{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:F57WJML7FUNZFIWBSBX6M2UDWR","short_pith_number":"pith:F57WJML7","schema_version":"1.0","canonical_sha256":"2f7f64b17f2d1b92a2c1906fe66a83b477a455dab933ac9ae30bc60939bfd17e","source":{"kind":"arxiv","id":"1510.04471","version":1},"attestation_state":"computed","paper":{"title":"Nearest points and delta convex functions in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jonathan M. Borwein, Ohad Giladi","submitted_at":"2015-10-15T11:12:10Z","abstract_excerpt":"Given a closed set $C$ in a Banach space $(X, \\|\\cdot\\|)$, a point $x\\in X$ is said to have a nearest point in $C$ if there exists $z\\in C$ such that $d_C(x) =\\|x-z\\|$, where $d_C$ is the distance of $x$ from $C$. We shortly survey the problem of studying how large is the set of points in $X$ which have nearest points in $C$. We then discuss the topic of delta-convex functions and how it is related to finding nearest points."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1510.04471","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-10-15T11:12:10Z","cross_cats_sorted":[],"title_canon_sha256":"5090c9c20915fcc2ae2fdd01f169afa142fc570cb76a5ab69e4238d028cdaf87","abstract_canon_sha256":"53d04c78612d288958d9c8e31dc5071c796251f373c69cae95e7cfad51ccbd43"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:34.362400Z","signature_b64":"D25N1laPNbm8tN4kRzlMeI/lcuGHemeVEYCynbx69o+G+kHCNebQzshfTrMWS7mgII/0xzgLfYHhIJCHdgWYAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f7f64b17f2d1b92a2c1906fe66a83b477a455dab933ac9ae30bc60939bfd17e","last_reissued_at":"2026-05-17T23:53:34.361867Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:34.361867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nearest points and delta convex functions in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jonathan M. Borwein, Ohad Giladi","submitted_at":"2015-10-15T11:12:10Z","abstract_excerpt":"Given a closed set $C$ in a Banach space $(X, \\|\\cdot\\|)$, a point $x\\in X$ is said to have a nearest point in $C$ if there exists $z\\in C$ such that $d_C(x) =\\|x-z\\|$, where $d_C$ is the distance of $x$ from $C$. We shortly survey the problem of studying how large is the set of points in $X$ which have nearest points in $C$. We then discuss the topic of delta-convex functions and how it is related to finding nearest points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04471","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1510.04471","created_at":"2026-05-17T23:53:34.361952+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.04471v1","created_at":"2026-05-17T23:53:34.361952+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04471","created_at":"2026-05-17T23:53:34.361952+00:00"},{"alias_kind":"pith_short_12","alias_value":"F57WJML7FUNZ","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"F57WJML7FUNZFIWB","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"F57WJML7","created_at":"2026-05-18T12:29:19.899920+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/F57WJML7FUNZFIWBSBX6M2UDWR","json":"https://pith.science/pith/F57WJML7FUNZFIWBSBX6M2UDWR.json","graph_json":"https://pith.science/api/pith-number/F57WJML7FUNZFIWBSBX6M2UDWR/graph.json","events_json":"https://pith.science/api/pith-number/F57WJML7FUNZFIWBSBX6M2UDWR/events.json","paper":"https://pith.science/paper/F57WJML7"},"agent_actions":{"view_html":"https://pith.science/pith/F57WJML7FUNZFIWBSBX6M2UDWR","download_json":"https://pith.science/pith/F57WJML7FUNZFIWBSBX6M2UDWR.json","view_paper":"https://pith.science/paper/F57WJML7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.04471&json=true","fetch_graph":"https://pith.science/api/pith-number/F57WJML7FUNZFIWBSBX6M2UDWR/graph.json","fetch_events":"https://pith.science/api/pith-number/F57WJML7FUNZFIWBSBX6M2UDWR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F57WJML7FUNZFIWBSBX6M2UDWR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F57WJML7FUNZFIWBSBX6M2UDWR/action/storage_attestation","attest_author":"https://pith.science/pith/F57WJML7FUNZFIWBSBX6M2UDWR/action/author_attestation","sign_citation":"https://pith.science/pith/F57WJML7FUNZFIWBSBX6M2UDWR/action/citation_signature","submit_replication":"https://pith.science/pith/F57WJML7FUNZFIWBSBX6M2UDWR/action/replication_record"}},"created_at":"2026-05-17T23:53:34.361952+00:00","updated_at":"2026-05-17T23:53:34.361952+00:00"}