{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5WXWWRUQ5ZV5NXNCJFD6MOBQKP","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":"26342dd18b217d00baa82beb30f5447b642d0fa6cf6f22084e709af72afe13f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-08T11:36:00Z","title_canon_sha256":"684b2797d1908a8f013ba346822e56bfbe3bbdf5e30a9a0ef8e56f819bc7221c"},"schema_version":"1.0","source":{"id":"1611.02484","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02484","created_at":"2026-05-18T00:59:51Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02484v1","created_at":"2026-05-18T00:59:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02484","created_at":"2026-05-18T00:59:51Z"},{"alias_kind":"pith_short_12","alias_value":"5WXWWRUQ5ZV5","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5WXWWRUQ5ZV5NXNC","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5WXWWRUQ","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:28d41cc80322860c1c69cbc94092ea1d8bcf7c6805aa36291270a9b2e5d5bd53","target":"graph","created_at":"2026-05-18T00:59:51Z","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":"Let $(A, B)$ be a nonempty bounded closed convex proximal parallel pair in a nearly uniformly convex Banach space and $T: A\\cup B \\rightarrow A\\cup B$ be a continuous and asymptotically relatively nonexpansive map. We prove that there exists $x \\in A\\cup B$ such that $\\|x - Tx\\| = \\emph{dist}(A, B)$ whenever $T(A) \\subseteq B$, $T(B) \\subseteq A$. Also, we establish that if $T(A) \\subseteq A$ and $T(B) \\subseteq B$, then there exist $x \\in A$ and $y\\in B$ such that $Tx = x$, $Ty = y$ and $\\|x - y\\| = \\emph{dist}(A, B)$. We prove the aforesaid results when the pair $(A, B)$ has the rectangle pr","authors_text":"P. Veeramani, S. Rajesh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-08T11:36:00Z","title":"Best Proximity Point Theorems for Asymptotically Relatively Nonexpansive Mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02484","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:f8e4a05e38c025fe0eef248cec0e910a0cdf9e68d45082dac3ea901cdb12526e","target":"record","created_at":"2026-05-18T00:59:51Z","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":"26342dd18b217d00baa82beb30f5447b642d0fa6cf6f22084e709af72afe13f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-08T11:36:00Z","title_canon_sha256":"684b2797d1908a8f013ba346822e56bfbe3bbdf5e30a9a0ef8e56f819bc7221c"},"schema_version":"1.0","source":{"id":"1611.02484","kind":"arxiv","version":1}},"canonical_sha256":"edaf6b4690ee6bd6dda24947e6383053cf1bbd65353777e680b59dbac2164872","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edaf6b4690ee6bd6dda24947e6383053cf1bbd65353777e680b59dbac2164872","first_computed_at":"2026-05-18T00:59:51.919219Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:51.919219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZTXsZAtGsLFyvC8L1nToHLU8P1YaWR1yPFxZ0aDvVOUJEks762ewPipyF89BH27YTHbGCoVYJJFNACj9Un3/DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:51.919890Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.02484","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8e4a05e38c025fe0eef248cec0e910a0cdf9e68d45082dac3ea901cdb12526e","sha256:28d41cc80322860c1c69cbc94092ea1d8bcf7c6805aa36291270a9b2e5d5bd53"],"state_sha256":"958b6dcd0484f49cb285d2bd09d439d1167c3a6eddd76569b999c48cdfc3795d"}