{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:JIYJRDVU3CFT5XIUV7YUGNIWD4","short_pith_number":"pith:JIYJRDVU","canonical_record":{"source":{"id":"1904.02227","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-04-03T20:11:30Z","cross_cats_sorted":[],"title_canon_sha256":"222285ebfbb4477013355de1e845fff5d6fc241d00b609986bbf4961c07a4412","abstract_canon_sha256":"a4a3072869d697c62b568061c7e530b60ca32361513d139127432249fcfcc557"},"schema_version":"1.0"},"canonical_sha256":"4a30988eb4d88b3edd14aff14335161f1f36b6bd6d88788ce21e088286dadfc8","source":{"kind":"arxiv","id":"1904.02227","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02227","created_at":"2026-05-17T23:49:24Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02227v1","created_at":"2026-05-17T23:49:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02227","created_at":"2026-05-17T23:49:24Z"},{"alias_kind":"pith_short_12","alias_value":"JIYJRDVU3CFT","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JIYJRDVU3CFT5XIU","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JIYJRDVU","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:JIYJRDVU3CFT5XIUV7YUGNIWD4","target":"record","payload":{"canonical_record":{"source":{"id":"1904.02227","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-04-03T20:11:30Z","cross_cats_sorted":[],"title_canon_sha256":"222285ebfbb4477013355de1e845fff5d6fc241d00b609986bbf4961c07a4412","abstract_canon_sha256":"a4a3072869d697c62b568061c7e530b60ca32361513d139127432249fcfcc557"},"schema_version":"1.0"},"canonical_sha256":"4a30988eb4d88b3edd14aff14335161f1f36b6bd6d88788ce21e088286dadfc8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:24.154380Z","signature_b64":"it5SdO9E/BSbO8tRHqzljhSTn8FJqS41FT16525yVLc3UwuEAewHPf7l55uaHsrVWg+87CVlgWLEV4kKYp4ZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a30988eb4d88b3edd14aff14335161f1f36b6bd6d88788ce21e088286dadfc8","last_reissued_at":"2026-05-17T23:49:24.153899Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:24.153899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.02227","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":"2026-05-17T23:49:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6X54waauDgrzNDLZCc6TlgWOnqsZACZlCdRjzZc4SmPq/K3aL8V8dVTB6iebjlZrorgm3DH4vA3qpEqN/iZIBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:07:54.991359Z"},"content_sha256":"abf9db66f705f5bf49c77d228ef02d46ce58ff78009c2da1fe404b1cd1a31268","schema_version":"1.0","event_id":"sha256:abf9db66f705f5bf49c77d228ef02d46ce58ff78009c2da1fe404b1cd1a31268"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:JIYJRDVU3CFT5XIUV7YUGNIWD4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on large deviations for unbounded observables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Andrew Torok, Matthew Nicol","submitted_at":"2019-04-03T20:11:30Z","abstract_excerpt":"We consider exponential large deviations estimates for unbounded observables on uniformly expanding dynamical systems. We show that uniform expansion does not imply the existence of a rate function for unbounded observables no matter the tail behavior of the cumulative distribution function. We give examples of unbounded observables with exponential decay of autocorrelations, exponential decay under the transfer operator in each $L^p$, $1\\le p < \\infty$, and strictly stretched exponential large deviation. For observables of form $|\\log d(x,p)|^{\\alpha}$, $p$ periodic, on uniformly expanding sy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02227","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":"2026-05-17T23:49:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PYEt0BkVKygeAMCjzr1NBXlxB7yHPeOfZdVGLEU/D4ylnLj5TBXBysJRFeSnc8KBjSMPle49J7Jwr7zsW3SnBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:07:54.991699Z"},"content_sha256":"335ba83639474a52fd98542d8cba758dde24223fd51007fca1499a9b0a436b31","schema_version":"1.0","event_id":"sha256:335ba83639474a52fd98542d8cba758dde24223fd51007fca1499a9b0a436b31"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JIYJRDVU3CFT5XIUV7YUGNIWD4/bundle.json","state_url":"https://pith.science