{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:R6TLF6XNW4UWFQXUNKPDWZIVLO","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":"b9d9268c227671a2f43f5c03356a0a7ff88680a3216994150176b9d79a4ed71e","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-06-16T18:09:42Z","title_canon_sha256":"1027e5266966ed5c93ea94a11551bba912470038ce71fab040dacac5bd74afc1"},"schema_version":"1.0","source":{"id":"1606.05300","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.05300","created_at":"2026-05-18T00:51:57Z"},{"alias_kind":"arxiv_version","alias_value":"1606.05300v2","created_at":"2026-05-18T00:51:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.05300","created_at":"2026-05-18T00:51:57Z"},{"alias_kind":"pith_short_12","alias_value":"R6TLF6XNW4UW","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"R6TLF6XNW4UWFQXU","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"R6TLF6XN","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:85bdaaf33f5785f96dbfbc0133adfc9c2e4c53f55c662c7dbce8de26e175a006","target":"graph","created_at":"2026-05-18T00:51:57Z","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 establish sharp estimates for the convergence rate of the Kranosel'ski\\v{\\i}-Mann fixed point iteration in general normed spaces, and we use them to show that the asymptotic regularity bound recently proved in [11] (Israel Journal of Mathematics 199(2), 757-772, 2014) with constant $1/\\sqrt{\\pi}$ is sharp and cannot be improved. To this end we consider the recursive bounds introduced in [3] (Proceedings of the 2nd International Conference on Fixed Point Theory and Applications, World Scientific Press, London, 27-66, 1992) which we reinterpret in terms of a nested family of optimal transport","authors_text":"Mario Bravo, Roberto Cominetti","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-06-16T18:09:42Z","title":"Sharp convergence rates for averaged nonexpansive maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05300","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:db4c1a85e452d38cc88cdbaa1bf00fda53a8a0bbf8262c02e1982c0beabd2d3c","target":"record","created_at":"2026-05-18T00:51:57Z","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":"b9d9268c227671a2f43f5c03356a0a7ff88680a3216994150176b9d79a4ed71e","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-06-16T18:09:42Z","title_canon_sha256":"1027e5266966ed5c93ea94a11551bba912470038ce71fab040dacac5bd74afc1"},"schema_version":"1.0","source":{"id":"1606.05300","kind":"arxiv","version":2}},"canonical_sha256":"8fa6b2faedb72962c2f46a9e3b65155b8369f49862960461952400eb4703bca7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8fa6b2faedb72962c2f46a9e3b65155b8369f49862960461952400eb4703bca7","first_computed_at":"2026-05-18T00:51:57.841852Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:57.841852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p69WEhXItWM3JANZ6/xhsEoEGA/eG2KYrbfVp0pTn/SAZ+RsxcQrkXIpFGA9g5TPoOET/+kfgf27Zz1sr27ZDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:57.842451Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.05300","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db4c1a85e452d38cc88cdbaa1bf00fda53a8a0bbf8262c02e1982c0beabd2d3c","sha256:85bdaaf33f5785f96dbfbc0133adfc9c2e4c53f55c662c7dbce8de26e175a006"],"state_sha256":"103c1fa04bfa32b951b485617a1513ea307fdcf59455a0cfea827a1bf6915fae"}