{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:Z5JLHIKJFU5DMKOLCWFLD32DUS","short_pith_number":"pith:Z5JLHIKJ","canonical_record":{"source":{"id":"1606.03895","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-13T11:11:07Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"11ac2f1c3eeee3e417140053690232156babcc7352881003d947a439d347880a","abstract_canon_sha256":"32a7ab962fb255e6e0b5a2ad32631d1c75f8cce035d0b3f1625f756a435265b9"},"schema_version":"1.0"},"canonical_sha256":"cf52b3a1492d3a3629cb158ab1ef43a4b96af49b06de8f968cdfad3a5af0fc9b","source":{"kind":"arxiv","id":"1606.03895","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03895","created_at":"2026-05-18T01:12:16Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03895v2","created_at":"2026-05-18T01:12:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03895","created_at":"2026-05-18T01:12:16Z"},{"alias_kind":"pith_short_12","alias_value":"Z5JLHIKJFU5D","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Z5JLHIKJFU5DMKOL","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Z5JLHIKJ","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:Z5JLHIKJFU5DMKOLCWFLD32DUS","target":"record","payload":{"canonical_record":{"source":{"id":"1606.03895","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-13T11:11:07Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"11ac2f1c3eeee3e417140053690232156babcc7352881003d947a439d347880a","abstract_canon_sha256":"32a7ab962fb255e6e0b5a2ad32631d1c75f8cce035d0b3f1625f756a435265b9"},"schema_version":"1.0"},"canonical_sha256":"cf52b3a1492d3a3629cb158ab1ef43a4b96af49b06de8f968cdfad3a5af0fc9b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:16.395614Z","signature_b64":"BrfBIuvd1vgrVf5sFtU1RLKQDEcei8pxbZjwTRQhHNcRGhvweI3pHjmS7PHSp/Av0jtkd91zjYmu+hhRODvHDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf52b3a1492d3a3629cb158ab1ef43a4b96af49b06de8f968cdfad3a5af0fc9b","last_reissued_at":"2026-05-18T01:12:16.395234Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:16.395234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.03895","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":"2026-05-18T01:12:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h8W4nctNCtg2Blh12rUKA93vBIt7WGnBlN3jb6gsFK/sOt4Q9d4N2Hyhq7FETHEVphA8X1at3Kd4+0SuSJchBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T03:01:32.061047Z"},"content_sha256":"28c585e4ff921ca35176c24393a1c88ace20ad2ed2f4d70a353250164afb68cb","schema_version":"1.0","event_id":"sha256:28c585e4ff921ca35176c24393a1c88ace20ad2ed2f4d70a353250164afb68cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:Z5JLHIKJFU5DMKOLCWFLD32DUS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Effective results on a fixed point algorithm for families of nonlinear mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.FA","authors_text":"Andrei Sipos","submitted_at":"2016-06-13T11:11:07Z","abstract_excerpt":"We use proof mining techniques to obtain a uniform rate of asymptotic regularity for the instance of the parallel algorithm used by L\\'opez-Acedo and Xu to find common fixed points of finite families of $k$-strict pseudocontractive self-mappings of convex subsets of Hilbert spaces. We show that these results are guaranteed by a number of logical metatheorems for classical and semi-intuitionistic systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03895","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":"2026-05-18T01:12:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1WXEY9KX45bZm9t/B7B1ZEn7kojDhJ3JQqod1/BLK94YpL3hWUyaUGVLBpby8UIyXS+x60SFZX+5ghKH1W9MCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T03:01:32.061412Z"},"content_sha256":"ea487c1e3aec6e5ddc7fa4b15601d83203bb6bb8b8d808931eb4b1534e6995a5","schema_version":"1.0","event_id":"sha256:ea487c1e3aec6e5ddc7fa4b15601d83203bb6bb8b8d808931eb4b1534e6995a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z5JLHIKJFU5DMKOLCWFLD32DUS/bundle.json","state_url":"https