{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:74TUKATQ5OT3WGAFBGVHG66MTR","short_pith_number":"pith:74TUKATQ","canonical_record":{"source":{"id":"1811.09094","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-22T10:37:59Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"a560b0e43814d7ad3aa5858fe9426ad426b820995dba2d02041be9175bf16d73","abstract_canon_sha256":"19f643b3bd6b46025cf82219a5ce5c567ccff20eaa208b78ef802fc06afd7bd7"},"schema_version":"1.0"},"canonical_sha256":"ff27450270eba7bb180509aa737bcc9c7f88a87946e9c6fe50610b64ae381784","source":{"kind":"arxiv","id":"1811.09094","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09094","created_at":"2026-05-18T00:00:07Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09094v1","created_at":"2026-05-18T00:00:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09094","created_at":"2026-05-18T00:00:07Z"},{"alias_kind":"pith_short_12","alias_value":"74TUKATQ5OT3","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"74TUKATQ5OT3WGAF","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"74TUKATQ","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:74TUKATQ5OT3WGAFBGVHG66MTR","target":"record","payload":{"canonical_record":{"source":{"id":"1811.09094","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-22T10:37:59Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"a560b0e43814d7ad3aa5858fe9426ad426b820995dba2d02041be9175bf16d73","abstract_canon_sha256":"19f643b3bd6b46025cf82219a5ce5c567ccff20eaa208b78ef802fc06afd7bd7"},"schema_version":"1.0"},"canonical_sha256":"ff27450270eba7bb180509aa737bcc9c7f88a87946e9c6fe50610b64ae381784","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:07.102657Z","signature_b64":"e0DOKYufrEIpWBC+z+2nVM7Gh/kFQujEWnYYZl5rad6RZp9ekz+zFdvNkXwUISv+KaOWK9V0+yNMCmk3RZ9TCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff27450270eba7bb180509aa737bcc9c7f88a87946e9c6fe50610b64ae381784","last_reissued_at":"2026-05-18T00:00:07.102104Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:07.102104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.09094","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:00:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZUf/SF7eqaDOd27BnDmoGcKiNRwFpC9UUKPtlC3Zaln1JjMsozFepX5knm4fQdbNKRSvRvVI0cTZ4wKNFa2/Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:48:15.363148Z"},"content_sha256":"e8427db329e71715312766dd17626d296c717a6fe2d086d9fb16e92b38379b06","schema_version":"1.0","event_id":"sha256:e8427db329e71715312766dd17626d296c717a6fe2d086d9fb16e92b38379b06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:74TUKATQ5OT3WGAFBGVHG66MTR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rates in almost sure invariance principle for quickly mixing dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"A Korepanov, C Cuny (LMBA), Florence Merlev\\`ede (LAMA), J Dedecker (MAP5 - UMR 8145)","submitted_at":"2018-11-22T10:37:59Z","abstract_excerpt":"For a large class of quickly mixing dynamical systems, we prove that the error in the almost sure approximation with a Brownian motion is of order O((log n)^a) with a $\\ge$ 2. Specifically, we consider nonuniformly expanding maps with exponential and stretched exponential decay of correlations, with one-dimensional H{\\\"o}lder continuous observables."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09094","kind":"arxiv","version":1},"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":"2026-05-18T00:00:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wkiYffVruXMp/k86wsXuD7zXAIJmrOzrqs4pNwbOnOa7Wg9NtEAKvSqcIN+0/if1dDpCYfjaMRB2OvNp9hexDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:48:15.363520Z"},"content_sha256":"c0353a1670c91933b7a822622eca24043aa8dbddfe7cdb5ed3c5ab3c8c33bbdb","schema_version":"1.0","event_id":"sha256:c0353a1670c91933b7a822622eca24043aa8dbddfe7cdb5ed3c5ab3c8c33bbdb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/74TUKATQ5OT3WGAFBGVHG66MTR/bundle.json","state_url":"https://