{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:LTDPSJTYZ4ELDBONVYBN7SDHFZ","short_pith_number":"pith:LTDPSJTY","schema_version":"1.0","canonical_sha256":"5cc6f92678cf08b185cdae02dfc8672e4142cfe8bd20cbc3e5816cccd83e925c","source":{"kind":"arxiv","id":"1709.04233","version":1},"attestation_state":"computed","paper":{"title":"Cone unrectifiable sets and non-differentiability of Lipschitz functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"David Preiss, Olga Maleva","submitted_at":"2017-09-13T10:14:44Z","abstract_excerpt":"We provide sufficient conditions for a set $E\\subset\\mathbb{R}^n$ to be a non-universal differentiability set, i.e. to be contained in the set of points of non-differentiability of a real-valued Lipschitz function. These conditions are motivated by a description of the ideal generated by sets of non-differentiability of Lipschitz self-maps of $\\mathbb{R}^n$ given by Alberti, Cs\\\"ornyei and Preiss, which eventually led to the result of Jones and Cs\\\"ornyei that for every Lebesgue null set $E$ in $\\mathbb{R}^n$ there is a Lipschitz map $f:\\mathbb{R}^n\\to\\mathbb{R}^n$ not differentiable at any po"},"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":"1709.04233","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-09-13T10:14:44Z","cross_cats_sorted":[],"title_canon_sha256":"e41ab4181f67afe90aedbc487029583940cb7c4174ddc1a6823a525237eb465b","abstract_canon_sha256":"05234a6a0be73ddb26f7cb3cf58b7e0d390fe0575fb2a1f78f12db3f91d6d487"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:14.905456Z","signature_b64":"zzuZLdcKErQAFIC8Wg7+5xfDoS5rl1KiCIWhbTn0+S8rYbKcyXB2kE/XsY147kFIISHnzlS6klFcEunlrJMWDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cc6f92678cf08b185cdae02dfc8672e4142cfe8bd20cbc3e5816cccd83e925c","last_reissued_at":"2026-05-18T00:35:14.904974Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:14.904974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cone unrectifiable sets and non-differentiability of Lipschitz functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"David Preiss, Olga Maleva","submitted_at":"2017-09-13T10:14:44Z","abstract_excerpt":"We provide sufficient conditions for a set $E\\subset\\mathbb{R}^n$ to be a non-universal differentiability set, i.e. to be contained in the set of points of non-differentiability of a real-valued Lipschitz function. These conditions are motivated by a description of the ideal generated by sets of non-differentiability of Lipschitz self-maps of $\\mathbb{R}^n$ given by Alberti, Cs\\\"ornyei and Preiss, which eventually led to the result of Jones and Cs\\\"ornyei that for every Lebesgue null set $E$ in $\\mathbb{R}^n$ there is a Lipschitz map $f:\\mathbb{R}^n\\to\\mathbb{R}^n$ not differentiable at any po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04233","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":"1709.04233","created_at":"2026-05-18T00:35:14.905050+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.04233v1","created_at":"2026-05-18T00:35:14.905050+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04233","created_at":"2026-05-18T00:35:14.905050+00:00"},{"alias_kind":"pith_short_12","alias_value":"LTDPSJTYZ4EL","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"LTDPSJTYZ4ELDBON","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"LTDPSJTY","created_at":"2026-05-18T12:31:28.150371+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/LTDPSJTYZ4ELDBONVYBN7SDHFZ","json":"https://pith.science/pith/LTDPSJTYZ4ELDBONVYBN7SDHFZ.json","graph_json":"https://pith.science/api/pith-number/LTDPSJTYZ4ELDBONVYBN7SDHFZ/graph.json","events_json":"https://pith.science/api/pith-number/LTDPSJTYZ4ELDBONVYBN7SDHFZ/events.json","paper":"https://pith.science/paper/LTDPSJTY"},"agent_actions":{"view_html":"https://pith.science/pith/LTDPSJTYZ4ELDBONVYBN7SDHFZ","download_json":"https://pith.science/pith/LTDPSJTYZ4ELDBONVYBN7SDHFZ.json","view_paper":"https://pith.science/paper/LTDPSJTY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.04233&json=true","fetch_graph":"https://pith.science/api/pith-number/LTDPSJTYZ4ELDBONVYBN7SDHFZ/graph.json","fetch_events":"https://pith.science/api/pith-number/LTDPSJTYZ4ELDBONVYBN7SDHFZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LTDPSJTYZ4ELDBONVYBN7SDHFZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LTDPSJTYZ4ELDBONVYBN7SDHFZ/action/storage_attestation","attest_author":"https://pith.science/pith/LTDPSJTYZ4ELDBONVYBN7SDHFZ/action/author_attestation","sign_citation":"https://pith.science/pith/LTDPSJTYZ4ELDBONVYBN7SDHFZ/action/citation_signature","submit_replication":"https://pith.science/pith/LTDPSJTYZ4ELDBONVYBN7SDHFZ/action/replication_record"}},"created_at":"2026-05-18T00:35:14.905050+00:00","updated_at":"2026-05-18T00:35:14.905050+00:00"}