{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:NKCO3P6OGMBFIH52EXA7AANVQN","short_pith_number":"pith:NKCO3P6O","canonical_record":{"source":{"id":"1108.5948","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-30T12:53:44Z","cross_cats_sorted":[],"title_canon_sha256":"d71694c4412d8ff60a47c25fc2e7bca7bf1e6595f4050e426222bbc7898e6cf8","abstract_canon_sha256":"20e129a00d812072d2ade9ea8c7c8f604151d8ff550da181e4542adc2b46868c"},"schema_version":"1.0"},"canonical_sha256":"6a84edbfce3302541fba25c1f001b5836f81c7b88c4b8b1f486d0f5e4575d6a8","source":{"kind":"arxiv","id":"1108.5948","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5948","created_at":"2026-05-18T02:00:44Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5948v3","created_at":"2026-05-18T02:00:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5948","created_at":"2026-05-18T02:00:44Z"},{"alias_kind":"pith_short_12","alias_value":"NKCO3P6OGMBF","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NKCO3P6OGMBFIH52","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NKCO3P6O","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:NKCO3P6OGMBFIH52EXA7AANVQN","target":"record","payload":{"canonical_record":{"source":{"id":"1108.5948","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-30T12:53:44Z","cross_cats_sorted":[],"title_canon_sha256":"d71694c4412d8ff60a47c25fc2e7bca7bf1e6595f4050e426222bbc7898e6cf8","abstract_canon_sha256":"20e129a00d812072d2ade9ea8c7c8f604151d8ff550da181e4542adc2b46868c"},"schema_version":"1.0"},"canonical_sha256":"6a84edbfce3302541fba25c1f001b5836f81c7b88c4b8b1f486d0f5e4575d6a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:44.677968Z","signature_b64":"89NFthzYzWBCq2GIUhdH/ryC9tTbwARitLVx2u8SpIs72t/2UCKvE0W3f3LXEA7y5R4Fa7mK6BvjQKyd9t+yDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a84edbfce3302541fba25c1f001b5836f81c7b88c4b8b1f486d0f5e4575d6a8","last_reissued_at":"2026-05-18T02:00:44.677342Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:44.677342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.5948","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":"2026-05-18T02:00:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rWj+G10SgQbWkfA57Z2cNm/KpCvl3H2945nOVG4cNYlZkBt7Yke2+IWdOkdfv/oqbK51Z095lBsxT3nJ6NUnDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T14:45:58.550938Z"},"content_sha256":"363576ac8e03e22ba34e0367e9ff889223ecf7b5d59ddfee66b93cddd5df1bce","schema_version":"1.0","event_id":"sha256:363576ac8e03e22ba34e0367e9ff889223ecf7b5d59ddfee66b93cddd5df1bce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:NKCO3P6OGMBFIH52EXA7AANVQN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistical Properties and Decay of Correlations for Interval Maps with Critical Points and Singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ian Melbourne, Stefano Luzzatto","submitted_at":"2011-08-30T12:53:44Z","abstract_excerpt":"We consider a class of piecewise smooth one-dimensional maps with critical points and singularities (possibly with infinite derivative). Under mild summability conditions on the growth of the derivative on critical orbits, we prove the central limit theorem and a vector-valued almost sure invariance principle. We also obtain results on decay of correlations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5948","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":"2026-05-18T02:00:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"is5d+jahsaqkPpVvrw9EHt2rh+B3j4UmTTx/V1mq8spZWM7zp3hYJlm4n//m4j1ZTJvyBys4jQPZZZbEC80EBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T14:45:58.551505Z"},"content_sha256":"58d2c877dc8cc08b01db4f4b6bbf8d9e798026ee29adb7872881b609eb61f278","schema_version":"1.0","event_id":"sha256:58d2c877dc8cc08b01db4f4b6bbf8d9e798026ee29adb7872881b609eb61f278"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NKCO3P6OGMBFIH52EXA7AANVQN/bundle.json","state_url":"https://pith.science