{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4X3JUTDSGTH4VXONTEPU6J7PXA","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":"f444cf41c81af9587c2f8f71de9d8b9cb0300b1d722fdd4facb065c1ec13cf47","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-12-17T20:31:16Z","title_canon_sha256":"26d03b9434298b8fb123576d908a04c056d47f1d18758c5293dcdf77966a2709"},"schema_version":"1.0","source":{"id":"1412.5563","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5563","created_at":"2026-05-18T01:34:55Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5563v2","created_at":"2026-05-18T01:34:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5563","created_at":"2026-05-18T01:34:55Z"},{"alias_kind":"pith_short_12","alias_value":"4X3JUTDSGTH4","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4X3JUTDSGTH4VXON","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4X3JUTDS","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:f6109274b9baa00c50034597b249761ba423848aa5cfcd0189006b726f461c45","target":"graph","created_at":"2026-05-18T01:34:55Z","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 provide in a unified way quantitative forms of strong convergence results for numerous iterative procedures which satisfy a general type of Fejer monotonicity where the convergence uses the compactness of the underlying set. These quantitative versions are in the form of explicit rates of so-called metastability in the sense of T. Tao. Our approach covers examples ranging from the proximal point algorithm for maximal monotone operators to various fixed point iterations (x_n) for firmly nonexpansive, asymptotically nonexpansive, strictly pseudo-contractive and other types of mappings. Many o","authors_text":"Adriana Nicolae, Laurentiu Leustean, Ulrick Kohlenbach","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-12-17T20:31:16Z","title":"Quantitative results on Fejer monotone sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5563","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":"sha256:7a6515ac05cb0db11f966c380039349993ff74940fd7f28fcb43a118ce548b7a","target":"record","created_at":"2026-05-18T01:34:55Z","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":"f444cf41c81af9587c2f8f71de9d8b9cb0300b1d722fdd4facb065c1ec13cf47","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-12-17T20:31:16Z","title_canon_sha256":"26d03b9434298b8fb123576d908a04c056d47f1d18758c5293dcdf77966a2709"},"schema_version":"1.0","source":{"id":"1412.5563","kind":"arxiv","version":2}},"canonical_sha256":"e5f69a4c7234cfcaddcd991f4f27efb80a6830bd8ef02fc3e7ef3bb94786b169","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5f69a4c7234cfcaddcd991f4f27efb80a6830bd8ef02fc3e7ef3bb94786b169","first_computed_at":"2026-05-18T01:34:55.142282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:55.142282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UuJunNz1uKogQHlR0oHfpQiciFk2sSdF0/MEBWrNYtDhnlJXk71MK+/IicDiHAQuAO6HS1OaPQoOuxShSyAwCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:55.142730Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5563","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a6515ac05cb0db11f966c380039349993ff74940fd7f28fcb43a118ce548b7a","sha256:f6109274b9baa00c50034597b249761ba423848aa5cfcd0189006b726f461c45"],"state_sha256":"c347f04e68c74f5783bcdc8755a1b74bd6d841454d03dc783f64a6300ba6c734"}