{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RRMX4A6CFGMAVLIWL7HFUY7Q7T","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":"1d552ab70bf04329cf390349fd3f43662865022e79b762a7f2b462aff00ec64f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-08T12:58:15Z","title_canon_sha256":"dce1ca26fbab4fadd8dbc721f215fded8786d82abb796dc148f4e87cf8dc27da"},"schema_version":"1.0","source":{"id":"1612.02895","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02895","created_at":"2026-05-18T00:52:22Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02895v2","created_at":"2026-05-18T00:52:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02895","created_at":"2026-05-18T00:52:22Z"},{"alias_kind":"pith_short_12","alias_value":"RRMX4A6CFGMA","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RRMX4A6CFGMAVLIW","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RRMX4A6C","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:3c872904c5db55331c70a08fd34a13400fda211bd2d2b0779135b4f02703c853","target":"graph","created_at":"2026-05-18T00:52:22Z","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 work, we deal with an iteration method for approximating a fixed point of a contraction mapping using the Mann's algorithm under functional random errors. We first show its almost complete convergence to the fixed point by mean of an exponential inequality and then we specify the induced rate of convergence. We finally build a confidence set for the fixed point.","authors_text":"Abdelnasser Dahmani, Bahia Barache, Idir Arab","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-08T12:58:15Z","title":"Exponential inequalities for Mann's iterative scheme with functional random errors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02895","kind":"arxiv","version":2},"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":"sha256:4b1b0e2b6fc55a34fab52900c5e72bdcd0511b2a74fbdc65b8dd30d387358322","target":"record","created_at":"2026-05-18T00:52:22Z","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":"1d552ab70bf04329cf390349fd3f43662865022e79b762a7f2b462aff00ec64f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-08T12:58:15Z","title_canon_sha256":"dce1ca26fbab4fadd8dbc721f215fded8786d82abb796dc148f4e87cf8dc27da"},"schema_version":"1.0","source":{"id":"1612.02895","kind":"arxiv","version":2}},"canonical_sha256":"8c597e03c229980aad165fce5a63f0fce01cc9bf3b69ddda20b7d20faa9120aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c597e03c229980aad165fce5a63f0fce01cc9bf3b69ddda20b7d20faa9120aa","first_computed_at":"2026-05-18T00:52:22.390194Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:22.390194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E13930KObWhJ2us1Uwtj9mLa+ynSeu+SXB8w0tphoJ8FlQVj1sAFBtw1olY4WVJ5Fi/ybKtc2DWD5fmJFQy0Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:22.390984Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.02895","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b1b0e2b6fc55a34fab52900c5e72bdcd0511b2a74fbdc65b8dd30d387358322","sha256:3c872904c5db55331c70a08fd34a13400fda211bd2d2b0779135b4f02703c853"],"state_sha256":"35311663327745a7f34b4493942ecf9bd2b9423e8d2c70f171e25bc639ea8f38"}