{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WXADHYF6VAZKLMR7UQSKN6VD3S","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":"9cca61c67fb8b5295664073c9546a09dedc0f5eef2e87dae2fed27d073f8c467","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-03-10T21:05:07Z","title_canon_sha256":"05207d36ebadf963df6fe47f4e00227569e67bd95c8963d683e1c89adc5ef57b"},"schema_version":"1.0","source":{"id":"1303.2375","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.2375","created_at":"2026-05-18T00:32:15Z"},{"alias_kind":"arxiv_version","alias_value":"1303.2375v1","created_at":"2026-05-18T00:32:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.2375","created_at":"2026-05-18T00:32:15Z"},{"alias_kind":"pith_short_12","alias_value":"WXADHYF6VAZK","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WXADHYF6VAZKLMR7","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WXADHYF6","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:4690234bd2a342937c48ec0fe8cce69cfa40cc72b40c13c50afd26e6a7793904","target":"graph","created_at":"2026-05-18T00:32:15Z","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 several new versions of the Hadamard-Perron Theorem, which relates infinitesimal dynamics to local dynamics for a sequence of local diffeomorphisms, and in particular establishes the existence of local stable and unstable manifolds. Our results imply the classical Hadamard-Perron Theorem in both its uniform and non-uniform versions, but also apply much more generally. We introduce a notion of \"effective hyperbolicity\" and show that if the rate of effective hyperbolicity is asymptotically positive, then the local manifolds are well-behaved with positive asymptotic frequency. By applyin","authors_text":"Vaughn Climenhaga, Yakov Pesin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-03-10T21:05:07Z","title":"Hadamard-Perron theorems and effective hyperbolicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2375","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":"sha256:002fec5ef6a26088e3e996607015bc8765ceb3e8a92e4fd24b572e6ddd5d739a","target":"record","created_at":"2026-05-18T00:32:15Z","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":"9cca61c67fb8b5295664073c9546a09dedc0f5eef2e87dae2fed27d073f8c467","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-03-10T21:05:07Z","title_canon_sha256":"05207d36ebadf963df6fe47f4e00227569e67bd95c8963d683e1c89adc5ef57b"},"schema_version":"1.0","source":{"id":"1303.2375","kind":"arxiv","version":1}},"canonical_sha256":"b5c033e0bea832a5b23fa424a6faa3dcae928f280548a41184566b6d11c29140","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5c033e0bea832a5b23fa424a6faa3dcae928f280548a41184566b6d11c29140","first_computed_at":"2026-05-18T00:32:15.579125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:15.579125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ERTDwmawiRv+8OXf+CEvAPt/FvhNYQZ10F9NjIpQqvlvKaw4uUWjzgA06PWHn7hnuFqsMKXsYn2ATEikhH0uAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:15.580409Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.2375","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:002fec5ef6a26088e3e996607015bc8765ceb3e8a92e4fd24b572e6ddd5d739a","sha256:4690234bd2a342937c48ec0fe8cce69cfa40cc72b40c13c50afd26e6a7793904"],"state_sha256":"53a278445d9f5062a7c84c62f08979773c8af29bcc8cef502c0e8b7f350f6767"}