{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:P35J3TC7OUWSTWFCRJPDEAW5YL","short_pith_number":"pith:P35J3TC7","canonical_record":{"source":{"id":"0711.3818","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2007-11-24T05:08:35Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"ba7c89331c1486f4ee41ebe47def22efd2d99b4237525c7ce30c6f74684441a3","abstract_canon_sha256":"5edd1b17982541f061164696dd1bdc970e195d067eb178a559e721e4c707e8ed"},"schema_version":"1.0"},"canonical_sha256":"7efa9dcc5f752d29d8a28a5e3202ddc2dbf50a6202feac0a9292ad63d0c5be95","source":{"kind":"arxiv","id":"0711.3818","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0711.3818","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"arxiv_version","alias_value":"0711.3818v1","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.3818","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"pith_short_12","alias_value":"P35J3TC7OUWS","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"P35J3TC7OUWSTWFC","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"P35J3TC7","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:P35J3TC7OUWSTWFCRJPDEAW5YL","target":"record","payload":{"canonical_record":{"source":{"id":"0711.3818","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2007-11-24T05:08:35Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"ba7c89331c1486f4ee41ebe47def22efd2d99b4237525c7ce30c6f74684441a3","abstract_canon_sha256":"5edd1b17982541f061164696dd1bdc970e195d067eb178a559e721e4c707e8ed"},"schema_version":"1.0"},"canonical_sha256":"7efa9dcc5f752d29d8a28a5e3202ddc2dbf50a6202feac0a9292ad63d0c5be95","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:57.545229Z","signature_b64":"BvHtLUNBeomukPVVbCoSKw0wXnxT3aEO5kQnETcMFDjWP+JtIwfo01Bm9SXHjqUuKYdqLDkFxRgk7zCqhjkyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7efa9dcc5f752d29d8a28a5e3202ddc2dbf50a6202feac0a9292ad63d0c5be95","last_reissued_at":"2026-05-18T04:10:57.544595Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:57.544595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0711.3818","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":"2026-05-18T04:10:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"khmPaaayxX25M17q5L8M6oxLL7Hn7dU9/aU3s48D7N8/iKOBpk6dimLkZr+gxVdO7aRczfiIWs1bjCvF0AvdDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:30:41.990205Z"},"content_sha256":"4631edcb2c35ab50f9a6b8cb6f24474ec8d34546edf20c4c4e75b7c60ea02bde","schema_version":"1.0","event_id":"sha256:4631edcb2c35ab50f9a6b8cb6f24474ec8d34546edf20c4c4e75b7c60ea02bde"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:P35J3TC7OUWSTWFCRJPDEAW5YL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quenched CLT for random toral automorphism","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"Arvind Ayyer, Carlangelo Liverani, Mikko Stenlund","submitted_at":"2007-11-24T05:08:35Z","abstract_excerpt":"We establish a quenched Central Limit Theorem (CLT) for a smooth observable of random sequences of iterated linear hyperbolic maps on the torus. To this end we also obtain an annealed CLT for the same system. We show that, almost surely, the variance of the quenched system is the same as for the annealed system. Our technique is the study of the transfer operator on an anisotropic Banach space specifically tailored to use the cone condition satisfied by the maps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.3818","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":"2026-05-18T04:10:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7o5vXIsxWpjZR0Pkkw7Tr3zEdMmZem0g/srdOieyQ+72N5zziPRogXnXT9emheCwcFiO0Nc13uDsoyauA8auBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:30:41.990560Z"},"content_sha256":"af85aeb76a7893cfc93c763625f45dad379d2076cb6a6c26680e6612c12b7786","schema_version":"1.0","event_id":"sha256:af85aeb76a7893cfc93c763625f45dad379d2076cb6a6c26680e6612c12b7786"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P35J3TC7OUWSTWFCRJPDEAW5YL/bundle.json","state_url":"https://pith.science/pith/P35J3TC7OUWSTWFCRJPDEAW5YL