{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:2PVEWRQ3IWFEJYWMCODPOWGYEP","short_pith_number":"pith:2PVEWRQ3","canonical_record":{"source":{"id":"1206.4195","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-06-19T13:07:01Z","cross_cats_sorted":["math.FA","math.NA","math.PR"],"title_canon_sha256":"cd10f4c9fe929fae190de85a9558b817b370205a643ad36491ef31d991d62ee3","abstract_canon_sha256":"b256645d7832028dc73ddba46dce7981cd2bd7c924e5575c65ca2921a62c2517"},"schema_version":"1.0"},"canonical_sha256":"d3ea4b461b458a44e2cc1386f758d823c2a2fbfcec9ac6880130d601ccbc5112","source":{"kind":"arxiv","id":"1206.4195","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.4195","created_at":"2026-05-18T03:11:09Z"},{"alias_kind":"arxiv_version","alias_value":"1206.4195v2","created_at":"2026-05-18T03:11:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.4195","created_at":"2026-05-18T03:11:09Z"},{"alias_kind":"pith_short_12","alias_value":"2PVEWRQ3IWFE","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2PVEWRQ3IWFEJYWM","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2PVEWRQ3","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:2PVEWRQ3IWFEJYWMCODPOWGYEP","target":"record","payload":{"canonical_record":{"source":{"id":"1206.4195","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-06-19T13:07:01Z","cross_cats_sorted":["math.FA","math.NA","math.PR"],"title_canon_sha256":"cd10f4c9fe929fae190de85a9558b817b370205a643ad36491ef31d991d62ee3","abstract_canon_sha256":"b256645d7832028dc73ddba46dce7981cd2bd7c924e5575c65ca2921a62c2517"},"schema_version":"1.0"},"canonical_sha256":"d3ea4b461b458a44e2cc1386f758d823c2a2fbfcec9ac6880130d601ccbc5112","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:09.677010Z","signature_b64":"nnCKLZaNrPyevXW+/N4s6wNxtFbo94MxBpL6KIiRLuzPQKR/4/0rUSMCqfylaz+GT7bobUQwiOyPMxum6HuBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3ea4b461b458a44e2cc1386f758d823c2a2fbfcec9ac6880130d601ccbc5112","last_reissued_at":"2026-05-18T03:11:09.676208Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:09.676208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.4195","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:11:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fyv9qyOHe3ZpfZRtiLGPZ/3lzCYTNjkgBDagD7g/mEmgdZtpeJP7J69Eop8ruQXZQwh7dUI7WMfwj1mtS22JAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:42:25.541367Z"},"content_sha256":"9931f5d8d5425de2c988139434adf4c643c2ffa3263bd38e573fb74f03aeb136","schema_version":"1.0","event_id":"sha256:9931f5d8d5425de2c988139434adf4c643c2ffa3263bd38e573fb74f03aeb136"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:2PVEWRQ3IWFEJYWMCODPOWGYEP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the rate of convergence of Krasnoselski-Mann iterations and their connection with sums of Bernoullis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.NA","math.PR"],"primary_cat":"math.OC","authors_text":"Jos\\'e A. Soto, Jos\\'e Vaisman, Roberto Cominetti","submitted_at":"2012-06-19T13:07:01Z","abstract_excerpt":"In this paper we establish an estimate for the rate of convergence of the Krasnosel'ski\\v{\\i}-Mann iteration for computing fixed points of non-expansive maps. Our main result settles the Baillon-Bruck conjecture [3] on the asymptotic regularity of this iteration. The proof proceeds by establishing a connection between these iterates and a stochastic process involving sums of non-homogeneous Bernoulli trials. We also exploit a new Hoeffding-type inequality to majorize the expected value of a convex function of these sums using Poisson distributions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4195","kind":"arxiv","version":2},"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":"2026-05-18T03:11:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7LGx0kJGB1aB+jbCYVhcvt4N3r2PmlhQ0uPe5C0VG2yH8sd9XnwrcfixcB+EOdIRyq875vdIcDgRfuAfFnZzAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:42:25.541721Z"},"content_sha256":"713189ddfcf67a841deeb128b94fe6db5a32ace43cb7b5a1d40f0a2eca78b3d3","schema_version":"1.0","event_id":"sha256:713189ddfcf67a841deeb128b94fe6db5a32ace43cb7b5a1d40f0a2eca78b3d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2PVEWRQ3IWFEJYWMCODPOWGYEP/bundle.json","state_url":"https