behavior is given by the generalized Lyapunov exponent $\\gamma(k)$ providing the logarithmic growth rate of the $k-$th moment of the distance. The Legendre transform of $\\gamma(k)$ is a large deviations function that gives the probability of rare fluctuations where the logarithmic rate of change of the distance is much larger or much smaller than the mean rate defining the first Lyapunov exponent. The only non-trivial zero of $\\gamma(k)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12923","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":"2026-05-17T23:42:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ab9HsA3y2RpI/HA/lR+4DGUHY2ThRoEHYFYnwIwaq34iyfqp3xAuU6OaDsojNywKZILPBra5/kplE/ALnol5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:48:58.595360Z"},"content_sha256":"078c311e44a4e7c716ae15d3b9f3139ef22ab3645965ba0ef0b8e7ee625fb562","schema_version":"1.0","event_id":"sha256:078c311e44a4e7c716ae15d3b9f3139ef22ab3645965ba0ef0b8e7ee625fb562"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6WWW4IQEAW6PQHYPT52SKP3MN5/bundle.json","state_url":"https://pith.science/pith/6WWW4IQEAW6PQHYPT52SKP3MN5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6WWW4IQEAW6PQHYPT52SKP3MN5/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":"2026-05-27T14:48:58Z","links":{"resolver":"https://pith.science/pith/6WWW4IQEAW6PQHYPT52SKP3MN5","bundle":"https://pith.science/pith/6WWW4IQEAW6PQHYPT52SKP3MN5/bundle.json","state":"https://pith.science/pith/6WWW4IQEAW6PQHYPT52SKP3MN5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6WWW4IQEAW6PQHYPT52SKP3MN5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6WWW4IQEAW6PQHYPT52SKP3MN5","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":"2ebb6a540c935276a573c9d84781c1f78b8294a73d878fa00ad007f2d9b136f1","cross_cats_sorted":["nlin.CD","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-04-29T19:44:46Z","title_canon_sha256":"2da6cee41688eccc1bf0fd2ed8ff45b3a38c975080f4285714a28c320eb6d182"},"schema_version":"1.0","source":{"id":"1904.12923","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.12923","created_at":"2026-05-17T23:42:08Z"},{"alias_kind":"arxiv_version","alias_value":"1904.12923v2","created_at":"2026-05-17T23:42:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.12923","created_at":"2026-05-17T23:42:08Z"},{"alias_kind":"pith_short_12","alias_value":"6WWW4IQEAW6P","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"6WWW4IQEAW6PQHYP","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"6WWW4IQE","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:078c311e44a4e7c716ae15d3b9f3139ef22ab3645965ba0ef0b8e7ee625fb562","target":"graph","created_at":"2026-05-17T23:42:08Z","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":"We consider the cumulant generating function of the logarithm of the distance between two infinitesimally close trajectories of a chaotic system. Its long-time behavior is given by the generalized Lyapunov exponent $\\gamma(k)$ providing the logarithmic growth rate of the $k-$th moment of the distance. The Legendre transform of $\\gamma(k)$ is a large deviations function that gives the probability of rare fluctuations where the logarithmic rate of change of the distance is much larger or much smaller than the mean rate defining the first Lyapunov exponent. The only non-trivial zero of $\\gamma(k)","authors_text":"Itzhak Fouxon, Jaan Kalda, Siim Ainsaar","cross_cats":["nlin.CD","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-04-29T19:44:46Z","title":"Fluctuations of separation of trajectories in chaos and correlation dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12923","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":"sha256:7f625d87d6dea3ddd2675f46f9b569f10a34ba378ce075caa279c4d9773c8d32","target":"record","created_at":"2026-05-17T23:42:08Z","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":"2ebb6a540c935276a573c9d84781c1f78b8294a73d878fa00ad007f2d9b136f1","cross_cats_sorted":["nlin.CD","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-04-29T19:44:46Z","title_canon_sha256":"2da6cee41688eccc1bf0fd2ed8ff45b3a38c975080f4285714a28c320eb6d182"},"schema_version":"1.0","source":{"id":"1904.12923","kind":"arxiv","version":2}},"canonical_sha256":"f5ad6e220405bcf81f0f9f75253f6c6f4732c415f19867b0f303b88d0f43f3a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5ad6e220405bcf81f0f9f75253f6c6f4732c415f19867b0f303b88d0f43f3a1","first_computed_at":"2026-05-17T23:42:08.016384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:08.016384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vjz9MouAMZqbgFtqyGlllz5gXee64hETc61uijsEVwXL0KncYqXPQNHbKyXcf9xEuy1zSOHTUtdC3iS+etUaBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:08.016931Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.12923","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f625d87d6dea3ddd2675f46f9b569f10a34ba378ce075caa279c4d9773c8d32","sha256:078c311e44a4e7c716ae15d3b9f3139ef22ab3645965ba0ef0b8e7ee625fb562"],"state_sha256":"9df6d0533285847628b19d29cd37cd2e1f540e335e0c0324d31d0bba673ada63"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i2ALJzWFOolhkQC1KcyBQd1/xpYizdmSfbMqjZYJ0HgWtq0OPHGiGj4WEEPkwxDWR1xs9vfMHT4f0xQrm8uuDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:48:58.598724Z","bundle_sha256":"e942028099ec592ab756e700d0fac8d46ed873bf127c9f40d723324545f69a7f"}}