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P35J3TC7OUWSTWFCRJPDEAW5YL/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":"2026-06-01T11:30:41Z","links":{"resolver":"https://pith.science/pith/P35J3TC7OUWSTWFCRJPDEAW5YL","bundle":"https://pith.science/pith/P35J3TC7OUWSTWFCRJPDEAW5YL/bundle.json","state":"https://pith.science/pith/P35J3TC7OUWSTWFCRJPDEAW5YL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P35J3TC7OUWSTWFCRJPDEAW5YL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:P35J3TC7OUWSTWFCRJPDEAW5YL","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":"5edd1b17982541f061164696dd1bdc970e195d067eb178a559e721e4c707e8ed","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"math.DS","submitted_at":"2007-11-24T05:08:35Z","title_canon_sha256":"ba7c89331c1486f4ee41ebe47def22efd2d99b4237525c7ce30c6f74684441a3"},"schema_version":"1.0","source":{"id":"0711.3818","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0711.3818","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"arxiv_version","alias_value":"0711.3818v1","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.3818","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"pith_short_12","alias_value":"P35J3TC7OUWS","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"P35J3TC7OUWSTWFC","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"P35J3TC7","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:af85aeb76a7893cfc93c763625f45dad379d2076cb6a6c26680e6612c12b7786","target":"graph","created_at":"2026-05-18T04:10:57Z","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 establish a quenched Central Limit Theorem (CLT) for a smooth observable of random sequences of iterated linear hyperbolic maps on the torus. To this end we also obtain an annealed CLT for the same system. We show that, almost surely, the variance of the quenched system is the same as for the annealed system. Our technique is the study of the transfer operator on an anisotropic Banach space specifically tailored to use the cone condition satisfied by the maps.","authors_text":"Arvind Ayyer, Carlangelo Liverani, Mikko Stenlund","cross_cats":["math.PR"],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"2007-11-24T05:08:35Z","title":"Quenched CLT for random toral automorphism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.3818","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":"sha256:4631edcb2c35ab50f9a6b8cb6f24474ec8d34546edf20c4c4e75b7c60ea02bde","target":"record","created_at":"2026-05-18T04:10:57Z","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":"5edd1b17982541f061164696dd1bdc970e195d067eb178a559e721e4c707e8ed","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"math.DS","submitted_at":"2007-11-24T05:08:35Z","title_canon_sha256":"ba7c89331c1486f4ee41ebe47def22efd2d99b4237525c7ce30c6f74684441a3"},"schema_version":"1.0","source":{"id":"0711.3818","kind":"arxiv","version":1}},"canonical_sha256":"7efa9dcc5f752d29d8a28a5e3202ddc2dbf50a6202feac0a9292ad63d0c5be95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7efa9dcc5f752d29d8a28a5e3202ddc2dbf50a6202feac0a9292ad63d0c5be95","first_computed_at":"2026-05-18T04:10:57.544595Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:57.544595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BvHtLUNBeomukPVVbCoSKw0wXnxT3aEO5kQnETcMFDjWP+JtIwfo01Bm9SXHjqUuKYdqLDkFxRgk7zCqhjkyBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:57.545229Z","signed_message":"canonical_sha256_bytes"},"source_id":"0711.3818","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4631edcb2c35ab50f9a6b8cb6f24474ec8d34546edf20c4c4e75b7c60ea02bde","sha256:af85aeb76a7893cfc93c763625f45dad379d2076cb6a6c26680e6612c12b7786"],"state_sha256":"81b3eb7546b0772c6c3ee1e39b1c3567826dabf481a9b367ec6188b179ccb394"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/HkfX6V6VrokiNz6zVvX3RrlQFH6byWVr8BJS5FZeMlJydPOcEU+nMvhwDEguuWr/Kkk2bQU8yz34cPpapyiCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T11:30:41.992429Z","bundle_sha256":"15deee94381d2521d74a78ef532b480f0b59e5241010f14dc3626506b82a35ec"}}