{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RM5LA7AW5Y2NGFNFIOBFH4BGFF","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":"28e9c8e824ea9af83cebcd161f28a13a38d520ac683e13895b9c8a5134faea91","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-08-16T22:47:21Z","title_canon_sha256":"e99a792b2a22da270243c841352fb0c34eb0afca7e976bb8277723906317cd24"},"schema_version":"1.0","source":{"id":"1308.3734","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.3734","created_at":"2026-05-18T03:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"1308.3734v1","created_at":"2026-05-18T03:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3734","created_at":"2026-05-18T03:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"RM5LA7AW5Y2N","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RM5LA7AW5Y2NGFNF","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RM5LA7AW","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:c7b2889c8803cf646022bc913d72cf3f85d7a411c3a8efa1ccd48a63023f56fd","target":"graph","created_at":"2026-05-18T03:14:29Z","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":"Weakly chaotic maps with unstable fixed points are investigated in the regime where the invariant density is non-normalizable. We propose that the infinite invariant density of these maps can be estimated using as the long time limit of t^(1-alpha) rho(x, t), in agreement with earlier work of Thaler. Here rho(x, t) is the normalizable density of particles. This definition uniquely determines the infinite density and is a valuable tool for numerical estimations. We use this density to estimate the subexponential separation lambda_alpha of nearby trajectories. For a particular map introduced by ","authors_text":"Eli Barkai, Nickolay Korabel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-08-16T22:47:21Z","title":"Numerical estimate of infinite invariant densities: application to Pesin-type identity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3734","kind":"arxiv","version":1},"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:e35b7304e6a3fd067d5314bd8db8adefffcf84b6ca54584035bd10b5c4cf0582","target":"record","created_at":"2026-05-18T03:14:29Z","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":"28e9c8e824ea9af83cebcd161f28a13a38d520ac683e13895b9c8a5134faea91","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-08-16T22:47:21Z","title_canon_sha256":"e99a792b2a22da270243c841352fb0c34eb0afca7e976bb8277723906317cd24"},"schema_version":"1.0","source":{"id":"1308.3734","kind":"arxiv","version":1}},"canonical_sha256":"8b3ab07c16ee34d315a5438253f026294de91b2c8fe0ea99577a6cbdc6946ad4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b3ab07c16ee34d315a5438253f026294de91b2c8fe0ea99577a6cbdc6946ad4","first_computed_at":"2026-05-18T03:14:29.139679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:29.139679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LUGwpcH9IrRoAV7nd1aw3lMCv3vSEv0xIJN0aA86b5Exiqb3l0UapK9e1E4o1iSpUjZoDRnJgsoISh24PVTTDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:29.140739Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.3734","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e35b7304e6a3fd067d5314bd8db8adefffcf84b6ca54584035bd10b5c4cf0582","sha256:c7b2889c8803cf646022bc913d72cf3f85d7a411c3a8efa1ccd48a63023f56fd"],"state_sha256":"4cb80a8d095770d0589ef13305ed8af80cb5462df337f091b49ec6e68311bcf8"}