pith.science/pith/74TUKATQ5OT3WGAFBGVHG66MTR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/74TUKATQ5OT3WGAFBGVHG66MTR/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":"2026-06-03T06:48:15Z","links":{"resolver":"https://pith.science/pith/74TUKATQ5OT3WGAFBGVHG66MTR","bundle":"https://pith.science/pith/74TUKATQ5OT3WGAFBGVHG66MTR/bundle.json","state":"https://pith.science/pith/74TUKATQ5OT3WGAFBGVHG66MTR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/74TUKATQ5OT3WGAFBGVHG66MTR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:74TUKATQ5OT3WGAFBGVHG66MTR","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":"19f643b3bd6b46025cf82219a5ce5c567ccff20eaa208b78ef802fc06afd7bd7","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-22T10:37:59Z","title_canon_sha256":"a560b0e43814d7ad3aa5858fe9426ad426b820995dba2d02041be9175bf16d73"},"schema_version":"1.0","source":{"id":"1811.09094","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09094","created_at":"2026-05-18T00:00:07Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09094v1","created_at":"2026-05-18T00:00:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09094","created_at":"2026-05-18T00:00:07Z"},{"alias_kind":"pith_short_12","alias_value":"74TUKATQ5OT3","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"74TUKATQ5OT3WGAF","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"74TUKATQ","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:c0353a1670c91933b7a822622eca24043aa8dbddfe7cdb5ed3c5ab3c8c33bbdb","target":"graph","created_at":"2026-05-18T00:00:07Z","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":"For a large class of quickly mixing dynamical systems, we prove that the error in the almost sure approximation with a Brownian motion is of order O((log n)^a) with a $\\ge$ 2. Specifically, we consider nonuniformly expanding maps with exponential and stretched exponential decay of correlations, with one-dimensional H{\\\"o}lder continuous observables.","authors_text":"A Korepanov, C Cuny (LMBA), Florence Merlev\\`ede (LAMA), J Dedecker (MAP5 - UMR 8145)","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-22T10:37:59Z","title":"Rates in almost sure invariance principle for quickly mixing dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09094","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:e8427db329e71715312766dd17626d296c717a6fe2d086d9fb16e92b38379b06","target":"record","created_at":"2026-05-18T00:00:07Z","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":"19f643b3bd6b46025cf82219a5ce5c567ccff20eaa208b78ef802fc06afd7bd7","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-22T10:37:59Z","title_canon_sha256":"a560b0e43814d7ad3aa5858fe9426ad426b820995dba2d02041be9175bf16d73"},"schema_version":"1.0","source":{"id":"1811.09094","kind":"arxiv","version":1}},"canonical_sha256":"ff27450270eba7bb180509aa737bcc9c7f88a87946e9c6fe50610b64ae381784","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff27450270eba7bb180509aa737bcc9c7f88a87946e9c6fe50610b64ae381784","first_computed_at":"2026-05-18T00:00:07.102104Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:07.102104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e0DOKYufrEIpWBC+z+2nVM7Gh/kFQujEWnYYZl5rad6RZp9ekz+zFdvNkXwUISv+KaOWK9V0+yNMCmk3RZ9TCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:07.102657Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.09094","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8427db329e71715312766dd17626d296c717a6fe2d086d9fb16e92b38379b06","sha256:c0353a1670c91933b7a822622eca24043aa8dbddfe7cdb5ed3c5ab3c8c33bbdb"],"state_sha256":"ef988bf080afc9024bb84537557a5700e785179438100effa8249141c4d37153"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V6kb6ec0P4dnUMQzAWfM+fMNJDmhMePkb6iJiEUMA32H2jmY5erCRQf7cgRrVFkMTwwkpE2P6UkA7L0v0jcGDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T06:48:15.365486Z","bundle_sha256":"3e2fa58af2927797634b16df6b5c111955a4185470b2a8de86bcc25163831d24"}}