{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:OBI64YAKMOKVSJCFGWJSFVKJBP","short_pith_number":"pith:OBI64YAK","canonical_record":{"source":{"id":"1010.3089","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-10-15T08:09:20Z","cross_cats_sorted":["math.CA","math.NA"],"title_canon_sha256":"87d1202c17ec275504baf0bf3806c079b8abb329bc86c265fed781bb10772ea1","abstract_canon_sha256":"88964394b0a58f2142557590357235bc7319ee04394022faef51cf1d4e17539d"},"schema_version":"1.0"},"canonical_sha256":"7051ee600a6395592445359322d5490be83924d3bd50714bfa1a9036c63eb043","source":{"kind":"arxiv","id":"1010.3089","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3089","created_at":"2026-05-18T04:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3089v1","created_at":"2026-05-18T04:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3089","created_at":"2026-05-18T04:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"OBI64YAKMOKV","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OBI64YAKMOKVSJCF","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OBI64YAK","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:OBI64YAKMOKVSJCFGWJSFVKJBP","target":"record","payload":{"canonical_record":{"source":{"id":"1010.3089","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-10-15T08:09:20Z","cross_cats_sorted":["math.CA","math.NA"],"title_canon_sha256":"87d1202c17ec275504baf0bf3806c079b8abb329bc86c265fed781bb10772ea1","abstract_canon_sha256":"88964394b0a58f2142557590357235bc7319ee04394022faef51cf1d4e17539d"},"schema_version":"1.0"},"canonical_sha256":"7051ee600a6395592445359322d5490be83924d3bd50714bfa1a9036c63eb043","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:17.825524Z","signature_b64":"S7OlQka8j/vYq6mmHqyLv/nK+ZIqcVCd3uFL6ebO40Wb6QmAzGLmZu/BeNIf26N/fT6CAqA5XIJQh98WXit3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7051ee600a6395592445359322d5490be83924d3bd50714bfa1a9036c63eb043","last_reissued_at":"2026-05-18T04:39:17.824732Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:17.824732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.3089","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6h+rmSBGDA8SzGtuQfZjr56TOAB4Hq6JMFcLPKDGnMGCMzGeeyhNGqC/oiDY5IOkLWftZzZg153UL1n1D4G/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:14:19.603880Z"},"content_sha256":"f29f0ec2e177541181a9868a169ac1bfde7a00e5a1ab6d5c3b0ae7e9f84bb569","schema_version":"1.0","event_id":"sha256:f29f0ec2e177541181a9868a169ac1bfde7a00e5a1ab6d5c3b0ae7e9f84bb569"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:OBI64YAKMOKVSJCFGWJSFVKJBP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weak and strong convergence of an implicit iterative process with errors for a finite family of asymptotically quasi $I-$nonexpansive mappings in Banach space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.NA"],"primary_cat":"math.FA","authors_text":"Farrukh Mukhamedov, Mansoor Saburov","submitted_at":"2010-10-15T08:09:20Z","abstract_excerpt":"In this paper we prove the weak and strong convergence of the implicit iterative process with errors to a common fixed point of a finite family $\\{T_j\\}_{i=1}^N$ of asymptotically quasi $I_j-$nonexpansive mappings as well as a family of $\\{I_j\\}_{j=1}^N$ of asymptotically quasi nonexpansive mappings in the framework of Banach spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3089","kind":"arxiv","version":1},"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":"2026-05-18T04:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+MVZlq2zEmcqW9Db223CAoHo3fRQDyavv+kIjEHimhkg/EdzLZTSGKWXb3AamxKWYU6dnhyyt5bQDY8afmaVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:14:19.604246Z"},"content_sha256":"964ec85cc1740698cec82f816f9168adefda424894434dd5a7c2359b9059928f","schema_version":"1.0","event_id":"sha256:964ec85cc1740698cec82f816f9168adefda424894434dd5a7c2359b9059928f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OBI64YAKMOKVSJCFGWJSFVKJBP/bundle.json","state_url":"https://pith.science/pith/OBI64YAKMOKVSJCFGWJSFVKJBP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OBI64YAKMOKVSJCFGWJSFVKJBP/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":"2026-06-01T04:14:19Z","links":{"resolver":"https://pith.science/pith/OBI64YAKMOKVSJCFGWJSFVKJBP","bundle":"https://pith.science/pith/OBI64YAKMOKVSJCFGWJSFVKJBP/bundle.json","state":"https://pith.science/pith/OBI64YAKMOKVSJCFGWJSFVKJBP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OBI64YAKMOKVSJCFGWJSFVKJBP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OBI64YAKMOKVSJCFGWJSFVKJBP","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":"88964394b0a58f2142557590357235bc7319ee04394022faef51cf1d4e17539d","cross_cats_sorted":["math.CA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-10-15T08:09:20Z","title_canon_sha256":"87d1202c17ec275504baf0bf3806c079b8abb329bc86c265fed781bb10772ea1"},"schema_version":"1.0","source":{"id":"1010.3089","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3089","created_at":"2026-05-18T04:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3089v1","created_at":"2026-05-18T04:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3089","created_at":"2026-05-18T04:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"OBI64YAKMOKV","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OBI64YAKMOKVSJCF","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OBI64YAK","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:964ec85cc1740698cec82f816f9168adefda424894434dd5a7c2359b9059928f","target":"graph","created_at":"2026-05-18T04:39:17Z","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 prove the weak and strong convergence of the implicit iterative process with errors to a common fixed point of a finite family $\\{T_j\\}_{i=1}^N$ of asymptotically quasi $I_j-$nonexpansive mappings as well as a family of $\\{I_j\\}_{j=1}^N$ of asymptotically quasi nonexpansive mappings in the framework of Banach spaces.","authors_text":"Farrukh Mukhamedov, Mansoor Saburov","cross_cats":["math.CA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-10-15T08:09:20Z","title":"Weak and strong convergence of an implicit iterative process with errors for a finite family of asymptotically quasi $I-$nonexpansive mappings in Banach space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3089","kind":"arxiv","version":1},"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:f29f0ec2e177541181a9868a169ac1bfde7a00e5a1ab6d5c3b0ae7e9f84bb569","target":"record","created_at":"2026-05-18T04:39:17Z","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":"88964394b0a58f2142557590357235bc7319ee04394022faef51cf1d4e17539d","cross_cats_sorted":["math.CA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-10-15T08:09:20Z","title_canon_sha256":"87d1202c17ec275504baf0bf3806c079b8abb329bc86c265fed781bb10772ea1"},"schema_version":"1.0","source":{"id":"1010.3089","kind":"arxiv","version":1}},"canonical_sha256":"7051ee600a6395592445359322d5490be83924d3bd50714bfa1a9036c63eb043","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7051ee600a6395592445359322d5490be83924d3bd50714bfa1a9036c63eb043","first_computed_at":"2026-05-18T04:39:17.824732Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:17.824732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S7OlQka8j/vYq6mmHqyLv/nK+ZIqcVCd3uFL6ebO40Wb6QmAzGLmZu/BeNIf26N/fT6CAqA5XIJQh98WXit3Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:17.825524Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.3089","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f29f0ec2e177541181a9868a169ac1bfde7a00e5a1ab6d5c3b0ae7e9f84bb569","sha256:964ec85cc1740698cec82f816f9168adefda424894434dd5a7c2359b9059928f"],"state_sha256":"84efd9272bfd8f149898607de29141a3c45f1744c1b4c88a45d987e41a29f6d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pevF5XXsHackbgy+ajnuAg78GmFxTPxOcXIRo8WrUx+zEYBtrp0tPHu9hcbbB3oI25ATCkGXih7OLM3r7iPgCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T04:14:19.606244Z","bundle_sha256":"e0048ac8ae9a12f5c90ddd4f8f112ac6f4a75957f1b1cfa1c60df3eeb8b094ea"}}