{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FCK4GFO6EOTV5IWJBLKGO4GU57","short_pith_number":"pith:FCK4GFO6","canonical_record":{"source":{"id":"1506.03269","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-06-10T12:15:25Z","cross_cats_sorted":["cond-mat.stat-mech","math.DS"],"title_canon_sha256":"ed46e949163c328b7ad92a15b0a51f2e29b9bccd08b857ae13df3b19e19e4ab5","abstract_canon_sha256":"960b088d737a6642a71c7f1af5dd1060eb479b9c994e0d75d95a3ddd4201647f"},"schema_version":"1.0"},"canonical_sha256":"2895c315de23a75ea2c90ad46770d4efca4c1492b9f33faccb481c1aff753100","source":{"kind":"arxiv","id":"1506.03269","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03269","created_at":"2026-05-18T01:40:57Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03269v2","created_at":"2026-05-18T01:40:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03269","created_at":"2026-05-18T01:40:57Z"},{"alias_kind":"pith_short_12","alias_value":"FCK4GFO6EOTV","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FCK4GFO6EOTV5IWJ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FCK4GFO6","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FCK4GFO6EOTV5IWJBLKGO4GU57","target":"record","payload":{"canonical_record":{"source":{"id":"1506.03269","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-06-10T12:15:25Z","cross_cats_sorted":["cond-mat.stat-mech","math.DS"],"title_canon_sha256":"ed46e949163c328b7ad92a15b0a51f2e29b9bccd08b857ae13df3b19e19e4ab5","abstract_canon_sha256":"960b088d737a6642a71c7f1af5dd1060eb479b9c994e0d75d95a3ddd4201647f"},"schema_version":"1.0"},"canonical_sha256":"2895c315de23a75ea2c90ad46770d4efca4c1492b9f33faccb481c1aff753100","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:40:57.976544Z","signature_b64":"Ts0Mkabr9qngFdJotLmMQT04HjUw9RgqNfrqIMpe8mLRU6UY/UeBTvbMrBlQX9FtP2arf8lU4JJQcXT3dWhABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2895c315de23a75ea2c90ad46770d4efca4c1492b9f33faccb481c1aff753100","last_reissued_at":"2026-05-18T01:40:57.975888Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:40:57.975888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.03269","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":"2026-05-18T01:40:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qWdCULO0q5XhAP3XnIuMrjgvltHXWpmD05DL1CcOs1ET1b+0CA/Ue1nFQS8zOkJM7dqG6pJ2HTSVqxhqFcJlBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T22:25:55.598296Z"},"content_sha256":"c047fd8f4d9d1906e3a6e4b8ae8c2b6de129046397bc2ef82bcf52491398507f","schema_version":"1.0","event_id":"sha256:c047fd8f4d9d1906e3a6e4b8ae8c2b6de129046397bc2ef82bcf52491398507f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FCK4GFO6EOTV5IWJBLKGO4GU57","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact invariant measures: How the strength of measure settles the intensity of chaos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.DS"],"primary_cat":"nlin.CD","authors_text":"Roberto Venegeroles","submitted_at":"2015-06-10T12:15:25Z","abstract_excerpt":"The aim of this paper is to show how extracting dynamical behavior and ergodic properties from deterministic chaos with the assistance of exact invariant measures. On the one hand, we provide an approach to deal with the inverse problem of finding nonlinear interval maps from a given invariant measure. Then, we show how to identify ergodic properties by means of transitions along the phase space via exact measures. On the other hand, we discuss quantitatively how infinite measures imply maps having subexponential Lyapunov instability (weakly chaotic), as opposed to finite measure ergodic maps,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03269","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":"2026-05-18T01:40:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bo+R6XpgbKJH6QvhL3xzH4cbMKPEwOGooGNtMr+gxOoL2ovCZ0y9n8tabow2AevxHg2pciGjiNmnsSqKcn+0DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T22:25:55.599342Z"},"content_sha256":"4bb7a6c803fc609e4360e86d8f992221b5a4ec6bb809631c2ea5e96b1895d60d","schema_version":"1.0","event_id":"sha256:4bb7a6c803fc609e4360e86d8f992221b5a4ec6bb809631c2ea5e96b1895d60d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FCK4GFO6EOTV5IWJBLKGO4GU57/bundle.json","state_url":"https://pith.science/pith