://pith.science/pith/Z5JLHIKJFU5DMKOLCWFLD32DUS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z5JLHIKJFU5DMKOLCWFLD32DUS/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":"2026-06-20T03:01:32Z","links":{"resolver":"https://pith.science/pith/Z5JLHIKJFU5DMKOLCWFLD32DUS","bundle":"https://pith.science/pith/Z5JLHIKJFU5DMKOLCWFLD32DUS/bundle.json","state":"https://pith.science/pith/Z5JLHIKJFU5DMKOLCWFLD32DUS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z5JLHIKJFU5DMKOLCWFLD32DUS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Z5JLHIKJFU5DMKOLCWFLD32DUS","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":"32a7ab962fb255e6e0b5a2ad32631d1c75f8cce035d0b3f1625f756a435265b9","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-13T11:11:07Z","title_canon_sha256":"11ac2f1c3eeee3e417140053690232156babcc7352881003d947a439d347880a"},"schema_version":"1.0","source":{"id":"1606.03895","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03895","created_at":"2026-05-18T01:12:16Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03895v2","created_at":"2026-05-18T01:12:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03895","created_at":"2026-05-18T01:12:16Z"},{"alias_kind":"pith_short_12","alias_value":"Z5JLHIKJFU5D","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Z5JLHIKJFU5DMKOL","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Z5JLHIKJ","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:ea487c1e3aec6e5ddc7fa4b15601d83203bb6bb8b8d808931eb4b1534e6995a5","target":"graph","created_at":"2026-05-18T01:12:16Z","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 use proof mining techniques to obtain a uniform rate of asymptotic regularity for the instance of the parallel algorithm used by L\\'opez-Acedo and Xu to find common fixed points of finite families of $k$-strict pseudocontractive self-mappings of convex subsets of Hilbert spaces. We show that these results are guaranteed by a number of logical metatheorems for classical and semi-intuitionistic systems.","authors_text":"Andrei Sipos","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-13T11:11:07Z","title":"Effective results on a fixed point algorithm for families of nonlinear mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03895","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":"sha256:28c585e4ff921ca35176c24393a1c88ace20ad2ed2f4d70a353250164afb68cb","target":"record","created_at":"2026-05-18T01:12:16Z","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":"32a7ab962fb255e6e0b5a2ad32631d1c75f8cce035d0b3f1625f756a435265b9","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-13T11:11:07Z","title_canon_sha256":"11ac2f1c3eeee3e417140053690232156babcc7352881003d947a439d347880a"},"schema_version":"1.0","source":{"id":"1606.03895","kind":"arxiv","version":2}},"canonical_sha256":"cf52b3a1492d3a3629cb158ab1ef43a4b96af49b06de8f968cdfad3a5af0fc9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf52b3a1492d3a3629cb158ab1ef43a4b96af49b06de8f968cdfad3a5af0fc9b","first_computed_at":"2026-05-18T01:12:16.395234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:16.395234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BrfBIuvd1vgrVf5sFtU1RLKQDEcei8pxbZjwTRQhHNcRGhvweI3pHjmS7PHSp/Av0jtkd91zjYmu+hhRODvHDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:16.395614Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.03895","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28c585e4ff921ca35176c24393a1c88ace20ad2ed2f4d70a353250164afb68cb","sha256:ea487c1e3aec6e5ddc7fa4b15601d83203bb6bb8b8d808931eb4b1534e6995a5"],"state_sha256":"e63acb73ef5089195b5c46c20613209e7c6dbdecc0675a4b09ea8e177b74bf9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uzBZoqzANOurWzmlolCaCIfnmUTbuVOi/eDlF3QaZi7zQoAH4dC9ISHn5JXlh45RVtypw/uZhV5D7ehn1WriAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T03:01:32.063388Z","bundle_sha256":"4b9ced3c1f8eda2ed4d8310189c8f22b11721477b2d82fb4ab24feb245d95ed5"}}