{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:7WZ6FWFJL3XXDOPYOZMK5PB73H","short_pith_number":"pith:7WZ6FWFJ","schema_version":"1.0","canonical_sha256":"fdb3e2d8a95eef71b9f87658aebc3fd9fac15196221f7eb1d765327ef8cc5856","source":{"kind":"arxiv","id":"2010.09357","version":2},"attestation_state":"computed","paper":{"title":"Daugavet points and $\\Delta$-points in Lipschitz-free spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Abraham Rueda Zoca, Mingu Jung","submitted_at":"2020-10-19T09:50:04Z","abstract_excerpt":"We study Daugavet points and $\\Delta$-points in Lipschitz-free Banach spaces. We prove that, if $M$ is a compact metric space, then $\\mu\\in S_{\\mathcal F(M)}$ is a Daugavet point if, and only if, there is no denting point of $B_{\\mathcal F(M)}$ at distance strictly smaller than two from $\\mu$. Moreover, we prove that if $x$ and $y$ are connectable by rectifiable curves of lenght as close to $d(x,y)$ as we wish, then the molecule $m_{x,y}$ is a $\\Delta$-point. Some conditions on $M$ which guarantee that the previous implication reverses are also obtained. As a consequence of our work, we show t"},"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":"2010.09357","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-10-19T09:50:04Z","cross_cats_sorted":[],"title_canon_sha256":"3eee4fdbe75f789687489f2934ecb760699ef4cf5537223f8561a221155afbac","abstract_canon_sha256":"28240d5897bd71231cadcb39d3f18565dce93b477d22f2ac0beec8e016c37f2e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:06:15.721277Z","signature_b64":"4JEpjqKYAePNJ0Bv9NgmsIsu7rvbBr3JpsP8i+Exph5baMINtakHriHHz+02Yr182D70BSAPefSkVSo62uJXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fdb3e2d8a95eef71b9f87658aebc3fd9fac15196221f7eb1d765327ef8cc5856","last_reissued_at":"2026-07-05T02:06:15.720779Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:06:15.720779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Daugavet points and $\\Delta$-points in Lipschitz-free spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Abraham Rueda Zoca, Mingu Jung","submitted_at":"2020-10-19T09:50:04Z","abstract_excerpt":"We study Daugavet points and $\\Delta$-points in Lipschitz-free Banach spaces. We prove that, if $M$ is a compact metric space, then $\\mu\\in S_{\\mathcal F(M)}$ is a Daugavet point if, and only if, there is no denting point of $B_{\\mathcal F(M)}$ at distance strictly smaller than two from $\\mu$. Moreover, we prove that if $x$ and $y$ are connectable by rectifiable curves of lenght as close to $d(x,y)$ as we wish, then the molecule $m_{x,y}$ is a $\\Delta$-point. Some conditions on $M$ which guarantee that the previous implication reverses are also obtained. As a consequence of our work, we show t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.09357","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.09357/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2010.09357","created_at":"2026-07-05T02:06:15.720852+00:00"},{"alias_kind":"arxiv_version","alias_value":"2010.09357v2","created_at":"2026-07-05T02:06:15.720852+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.09357","created_at":"2026-07-05T02:06:15.720852+00:00"},{"alias_kind":"pith_short_12","alias_value":"7WZ6FWFJL3XX","created_at":"2026-07-05T02:06:15.720852+00:00"},{"alias_kind":"pith_short_16","alias_value":"7WZ6FWFJL3XXDOPY","created_at":"2026-07-05T02:06:15.720852+00:00"},{"alias_kind":"pith_short_8","alias_value":"7WZ6FWFJ","created_at":"2026-07-05T02:06:15.720852+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/7WZ6FWFJL3XXDOPYOZMK5PB73H","json":"https://pith.science/pith/7WZ6FWFJL3XXDOPYOZMK5PB73H.json","graph_json":"https://pith.science/api/pith-number/7WZ6FWFJL3XXDOPYOZMK5PB73H/graph.json","events_json":"https://pith.science/api/pith-number/7WZ6FWFJL3XXDOPYOZMK5PB73H/events.json","paper":"https://pith.science/paper/7WZ6FWFJ"},"agent_actions":{"view_html":"https://pith.science/pith/7WZ6FWFJL3XXDOPYOZMK5PB73H","download_json":"https://pith.science/pith/7WZ6FWFJL3XXDOPYOZMK5PB73H.json","view_paper":"https://pith.science/paper/7WZ6FWFJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2010.09357&json=true","fetch_graph":"https://pith.science/api/pith-number/7WZ6FWFJL3XXDOPYOZMK5PB73H/graph.json","fetch_events":"https://pith.science/api/pith-number/7WZ6FWFJL3XXDOPYOZMK5PB73H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7WZ6FWFJL3XXDOPYOZMK5PB73H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7WZ6FWFJL3XXDOPYOZMK5PB73H/action/storage_attestation","attest_author":"https://pith.science/pith/7WZ6FWFJL3XXDOPYOZMK5PB73H/action/author_attestation","sign_citation":"https://pith.science/pith/7WZ6FWFJL3XXDOPYOZMK5PB73H/action/citation_signature","submit_replication":"https://pith.science/pith/7WZ6FWFJL3XXDOPYOZMK5PB73H/action/replication_record"}},"created_at":"2026-07-05T02:06:15.720852+00:00","updated_at":"2026-07-05T02:06:15.720852+00:00"}