/FCK4GFO6EOTV5IWJBLKGO4GU57/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FCK4GFO6EOTV5IWJBLKGO4GU57/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":"2026-08-14T22:25:55Z","links":{"resolver":"https://pith.science/pith/FCK4GFO6EOTV5IWJBLKGO4GU57","bundle":"https://pith.science/pith/FCK4GFO6EOTV5IWJBLKGO4GU57/bundle.json","state":"https://pith.science/pith/FCK4GFO6EOTV5IWJBLKGO4GU57/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FCK4GFO6EOTV5IWJBLKGO4GU57/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FCK4GFO6EOTV5IWJBLKGO4GU57","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":"960b088d737a6642a71c7f1af5dd1060eb479b9c994e0d75d95a3ddd4201647f","cross_cats_sorted":["cond-mat.stat-mech","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-06-10T12:15:25Z","title_canon_sha256":"ed46e949163c328b7ad92a15b0a51f2e29b9bccd08b857ae13df3b19e19e4ab5"},"schema_version":"1.0","source":{"id":"1506.03269","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03269","created_at":"2026-05-18T01:40:57Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03269v2","created_at":"2026-05-18T01:40:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03269","created_at":"2026-05-18T01:40:57Z"},{"alias_kind":"pith_short_12","alias_value":"FCK4GFO6EOTV","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FCK4GFO6EOTV5IWJ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FCK4GFO6","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:4bb7a6c803fc609e4360e86d8f992221b5a4ec6bb809631c2ea5e96b1895d60d","target":"graph","created_at":"2026-05-18T01:40:57Z","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 aim of this paper is to show how extracting dynamical behavior and ergodic properties from deterministic chaos with the assistance of exact invariant measures. On the one hand, we provide an approach to deal with the inverse problem of finding nonlinear interval maps from a given invariant measure. Then, we show how to identify ergodic properties by means of transitions along the phase space via exact measures. On the other hand, we discuss quantitatively how infinite measures imply maps having subexponential Lyapunov instability (weakly chaotic), as opposed to finite measure ergodic maps,","authors_text":"Roberto Venegeroles","cross_cats":["cond-mat.stat-mech","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-06-10T12:15:25Z","title":"Exact invariant measures: How the strength of measure settles the intensity of chaos"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03269","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:c047fd8f4d9d1906e3a6e4b8ae8c2b6de129046397bc2ef82bcf52491398507f","target":"record","created_at":"2026-05-18T01:40:57Z","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":"960b088d737a6642a71c7f1af5dd1060eb479b9c994e0d75d95a3ddd4201647f","cross_cats_sorted":["cond-mat.stat-mech","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-06-10T12:15:25Z","title_canon_sha256":"ed46e949163c328b7ad92a15b0a51f2e29b9bccd08b857ae13df3b19e19e4ab5"},"schema_version":"1.0","source":{"id":"1506.03269","kind":"arxiv","version":2}},"canonical_sha256":"2895c315de23a75ea2c90ad46770d4efca4c1492b9f33faccb481c1aff753100","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2895c315de23a75ea2c90ad46770d4efca4c1492b9f33faccb481c1aff753100","first_computed_at":"2026-05-18T01:40:57.975888Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:40:57.975888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ts0Mkabr9qngFdJotLmMQT04HjUw9RgqNfrqIMpe8mLRU6UY/UeBTvbMrBlQX9FtP2arf8lU4JJQcXT3dWhABw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:40:57.976544Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.03269","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c047fd8f4d9d1906e3a6e4b8ae8c2b6de129046397bc2ef82bcf52491398507f","sha256:4bb7a6c803fc609e4360e86d8f992221b5a4ec6bb809631c2ea5e96b1895d60d"],"state_sha256":"a437997cd36e8ad93f8aba7ef4bfee3b2a2aa520b31e601c9b242b5ea5352374"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z8eQcLDfVP1PBdiNS+Fu4nF1ym/ZFAVqlrFTp57JJcAt1ulpfm9sAX5cV6MdSwwduYhnr3VGCrcVq5XHeRX/BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T22:25:55.610823Z","bundle_sha256":"c143a6fba804ce4f6ba92a835f2201ab94c1f139aee0cd87b5b25b6e4a5b032e"}}