{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QVXHWXUQSE7CI33ZS6AAWPOHRB","short_pith_number":"pith:QVXHWXUQ","canonical_record":{"source":{"id":"1610.07361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-24T11:23:22Z","cross_cats_sorted":[],"title_canon_sha256":"61d1b94973b166d67feb12e83205ccc08ac6af00397c8214122e5bab79c3f433","abstract_canon_sha256":"36f11b59fb5ebd7321f00890bcecb7adb25a7a0ac14c52ff815818a2edb5efd0"},"schema_version":"1.0"},"canonical_sha256":"856e7b5e90913e246f7997800b3dc7884c8935545715d3278dc59609ae8e0c03","source":{"kind":"arxiv","id":"1610.07361","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.07361","created_at":"2026-05-18T01:01:30Z"},{"alias_kind":"arxiv_version","alias_value":"1610.07361v1","created_at":"2026-05-18T01:01:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07361","created_at":"2026-05-18T01:01:30Z"},{"alias_kind":"pith_short_12","alias_value":"QVXHWXUQSE7C","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"QVXHWXUQSE7CI33Z","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"QVXHWXUQ","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QVXHWXUQSE7CI33ZS6AAWPOHRB","target":"record","payload":{"canonical_record":{"source":{"id":"1610.07361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-24T11:23:22Z","cross_cats_sorted":[],"title_canon_sha256":"61d1b94973b166d67feb12e83205ccc08ac6af00397c8214122e5bab79c3f433","abstract_canon_sha256":"36f11b59fb5ebd7321f00890bcecb7adb25a7a0ac14c52ff815818a2edb5efd0"},"schema_version":"1.0"},"canonical_sha256":"856e7b5e90913e246f7997800b3dc7884c8935545715d3278dc59609ae8e0c03","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:30.320164Z","signature_b64":"hF67SjNP8tIo/aRNpVcOjhbZjlFPh3s2AjlnuvHyuzWIx4bqqc2IfDPnN3y8cZGQnqeYxZBwPXyBOSifTg/ECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"856e7b5e90913e246f7997800b3dc7884c8935545715d3278dc59609ae8e0c03","last_reissued_at":"2026-05-18T01:01:30.319732Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:30.319732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.07361","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":"2026-05-18T01:01:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5mqeTw37/y6EicF7QmnPXdVEANNRe8kVBsWS1pd8gbTpa+F3yhzeKUer0Z4ZXdMD++393SVITSn/BM7V5sS+CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:53:04.630996Z"},"content_sha256":"a510ee4018b1d4d025befb8d92b54270361014b6fcb957f192f87400e87c8eee","schema_version":"1.0","event_id":"sha256:a510ee4018b1d4d025befb8d92b54270361014b6fcb957f192f87400e87c8eee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QVXHWXUQSE7CI33ZS6AAWPOHRB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large and moderate deviations for the left random walk on GL d (R)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christophe Cuny, Florence Merlev\\`ede (LAMA), J\\'er\\^ome Dedecker (MAP5)","submitted_at":"2016-10-24T11:23:22Z","abstract_excerpt":"Using martingale methods, we obtain some upper bounds for large and moderate deviations of products of independent and identically distributed elements of GL d (R). We investigate all the possible moment conditions, from super-exponential moments to weak moments of order p \\textgreater{} 1, to get a complete picture of the situation. We also prove a moderate deviation principle under an appropriate tail condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07361","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":"2026-05-18T01:01:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pcXCK/kLKtEVwXJij/ccNQNNeFO6KlWhUnB3BqCEL8fMDzwr8EBZBBYjBwtqKOx1Tddm8s7N6Jptv+FCpy/eCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:53:04.631803Z"},"content_sha256":"5918b5cd3ac9e1e704fd4f9ddcd4075353e418555bfdd3b479390031ee5111de","schema_version":"1.0","event_id":"sha256:5918b5cd3ac9e1e704fd4f9ddcd4075353e418555bfdd3b479390031ee5111de"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QVXHWXUQSE7CI33ZS6AAWPOHRB/bundle.json","state_url":"https://pith.science