{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DPZPJ4RAWXELNEGNCB4XWBCVQH","short_pith_number":"pith:DPZPJ4RA","canonical_record":{"source":{"id":"1507.00462","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-07-02T08:16:15Z","cross_cats_sorted":[],"title_canon_sha256":"a15f7ca6cf961c4e3c9291b64212e4eaa73a024a9050c4918dcfb744c5e552a9","abstract_canon_sha256":"94ec49674b9f309563f346ab2cceae03b404ce41e48733277bb067cbc2c466fd"},"schema_version":"1.0"},"canonical_sha256":"1bf2f4f220b5c8b690cd10797b045581fa5377ca0e9ce46e5177f2933832d776","source":{"kind":"arxiv","id":"1507.00462","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00462","created_at":"2026-05-18T01:23:38Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00462v2","created_at":"2026-05-18T01:23:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00462","created_at":"2026-05-18T01:23:38Z"},{"alias_kind":"pith_short_12","alias_value":"DPZPJ4RAWXEL","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DPZPJ4RAWXELNEGN","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DPZPJ4RA","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DPZPJ4RAWXELNEGNCB4XWBCVQH","target":"record","payload":{"canonical_record":{"source":{"id":"1507.00462","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-07-02T08:16:15Z","cross_cats_sorted":[],"title_canon_sha256":"a15f7ca6cf961c4e3c9291b64212e4eaa73a024a9050c4918dcfb744c5e552a9","abstract_canon_sha256":"94ec49674b9f309563f346ab2cceae03b404ce41e48733277bb067cbc2c466fd"},"schema_version":"1.0"},"canonical_sha256":"1bf2f4f220b5c8b690cd10797b045581fa5377ca0e9ce46e5177f2933832d776","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:38.151629Z","signature_b64":"uO+OjAYsb9bz6RMHdKS2zF1QXFSTQjfSxGH3ag65b2xiSw3BVEBqLjj2XcLwDGOGxkEGQTBjt8mm9Uy4DBSzCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bf2f4f220b5c8b690cd10797b045581fa5377ca0e9ce46e5177f2933832d776","last_reissued_at":"2026-05-18T01:23:38.150875Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:38.150875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.00462","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":"2026-05-18T01:23:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lhkCwLezV5dc2RqcFV5tTqwDdEtTjRpFCw4yiNeqGRlazBp8CA3rvP3BnovKqcD70EvqwxTk54GG2tVc4q8tDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:51:41.411836Z"},"content_sha256":"08d03e633fbdb76459ca5ba6dcd3e563b2fbd851dc58d69947209dbbf719d5c1","schema_version":"1.0","event_id":"sha256:08d03e633fbdb76459ca5ba6dcd3e563b2fbd851dc58d69947209dbbf719d5c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DPZPJ4RAWXELNEGNCB4XWBCVQH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Neighborhoods of periodic orbits and the stationary distribution of a noisy chaotic system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Domenico Lippolis, Jeffrey M. Heninger, Predrag Cvitanovic","submitted_at":"2015-07-02T08:16:15Z","abstract_excerpt":"The finest state space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation the neighborhoods of deterministic periodic orbits can be computed as distributions stationary under the action of a local Fokker-Planck operator and its adjoint. We derive explicit formulae for widths of these distributions in the case of chaotic dynamics, when the periodic orbits are hyperbolic. The resulting neighborhoods form a basis for functions on the attractor. The global stationary distribution, needed for calculation of long-time e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00462","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":"2026-05-18T01:23:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UJfYVokFY58rmqIj8ey+pOhsBhX2N++aMeJPV1kCQQ4dl1kjp81yLPlXDwl5v02vK+4RELklYKWQoqNJg+46AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:51:41.412186Z"},"content_sha256":"405c72325830cc323c71ce0c8d0cc51ade5bf3c820f488103000b9e84267c992","schema_version":"1.0","event_id":"sha256:405c72325830cc323c71ce0c8d0cc51ade5bf3c820f488103000b9e84267c992"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DPZPJ4RAWXELNEGNCB4XWBCVQH/bundle.json","state_url":"https://pith.science/pith