{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:G3HJGSJREKQGDN7BBFKZLNTASA","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":"0ce8f12136aa25b06cb93f3d50f24adf7f848b3cf95524780526c968f11d9f86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-29T13:04:44Z","title_canon_sha256":"b6411808808ae708742281d18b41565b540897f32598daa5bfeaa48dd2ef7817"},"schema_version":"1.0","source":{"id":"1201.6036","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.6036","created_at":"2026-05-18T04:03:33Z"},{"alias_kind":"arxiv_version","alias_value":"1201.6036v1","created_at":"2026-05-18T04:03:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.6036","created_at":"2026-05-18T04:03:33Z"},{"alias_kind":"pith_short_12","alias_value":"G3HJGSJREKQG","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"G3HJGSJREKQGDN7B","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"G3HJGSJR","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:3930b86093675a6b3c4a3f0266c46cd71b9b36a311790b8b2e511e93ab67d15f","target":"graph","created_at":"2026-05-18T04:03:33Z","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":"In this paper, we establish a new H\\'ajek - R\\'enyi's type inequality and obtain strong law of large numbers (SLLN) for arbitrary random variables. We base our methods on demimartingales and convex functions techniques. We obtain wide extensions of avalaible results, particularly those of Amini et al. and Rao and related SLLN's.","authors_text":"Cheikha Hamallah Ndiaye, Gane Samb Lo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-29T13:04:44Z","title":"On H\\`ajek - R\\'enyi type inequality and application"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6036","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:e68ca2b9297079b8b5dfd861670fbae6958811544390624f06bb13b364fc8245","target":"record","created_at":"2026-05-18T04:03:33Z","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":"0ce8f12136aa25b06cb93f3d50f24adf7f848b3cf95524780526c968f11d9f86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-29T13:04:44Z","title_canon_sha256":"b6411808808ae708742281d18b41565b540897f32598daa5bfeaa48dd2ef7817"},"schema_version":"1.0","source":{"id":"1201.6036","kind":"arxiv","version":1}},"canonical_sha256":"36ce93493122a061b7e1095595b660901abf0fa85fbab602ce5ee64ed8abe253","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36ce93493122a061b7e1095595b660901abf0fa85fbab602ce5ee64ed8abe253","first_computed_at":"2026-05-18T04:03:33.908426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:33.908426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lHrREFhQPjTiZLjiMK0oO+uWXOTcCNhSmF56eDaCoagAkDE0P6Eiscj4zHaz5N0bRuCmYgjeUxVYHVRajQ8mAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:33.909167Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.6036","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e68ca2b9297079b8b5dfd861670fbae6958811544390624f06bb13b364fc8245","sha256:3930b86093675a6b3c4a3f0266c46cd71b9b36a311790b8b2e511e93ab67d15f"],"state_sha256":"b800316a0a0cd846d5033b3da85ca83f5e6fc4d88914d6a1d5d582d799ed16a3"}