{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:TAQ74NOIUPMEWR4DY3VGPCKBVV","short_pith_number":"pith:TAQ74NOI","schema_version":"1.0","canonical_sha256":"9821fe35c8a3d84b4783c6ea678941ad462ef504443b01f460f26f9c61028870","source":{"kind":"arxiv","id":"1807.03363","version":2},"attestation_state":"computed","paper":{"title":"On strongly norm attaining Lipschitz maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Abraham Rueda Zoca, Bernardo Cascales, Luis Garcia-Lirola, Miguel Martin, Rafa Chiclana","submitted_at":"2018-07-09T19:56:05Z","abstract_excerpt":"We study the set $\\operatorname{SNA}(M,Y)$ of those Lipschitz maps from a (complete pointed) metric space $M$ to a Banach space $Y$ which (strongly) attain their Lipschitz norm (i.e.\\ the supremum defining the Lipschitz norm is a maximum). Extending previous results, we prove that this set is not norm dense when $M$ is a length space (or local) or when $M$ is a closed subset of $\\mathbb{R}$ with positive Lebesgue measure, providing new examples which have very different topological properties than the previously known ones. On the other hand, we study the linear properties which are sufficient"},"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":"1807.03363","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-07-09T19:56:05Z","cross_cats_sorted":[],"title_canon_sha256":"f180722eed83610fc0d392f95ceb7e3cf999d52a4f978074765742af4210df89","abstract_canon_sha256":"732cc1269f121b9a0629185df9b7c9a151679ab956d727767244a195b1f4093c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:47.685983Z","signature_b64":"qgGS4v0AQFs9fdHP7egfiaGax+cVNzPcfmBeZ4+LhOYxGBFvaE01XQU3aajT2CAfnIfPt3C+kVyVIlolBWmoBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9821fe35c8a3d84b4783c6ea678941ad462ef504443b01f460f26f9c61028870","last_reissued_at":"2026-05-17T23:56:47.685477Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:47.685477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On strongly norm attaining Lipschitz maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Abraham Rueda Zoca, Bernardo Cascales, Luis Garcia-Lirola, Miguel Martin, Rafa Chiclana","submitted_at":"2018-07-09T19:56:05Z","abstract_excerpt":"We study the set $\\operatorname{SNA}(M,Y)$ of those Lipschitz maps from a (complete pointed) metric space $M$ to a Banach space $Y$ which (strongly) attain their Lipschitz norm (i.e.\\ the supremum defining the Lipschitz norm is a maximum). Extending previous results, we prove that this set is not norm dense when $M$ is a length space (or local) or when $M$ is a closed subset of $\\mathbb{R}$ with positive Lebesgue measure, providing new examples which have very different topological properties than the previously known ones. On the other hand, we study the linear properties which are sufficient"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03363","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1807.03363","created_at":"2026-05-17T23:56:47.685569+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.03363v2","created_at":"2026-05-17T23:56:47.685569+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03363","created_at":"2026-05-17T23:56:47.685569+00:00"},{"alias_kind":"pith_short_12","alias_value":"TAQ74NOIUPME","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_16","alias_value":"TAQ74NOIUPMEWR4D","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_8","alias_value":"TAQ74NOI","created_at":"2026-05-18T12:32:53.628368+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/TAQ74NOIUPMEWR4DY3VGPCKBVV","json":"https://pith.science/pith/TAQ74NOIUPMEWR4DY3VGPCKBVV.json","graph_json":"https://pith.science/api/pith-number/TAQ74NOIUPMEWR4DY3VGPCKBVV/graph.json","events_json":"https://pith.science/api/pith-number/TAQ74NOIUPMEWR4DY3VGPCKBVV/events.json","paper":"https://pith.science/paper/TAQ74NOI"},"agent_actions":{"view_html":"https://pith.science/pith/TAQ74NOIUPMEWR4DY3VGPCKBVV","download_json":"https://pith.science/pith/TAQ74NOIUPMEWR4DY3VGPCKBVV.json","view_paper":"https://pith.science/paper/TAQ74NOI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.03363&json=true","fetch_graph":"https://pith.science/api/pith-number/TAQ74NOIUPMEWR4DY3VGPCKBVV/graph.json","fetch_events":"https://pith.science/api/pith-number/TAQ74NOIUPMEWR4DY3VGPCKBVV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TAQ74NOIUPMEWR4DY3VGPCKBVV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TAQ74NOIUPMEWR4DY3VGPCKBVV/action/storage_attestation","attest_author":"https://pith.science/pith/TAQ74NOIUPMEWR4DY3VGPCKBVV/action/author_attestation","sign_citation":"https://pith.science/pith/TAQ74NOIUPMEWR4DY3VGPCKBVV/action/citation_signature","submit_replication":"https://pith.science/pith/TAQ74NOIUPMEWR4DY3VGPCKBVV/action/replication_record"}},"created_at":"2026-05-17T23:56:47.685569+00:00","updated_at":"2026-05-17T23:56:47.685569+00:00"}