/pith/QVXHWXUQSE7CI33ZS6AAWPOHRB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QVXHWXUQSE7CI33ZS6AAWPOHRB/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":"2026-05-30T23:53:04Z","links":{"resolver":"https://pith.science/pith/QVXHWXUQSE7CI33ZS6AAWPOHRB","bundle":"https://pith.science/pith/QVXHWXUQSE7CI33ZS6AAWPOHRB/bundle.json","state":"https://pith.science/pith/QVXHWXUQSE7CI33ZS6AAWPOHRB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QVXHWXUQSE7CI33ZS6AAWPOHRB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QVXHWXUQSE7CI33ZS6AAWPOHRB","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":"36f11b59fb5ebd7321f00890bcecb7adb25a7a0ac14c52ff815818a2edb5efd0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-24T11:23:22Z","title_canon_sha256":"61d1b94973b166d67feb12e83205ccc08ac6af00397c8214122e5bab79c3f433"},"schema_version":"1.0","source":{"id":"1610.07361","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.07361","created_at":"2026-05-18T01:01:30Z"},{"alias_kind":"arxiv_version","alias_value":"1610.07361v1","created_at":"2026-05-18T01:01:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07361","created_at":"2026-05-18T01:01:30Z"},{"alias_kind":"pith_short_12","alias_value":"QVXHWXUQSE7C","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"QVXHWXUQSE7CI33Z","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"QVXHWXUQ","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:5918b5cd3ac9e1e704fd4f9ddcd4075353e418555bfdd3b479390031ee5111de","target":"graph","created_at":"2026-05-18T01:01:30Z","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":"Using martingale methods, we obtain some upper bounds for large and moderate deviations of products of independent and identically distributed elements of GL d (R). We investigate all the possible moment conditions, from super-exponential moments to weak moments of order p \\textgreater{} 1, to get a complete picture of the situation. We also prove a moderate deviation principle under an appropriate tail condition.","authors_text":"Christophe Cuny, Florence Merlev\\`ede (LAMA), J\\'er\\^ome Dedecker (MAP5)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-24T11:23:22Z","title":"Large and moderate deviations for the left random walk on GL d (R)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07361","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:a510ee4018b1d4d025befb8d92b54270361014b6fcb957f192f87400e87c8eee","target":"record","created_at":"2026-05-18T01:01:30Z","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":"36f11b59fb5ebd7321f00890bcecb7adb25a7a0ac14c52ff815818a2edb5efd0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-24T11:23:22Z","title_canon_sha256":"61d1b94973b166d67feb12e83205ccc08ac6af00397c8214122e5bab79c3f433"},"schema_version":"1.0","source":{"id":"1610.07361","kind":"arxiv","version":1}},"canonical_sha256":"856e7b5e90913e246f7997800b3dc7884c8935545715d3278dc59609ae8e0c03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"856e7b5e90913e246f7997800b3dc7884c8935545715d3278dc59609ae8e0c03","first_computed_at":"2026-05-18T01:01:30.319732Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:30.319732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hF67SjNP8tIo/aRNpVcOjhbZjlFPh3s2AjlnuvHyuzWIx4bqqc2IfDPnN3y8cZGQnqeYxZBwPXyBOSifTg/ECw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:30.320164Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.07361","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a510ee4018b1d4d025befb8d92b54270361014b6fcb957f192f87400e87c8eee","sha256:5918b5cd3ac9e1e704fd4f9ddcd4075353e418555bfdd3b479390031ee5111de"],"state_sha256":"f0faf59a8856d8c15279d03093ddae643cdf9336ad4c899221d02b4f23185d1a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NeskkmFL4vlqLSiBUiBf2A9c1gUX62CzE5pqyfb6CXSLOwPIH+cW5O+2I9TVL/0XBRr9I78UmTKSfcUagk+OCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:53:04.636889Z","bundle_sha256":"6d1d31488247a87c385c595df47b3cd784aac8dc52fa6ea1e19718d639aa9b1b"}}