{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BU2BOE3B466Y5MXX6NKVDDZQQA","short_pith_number":"pith:BU2BOE3B","canonical_record":{"source":{"id":"1306.1479","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-06-06T17:27:57Z","cross_cats_sorted":[],"title_canon_sha256":"980bc347f371fd77b0edb7d08346404f0cb7941fee8249c91e499ddc3c6e9904","abstract_canon_sha256":"a759e2039dfa22553090cd70c9579ae182871341b96694acc4f0b562dbe7ce94"},"schema_version":"1.0"},"canonical_sha256":"0d34171361e7bd8eb2f7f355518f3080292ce33f205555b90a4510c1ced9531f","source":{"kind":"arxiv","id":"1306.1479","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1479","created_at":"2026-05-18T02:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1479v3","created_at":"2026-05-18T02:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1479","created_at":"2026-05-18T02:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"BU2BOE3B466Y","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BU2BOE3B466Y5MXX","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BU2BOE3B","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BU2BOE3B466Y5MXX6NKVDDZQQA","target":"record","payload":{"canonical_record":{"source":{"id":"1306.1479","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-06-06T17:27:57Z","cross_cats_sorted":[],"title_canon_sha256":"980bc347f371fd77b0edb7d08346404f0cb7941fee8249c91e499ddc3c6e9904","abstract_canon_sha256":"a759e2039dfa22553090cd70c9579ae182871341b96694acc4f0b562dbe7ce94"},"schema_version":"1.0"},"canonical_sha256":"0d34171361e7bd8eb2f7f355518f3080292ce33f205555b90a4510c1ced9531f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:46.255433Z","signature_b64":"FxpSX8Dtjwt2nWW/eOZd+kUtnTYEjnZ8EcC0keFhPnPKeqCkX9F3IR0kRiGGOQ7ocTUB9RePE7aII6rab5gGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d34171361e7bd8eb2f7f355518f3080292ce33f205555b90a4510c1ced9531f","last_reissued_at":"2026-05-18T02:38:46.254918Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:46.254918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.1479","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H56xz7gzAlj5K4uRKeznLMTL92Vzgq1Z3qLdr+rGjwUwWYrJZwq4JUHx0gpo7OjpPwZKwUNTmTZmKPr9hmPvAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:42:12.375515Z"},"content_sha256":"f9e1f555dda2b5f9d077826354acf132acfcc02e74b17be30e8a93e0d766ce91","schema_version":"1.0","event_id":"sha256:f9e1f555dda2b5f9d077826354acf132acfcc02e74b17be30e8a93e0d766ce91"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BU2BOE3B466Y5MXX6NKVDDZQQA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Adapted random perturbations for non-uniformly expanding maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Maria Jose Pacifico, Mariana Pinheiro, Vitor Araujo","submitted_at":"2013-06-06T17:27:57Z","abstract_excerpt":"We obtain stochastic stability of C2 non-uniformly expanding one-dimensional endomorphisms, requiring only that the first hyperbolic time map be L^{p}-integrable for p>3. We show that, under this condition (which depends only on the unperturbed dynamics), we can construct a random perturbation that preserves the original hyperbolic times of the unperturbed map and, therefore, to obtain non-uniform expansion for random orbits. This ensures that the first hyperbolic time map is uniformly integrable for all small enough noise levels, which is known to imply stochastic stability. The method enable"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1479","kind":"arxiv","version":3},"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":"2026-05-18T02:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4e5S3PX2aeFsyko+1aWbXe5shXkEROra9CkoCg0Q1N2ybvBAqTFNJ0sq1SfqD9Ryk4sVPJhHnAEYcpxzYstACw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:42:12.376240Z"},"content_sha256":"a041241459b07488a5137d7f9b092a517b2b3e805ed701b2157e1e632aa0578b","schema_version":"1.0","event_id":"sha256:a041241459b07488a5137d7f9b092a517b2b3e805ed701b2157e1e632aa0578b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BU2BOE3B466Y5MXX6NKVDDZQQA/bundle.json","state_url":"https://pith.science/pith/BU2BOE3B466