/pith/NKCO3P6OGMBFIH52EXA7AANVQN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NKCO3P6OGMBFIH52EXA7AANVQN/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":"2026-08-03T14:45:58Z","links":{"resolver":"https://pith.science/pith/NKCO3P6OGMBFIH52EXA7AANVQN","bundle":"https://pith.science/pith/NKCO3P6OGMBFIH52EXA7AANVQN/bundle.json","state":"https://pith.science/pith/NKCO3P6OGMBFIH52EXA7AANVQN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NKCO3P6OGMBFIH52EXA7AANVQN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NKCO3P6OGMBFIH52EXA7AANVQN","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":"20e129a00d812072d2ade9ea8c7c8f604151d8ff550da181e4542adc2b46868c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-30T12:53:44Z","title_canon_sha256":"d71694c4412d8ff60a47c25fc2e7bca7bf1e6595f4050e426222bbc7898e6cf8"},"schema_version":"1.0","source":{"id":"1108.5948","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5948","created_at":"2026-05-18T02:00:44Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5948v3","created_at":"2026-05-18T02:00:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5948","created_at":"2026-05-18T02:00:44Z"},{"alias_kind":"pith_short_12","alias_value":"NKCO3P6OGMBF","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NKCO3P6OGMBFIH52","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NKCO3P6O","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:58d2c877dc8cc08b01db4f4b6bbf8d9e798026ee29adb7872881b609eb61f278","target":"graph","created_at":"2026-05-18T02:00:44Z","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 consider a class of piecewise smooth one-dimensional maps with critical points and singularities (possibly with infinite derivative). Under mild summability conditions on the growth of the derivative on critical orbits, we prove the central limit theorem and a vector-valued almost sure invariance principle. We also obtain results on decay of correlations.","authors_text":"Ian Melbourne, Stefano Luzzatto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-30T12:53:44Z","title":"Statistical Properties and Decay of Correlations for Interval Maps with Critical Points and Singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5948","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":"sha256:363576ac8e03e22ba34e0367e9ff889223ecf7b5d59ddfee66b93cddd5df1bce","target":"record","created_at":"2026-05-18T02:00:44Z","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":"20e129a00d812072d2ade9ea8c7c8f604151d8ff550da181e4542adc2b46868c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-30T12:53:44Z","title_canon_sha256":"d71694c4412d8ff60a47c25fc2e7bca7bf1e6595f4050e426222bbc7898e6cf8"},"schema_version":"1.0","source":{"id":"1108.5948","kind":"arxiv","version":3}},"canonical_sha256":"6a84edbfce3302541fba25c1f001b5836f81c7b88c4b8b1f486d0f5e4575d6a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a84edbfce3302541fba25c1f001b5836f81c7b88c4b8b1f486d0f5e4575d6a8","first_computed_at":"2026-05-18T02:00:44.677342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:44.677342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"89NFthzYzWBCq2GIUhdH/ryC9tTbwARitLVx2u8SpIs72t/2UCKvE0W3f3LXEA7y5R4Fa7mK6BvjQKyd9t+yDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:44.677968Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5948","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:363576ac8e03e22ba34e0367e9ff889223ecf7b5d59ddfee66b93cddd5df1bce","sha256:58d2c877dc8cc08b01db4f4b6bbf8d9e798026ee29adb7872881b609eb61f278"],"state_sha256":"cb2eb00a1787a2c941f4a139957a64ec3b4b851290497a967390383b2e08d989"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RwhcXBTrMxeM+Nkw/PathSfG+D1rFUmr+yq2JRbBd92pZl74P17SsbqjIs91eN8Jl0vYR/TOFrXHOs102bTfDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T14:45:58.555297Z","bundle_sha256":"d4baa953652d9191cc6207014a050e632877ccbc69c16fecf35ac8a7bd43d337"}}