{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:L736ZIMSLPSXCXPVLGIINZPZCO","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":"6f0f8bd7ae7c7cca19e754bd620198062d8437c82348cc8ae7e554d04f966ab5","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-07-03T10:36:47Z","title_canon_sha256":"5691cac1abffd54fab6d68a329b23847ac3a36086f1c53f58e26b1919bf71c82"},"schema_version":"1.0","source":{"id":"0907.0585","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.0585","created_at":"2026-05-18T02:13:05Z"},{"alias_kind":"arxiv_version","alias_value":"0907.0585v3","created_at":"2026-05-18T02:13:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.0585","created_at":"2026-05-18T02:13:05Z"},{"alias_kind":"pith_short_12","alias_value":"L736ZIMSLPSX","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"L736ZIMSLPSXCXPV","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"L736ZIMS","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:cd60ad9fb3dc570dde78638dc37f13af6e056acbe73b55b9c45acccfb20a8832","target":"graph","created_at":"2026-05-18T02:13:05Z","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 study subexponential instability to characterize a dynamical instability of weak chaos. We show that a dynamical system with subexponential instability has an infinite invariant measure, and then we present the generalized Lyapunov exponent to characterize subexponential instability.","authors_text":"Takuma Akimoto, Yoji Aizawa","cross_cats":["nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-07-03T10:36:47Z","title":"Subexponential instability implies infinite invariant measure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0585","kind":"arxiv","version":3},"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":"sha256:277a9e1823100d154ad838e66e0e400c1301e347625824d9f1535f52a2fd9e7e","target":"record","created_at":"2026-05-18T02:13:05Z","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":"6f0f8bd7ae7c7cca19e754bd620198062d8437c82348cc8ae7e554d04f966ab5","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-07-03T10:36:47Z","title_canon_sha256":"5691cac1abffd54fab6d68a329b23847ac3a36086f1c53f58e26b1919bf71c82"},"schema_version":"1.0","source":{"id":"0907.0585","kind":"arxiv","version":3}},"canonical_sha256":"5ff7eca1925be5715df5599086e5f913b7d07fe82b96ca71d6dee57c986d0ae0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ff7eca1925be5715df5599086e5f913b7d07fe82b96ca71d6dee57c986d0ae0","first_computed_at":"2026-05-18T02:13:05.512004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:13:05.512004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P89aqVYo+fisbFXgMnUdsbVARs9NOGlren+rOv82lHQWI6hlhJY3snGdgL6DhmsqTactBsqnD2cGfYFhIP4qDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:13:05.512728Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.0585","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:277a9e1823100d154ad838e66e0e400c1301e347625824d9f1535f52a2fd9e7e","sha256:cd60ad9fb3dc570dde78638dc37f13af6e056acbe73b55b9c45acccfb20a8832"],"state_sha256":"4ea1824ca4ca68e01dcdc6ddc9741f984b290e3947f86508c658d257a4629d4a"}