/pith/JIYJRDVU3CFT5XIUV7YUGNIWD4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JIYJRDVU3CFT5XIUV7YUGNIWD4/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":"2026-06-03T18:07:54Z","links":{"resolver":"https://pith.science/pith/JIYJRDVU3CFT5XIUV7YUGNIWD4","bundle":"https://pith.science/pith/JIYJRDVU3CFT5XIUV7YUGNIWD4/bundle.json","state":"https://pith.science/pith/JIYJRDVU3CFT5XIUV7YUGNIWD4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JIYJRDVU3CFT5XIUV7YUGNIWD4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JIYJRDVU3CFT5XIUV7YUGNIWD4","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":"a4a3072869d697c62b568061c7e530b60ca32361513d139127432249fcfcc557","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-04-03T20:11:30Z","title_canon_sha256":"222285ebfbb4477013355de1e845fff5d6fc241d00b609986bbf4961c07a4412"},"schema_version":"1.0","source":{"id":"1904.02227","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02227","created_at":"2026-05-17T23:49:24Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02227v1","created_at":"2026-05-17T23:49:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02227","created_at":"2026-05-17T23:49:24Z"},{"alias_kind":"pith_short_12","alias_value":"JIYJRDVU3CFT","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JIYJRDVU3CFT5XIU","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JIYJRDVU","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:335ba83639474a52fd98542d8cba758dde24223fd51007fca1499a9b0a436b31","target":"graph","created_at":"2026-05-17T23:49:24Z","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 exponential large deviations estimates for unbounded observables on uniformly expanding dynamical systems. We show that uniform expansion does not imply the existence of a rate function for unbounded observables no matter the tail behavior of the cumulative distribution function. We give examples of unbounded observables with exponential decay of autocorrelations, exponential decay under the transfer operator in each $L^p$, $1\\le p < \\infty$, and strictly stretched exponential large deviation. For observables of form $|\\log d(x,p)|^{\\alpha}$, $p$ periodic, on uniformly expanding sy","authors_text":"Andrew Torok, Matthew Nicol","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-04-03T20:11:30Z","title":"A note on large deviations for unbounded observables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02227","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:abf9db66f705f5bf49c77d228ef02d46ce58ff78009c2da1fe404b1cd1a31268","target":"record","created_at":"2026-05-17T23:49:24Z","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":"a4a3072869d697c62b568061c7e530b60ca32361513d139127432249fcfcc557","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-04-03T20:11:30Z","title_canon_sha256":"222285ebfbb4477013355de1e845fff5d6fc241d00b609986bbf4961c07a4412"},"schema_version":"1.0","source":{"id":"1904.02227","kind":"arxiv","version":1}},"canonical_sha256":"4a30988eb4d88b3edd14aff14335161f1f36b6bd6d88788ce21e088286dadfc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a30988eb4d88b3edd14aff14335161f1f36b6bd6d88788ce21e088286dadfc8","first_computed_at":"2026-05-17T23:49:24.153899Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:24.153899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"it5SdO9E/BSbO8tRHqzljhSTn8FJqS41FT16525yVLc3UwuEAewHPf7l55uaHsrVWg+87CVlgWLEV4kKYp4ZDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:24.154380Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.02227","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:abf9db66f705f5bf49c77d228ef02d46ce58ff78009c2da1fe404b1cd1a31268","sha256:335ba83639474a52fd98542d8cba758dde24223fd51007fca1499a9b0a436b31"],"state_sha256":"672c955b60d34ddef734437cfe36e0f141538173d70def40c632f622a3fa8047"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FiXGBiVAYB05MpFfIpLPGSS+qeojXhuVEPp3tccq9m9hwGNS9ZVqo9yDzwiwZxYCezq2RGivywHKDoFBfQcmCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:07:54.993601Z","bundle_sha256":"5c251e150a59a35815e92e226ff4c7d378a87ca890c72cb072f06cd8b87bfd47"}}