Y5MXX6NKVDDZQQA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BU2BOE3B466Y5MXX6NKVDDZQQA/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":"2026-05-31T02:42:12Z","links":{"resolver":"https://pith.science/pith/BU2BOE3B466Y5MXX6NKVDDZQQA","bundle":"https://pith.science/pith/BU2BOE3B466Y5MXX6NKVDDZQQA/bundle.json","state":"https://pith.science/pith/BU2BOE3B466Y5MXX6NKVDDZQQA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BU2BOE3B466Y5MXX6NKVDDZQQA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BU2BOE3B466Y5MXX6NKVDDZQQA","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":"a759e2039dfa22553090cd70c9579ae182871341b96694acc4f0b562dbe7ce94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-06-06T17:27:57Z","title_canon_sha256":"980bc347f371fd77b0edb7d08346404f0cb7941fee8249c91e499ddc3c6e9904"},"schema_version":"1.0","source":{"id":"1306.1479","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1479","created_at":"2026-05-18T02:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1479v3","created_at":"2026-05-18T02:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1479","created_at":"2026-05-18T02:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"BU2BOE3B466Y","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BU2BOE3B466Y5MXX","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BU2BOE3B","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:a041241459b07488a5137d7f9b092a517b2b3e805ed701b2157e1e632aa0578b","target":"graph","created_at":"2026-05-18T02:38:46Z","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 obtain stochastic stability of C2 non-uniformly expanding one-dimensional endomorphisms, requiring only that the first hyperbolic time map be L^{p}-integrable for p>3. We show that, under this condition (which depends only on the unperturbed dynamics), we can construct a random perturbation that preserves the original hyperbolic times of the unperturbed map and, therefore, to obtain non-uniform expansion for random orbits. This ensures that the first hyperbolic time map is uniformly integrable for all small enough noise levels, which is known to imply stochastic stability. The method enable","authors_text":"Maria Jose Pacifico, Mariana Pinheiro, Vitor Araujo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-06-06T17:27:57Z","title":"Adapted random perturbations for non-uniformly expanding maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1479","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:f9e1f555dda2b5f9d077826354acf132acfcc02e74b17be30e8a93e0d766ce91","target":"record","created_at":"2026-05-18T02:38:46Z","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":"a759e2039dfa22553090cd70c9579ae182871341b96694acc4f0b562dbe7ce94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-06-06T17:27:57Z","title_canon_sha256":"980bc347f371fd77b0edb7d08346404f0cb7941fee8249c91e499ddc3c6e9904"},"schema_version":"1.0","source":{"id":"1306.1479","kind":"arxiv","version":3}},"canonical_sha256":"0d34171361e7bd8eb2f7f355518f3080292ce33f205555b90a4510c1ced9531f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d34171361e7bd8eb2f7f355518f3080292ce33f205555b90a4510c1ced9531f","first_computed_at":"2026-05-18T02:38:46.254918Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:46.254918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FxpSX8Dtjwt2nWW/eOZd+kUtnTYEjnZ8EcC0keFhPnPKeqCkX9F3IR0kRiGGOQ7ocTUB9RePE7aII6rab5gGAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:46.255433Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.1479","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9e1f555dda2b5f9d077826354acf132acfcc02e74b17be30e8a93e0d766ce91","sha256:a041241459b07488a5137d7f9b092a517b2b3e805ed701b2157e1e632aa0578b"],"state_sha256":"b9d6c57d13b7eefe0aeac9ad0b37e04746902d1f221cdf63b1390f7d6b166be3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nTXt3reZgucbyu8CrOPlwE803egpo762QwLlmhPXI+jYrXf/YvtvA0A/ratiN8pdGBD+QBzXZIgay0hZLadwAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:42:12.380925Z","bundle_sha256":"346023acf92648c6f545a6f10ea808a4ede6c76cddfd099c8e05448a19a5c6c5"}}