://pith.science/pith/2PVEWRQ3IWFEJYWMCODPOWGYEP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2PVEWRQ3IWFEJYWMCODPOWGYEP/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":"2026-05-28T09:42:25Z","links":{"resolver":"https://pith.science/pith/2PVEWRQ3IWFEJYWMCODPOWGYEP","bundle":"https://pith.science/pith/2PVEWRQ3IWFEJYWMCODPOWGYEP/bundle.json","state":"https://pith.science/pith/2PVEWRQ3IWFEJYWMCODPOWGYEP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2PVEWRQ3IWFEJYWMCODPOWGYEP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2PVEWRQ3IWFEJYWMCODPOWGYEP","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":"b256645d7832028dc73ddba46dce7981cd2bd7c924e5575c65ca2921a62c2517","cross_cats_sorted":["math.FA","math.NA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-06-19T13:07:01Z","title_canon_sha256":"cd10f4c9fe929fae190de85a9558b817b370205a643ad36491ef31d991d62ee3"},"schema_version":"1.0","source":{"id":"1206.4195","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.4195","created_at":"2026-05-18T03:11:09Z"},{"alias_kind":"arxiv_version","alias_value":"1206.4195v2","created_at":"2026-05-18T03:11:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.4195","created_at":"2026-05-18T03:11:09Z"},{"alias_kind":"pith_short_12","alias_value":"2PVEWRQ3IWFE","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2PVEWRQ3IWFEJYWM","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2PVEWRQ3","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:713189ddfcf67a841deeb128b94fe6db5a32ace43cb7b5a1d40f0a2eca78b3d3","target":"graph","created_at":"2026-05-18T03:11:09Z","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 an estimate for the rate of convergence of the Krasnosel'ski\\v{\\i}-Mann iteration for computing fixed points of non-expansive maps. Our main result settles the Baillon-Bruck conjecture [3] on the asymptotic regularity of this iteration. The proof proceeds by establishing a connection between these iterates and a stochastic process involving sums of non-homogeneous Bernoulli trials. We also exploit a new Hoeffding-type inequality to majorize the expected value of a convex function of these sums using Poisson distributions.","authors_text":"Jos\\'e A. Soto, Jos\\'e Vaisman, Roberto Cominetti","cross_cats":["math.FA","math.NA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-06-19T13:07:01Z","title":"On the rate of convergence of Krasnoselski-Mann iterations and their connection with sums of Bernoullis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4195","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":"sha256:9931f5d8d5425de2c988139434adf4c643c2ffa3263bd38e573fb74f03aeb136","target":"record","created_at":"2026-05-18T03:11:09Z","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":"b256645d7832028dc73ddba46dce7981cd2bd7c924e5575c65ca2921a62c2517","cross_cats_sorted":["math.FA","math.NA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-06-19T13:07:01Z","title_canon_sha256":"cd10f4c9fe929fae190de85a9558b817b370205a643ad36491ef31d991d62ee3"},"schema_version":"1.0","source":{"id":"1206.4195","kind":"arxiv","version":2}},"canonical_sha256":"d3ea4b461b458a44e2cc1386f758d823c2a2fbfcec9ac6880130d601ccbc5112","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3ea4b461b458a44e2cc1386f758d823c2a2fbfcec9ac6880130d601ccbc5112","first_computed_at":"2026-05-18T03:11:09.676208Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:09.676208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nnCKLZaNrPyevXW+/N4s6wNxtFbo94MxBpL6KIiRLuzPQKR/4/0rUSMCqfylaz+GT7bobUQwiOyPMxum6HuBAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:09.677010Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.4195","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9931f5d8d5425de2c988139434adf4c643c2ffa3263bd38e573fb74f03aeb136","sha256:713189ddfcf67a841deeb128b94fe6db5a32ace43cb7b5a1d40f0a2eca78b3d3"],"state_sha256":"ce5b0c0d1704573d06caf89fbee5329ad9524dba699d1c79aa2be8319ace71a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9wjAgJuHz2+YjAnFYgD0/nftQwxsUzcRTd6rasgOYu2AFGWkF6MZSRvEgMTiHqd+Pxo1/cg18dUoBAJUXduxDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T09:42:25.543653Z","bundle_sha256":"7f1b083158f2145f4126283fc8dcb0123630f3acee3181baed9de02feffd68b6"}}