/DPZPJ4RAWXELNEGNCB4XWBCVQH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DPZPJ4RAWXELNEGNCB4XWBCVQH/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":"2026-06-22T09:51:41Z","links":{"resolver":"https://pith.science/pith/DPZPJ4RAWXELNEGNCB4XWBCVQH","bundle":"https://pith.science/pith/DPZPJ4RAWXELNEGNCB4XWBCVQH/bundle.json","state":"https://pith.science/pith/DPZPJ4RAWXELNEGNCB4XWBCVQH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DPZPJ4RAWXELNEGNCB4XWBCVQH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DPZPJ4RAWXELNEGNCB4XWBCVQH","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":"94ec49674b9f309563f346ab2cceae03b404ce41e48733277bb067cbc2c466fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-07-02T08:16:15Z","title_canon_sha256":"a15f7ca6cf961c4e3c9291b64212e4eaa73a024a9050c4918dcfb744c5e552a9"},"schema_version":"1.0","source":{"id":"1507.00462","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00462","created_at":"2026-05-18T01:23:38Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00462v2","created_at":"2026-05-18T01:23:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00462","created_at":"2026-05-18T01:23:38Z"},{"alias_kind":"pith_short_12","alias_value":"DPZPJ4RAWXEL","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DPZPJ4RAWXELNEGN","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DPZPJ4RA","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:405c72325830cc323c71ce0c8d0cc51ade5bf3c820f488103000b9e84267c992","target":"graph","created_at":"2026-05-18T01:23:38Z","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 finest state space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation the neighborhoods of deterministic periodic orbits can be computed as distributions stationary under the action of a local Fokker-Planck operator and its adjoint. We derive explicit formulae for widths of these distributions in the case of chaotic dynamics, when the periodic orbits are hyperbolic. The resulting neighborhoods form a basis for functions on the attractor. The global stationary distribution, needed for calculation of long-time e","authors_text":"Domenico Lippolis, Jeffrey M. Heninger, Predrag Cvitanovic","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-07-02T08:16:15Z","title":"Neighborhoods of periodic orbits and the stationary distribution of a noisy chaotic system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00462","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":"sha256:08d03e633fbdb76459ca5ba6dcd3e563b2fbd851dc58d69947209dbbf719d5c1","target":"record","created_at":"2026-05-18T01:23:38Z","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":"94ec49674b9f309563f346ab2cceae03b404ce41e48733277bb067cbc2c466fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2015-07-02T08:16:15Z","title_canon_sha256":"a15f7ca6cf961c4e3c9291b64212e4eaa73a024a9050c4918dcfb744c5e552a9"},"schema_version":"1.0","source":{"id":"1507.00462","kind":"arxiv","version":2}},"canonical_sha256":"1bf2f4f220b5c8b690cd10797b045581fa5377ca0e9ce46e5177f2933832d776","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1bf2f4f220b5c8b690cd10797b045581fa5377ca0e9ce46e5177f2933832d776","first_computed_at":"2026-05-18T01:23:38.150875Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:38.150875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uO+OjAYsb9bz6RMHdKS2zF1QXFSTQjfSxGH3ag65b2xiSw3BVEBqLjj2XcLwDGOGxkEGQTBjt8mm9Uy4DBSzCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:38.151629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.00462","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08d03e633fbdb76459ca5ba6dcd3e563b2fbd851dc58d69947209dbbf719d5c1","sha256:405c72325830cc323c71ce0c8d0cc51ade5bf3c820f488103000b9e84267c992"],"state_sha256":"4713db9b9aafaddbef9dac115f397a832514ee37599ff7e7982a52e1b7e04b35"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xprAC+aw8S8ousjTyXJLpAlpEYSJmdFqWAKDZLqC+80/9pTexFJ3m3hFm31fenJrJ2lpVwGpN3BY5kLDj+98BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T09:51:41.414217Z","bundle_sha256":"3e6516c5c25dc0fe8a56851234546d617cd48bb31674f499d289fba4f5ce1b4b"}}