{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:B3N2BIIJE3KUOGKNG2Z4VHH63X","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":"723c76bea3d7252297d8cae78733376af31bd18b0e5f71e31c7fa7d1db64550e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-07-13T17:28:41Z","title_canon_sha256":"d9cedb95b3b9451abfa639c83aa03dba10e71b9fb66b502a94bcce99bf3f89d4"},"schema_version":"1.0","source":{"id":"1707.04231","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.04231","created_at":"2026-05-17T23:58:50Z"},{"alias_kind":"arxiv_version","alias_value":"1707.04231v2","created_at":"2026-05-17T23:58:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04231","created_at":"2026-05-17T23:58:50Z"},{"alias_kind":"pith_short_12","alias_value":"B3N2BIIJE3KU","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"B3N2BIIJE3KUOGKN","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"B3N2BIIJ","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:1232fd805fa2d20f4fb48b3d27f021b4205147968bff06baa61e9a572cfa2712","target":"graph","created_at":"2026-05-17T23:58:50Z","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 prove that transport in the phase space of the \"most strongly chaotic\" dynamical systems has three different stages. Consider a finite Markov partition (coarse graining) $\\xi$ of the phase space of such a system. In the first short times interval there is a hierarchy with respect to the values of the first passage probabilities for the elements of $\\xi$ and therefore finite time predictions can be made about which element of the Markov partition trajectories will be most likely to hit first at a given moment. In the third long times interval, which goes to infinity, there is an opposite hie","authors_text":"Leonid Bunimovich, Mark Bolding","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-07-13T17:28:41Z","title":"Where and When Orbits of Strongly Chaotic Systems Prefer to Go"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04231","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":"sha256:909dc225d2269655d7ff8cceadbe54240e4ec097f9999c17eddd691c7ddf8b0a","target":"record","created_at":"2026-05-17T23:58:50Z","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":"723c76bea3d7252297d8cae78733376af31bd18b0e5f71e31c7fa7d1db64550e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-07-13T17:28:41Z","title_canon_sha256":"d9cedb95b3b9451abfa639c83aa03dba10e71b9fb66b502a94bcce99bf3f89d4"},"schema_version":"1.0","source":{"id":"1707.04231","kind":"arxiv","version":2}},"canonical_sha256":"0edba0a10926d547194d36b3ca9cfeddfc1a48ad8d732af3e63a3ea2f2200443","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0edba0a10926d547194d36b3ca9cfeddfc1a48ad8d732af3e63a3ea2f2200443","first_computed_at":"2026-05-17T23:58:50.199031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:50.199031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X4MpaVbi97xNZ8/1S88vpmYouwe53D/g4pNngYtvVrhEn4P4zqxtqO9u/yoQR5JnGUqm2u6IGez56/LCDZumAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:50.199522Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.04231","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:909dc225d2269655d7ff8cceadbe54240e4ec097f9999c17eddd691c7ddf8b0a","sha256:1232fd805fa2d20f4fb48b3d27f021b4205147968bff06baa61e9a572cfa2712"],"state_sha256":"be5db1e91e435f2bb98d300190817ca5c9818796f21bfaea4d860210b7978338"}