{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:PXOJRAKBWSCCY2KADK6H4WF2KT","short_pith_number":"pith:PXOJRAKB","schema_version":"1.0","canonical_sha256":"7ddc988141b4842c69401abc7e58ba54c3b6c78bb6a7c9d56714babe2bbc0875","source":{"kind":"arxiv","id":"1402.3465","version":2},"attestation_state":"computed","paper":{"title":"Lipschitz extensions of definable p-adic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Tristan Kuijpers","submitted_at":"2014-02-14T14:05:54Z","abstract_excerpt":"In this paper, we prove a definable version of Kirszbraun's theorem in a non-Archimedean setting for definable families of functions in one variable. More precisely, we prove that every definable function $f : X \\times Y \\to \\mathbb{Q}_p^s$, where $X\\subset \\mathbb{Q}_p$ and $Y \\subset \\mathbb{Q}_p^r$, that is $\\lambda$-Lipschitz in the first variable, extends to a definable function $\\tilde{f}:\\mathbb{Q}_p\\times Y \\to \\mathbb{Q}_p^s$ that is $\\lambda$-Lipschitz in the first variable."},"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":"1402.3465","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-02-14T14:05:54Z","cross_cats_sorted":[],"title_canon_sha256":"8636028908ebc9e66468b7ae50dcee06d67f69532b3adf05386e688568425aba","abstract_canon_sha256":"3c5b1b0daa08d0303bcb7fe28f0ea8d54922374a1885116ce6f825ea10cda709"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:06.670498Z","signature_b64":"/9INtpLmVQYetYukoYKcYIxqRNstv3n0vZsa3YK/duH1L6KHhuvu+RoD87dTDUcuMO8MSFefm5FDPaA6HkKhCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ddc988141b4842c69401abc7e58ba54c3b6c78bb6a7c9d56714babe2bbc0875","last_reissued_at":"2026-05-18T02:54:06.669901Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:06.669901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lipschitz extensions of definable p-adic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Tristan Kuijpers","submitted_at":"2014-02-14T14:05:54Z","abstract_excerpt":"In this paper, we prove a definable version of Kirszbraun's theorem in a non-Archimedean setting for definable families of functions in one variable. More precisely, we prove that every definable function $f : X \\times Y \\to \\mathbb{Q}_p^s$, where $X\\subset \\mathbb{Q}_p$ and $Y \\subset \\mathbb{Q}_p^r$, that is $\\lambda$-Lipschitz in the first variable, extends to a definable function $\\tilde{f}:\\mathbb{Q}_p\\times Y \\to \\mathbb{Q}_p^s$ that is $\\lambda$-Lipschitz in the first variable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3465","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":"1402.3465","created_at":"2026-05-18T02:54:06.669991+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.3465v2","created_at":"2026-05-18T02:54:06.669991+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3465","created_at":"2026-05-18T02:54:06.669991+00:00"},{"alias_kind":"pith_short_12","alias_value":"PXOJRAKBWSCC","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PXOJRAKBWSCCY2KA","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PXOJRAKB","created_at":"2026-05-18T12:28:43.426989+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/PXOJRAKBWSCCY2KADK6H4WF2KT","json":"https://pith.science/pith/PXOJRAKBWSCCY2KADK6H4WF2KT.json","graph_json":"https://pith.science/api/pith-number/PXOJRAKBWSCCY2KADK6H4WF2KT/graph.json","events_json":"https://pith.science/api/pith-number/PXOJRAKBWSCCY2KADK6H4WF2KT/events.json","paper":"https://pith.science/paper/PXOJRAKB"},"agent_actions":{"view_html":"https://pith.science/pith/PXOJRAKBWSCCY2KADK6H4WF2KT","download_json":"https://pith.science/pith/PXOJRAKBWSCCY2KADK6H4WF2KT.json","view_paper":"https://pith.science/paper/PXOJRAKB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.3465&json=true","fetch_graph":"https://pith.science/api/pith-number/PXOJRAKBWSCCY2KADK6H4WF2KT/graph.json","fetch_events":"https://pith.science/api/pith-number/PXOJRAKBWSCCY2KADK6H4WF2KT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PXOJRAKBWSCCY2KADK6H4WF2KT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PXOJRAKBWSCCY2KADK6H4WF2KT/action/storage_attestation","attest_author":"https://pith.science/pith/PXOJRAKBWSCCY2KADK6H4WF2KT/action/author_attestation","sign_citation":"https://pith.science/pith/PXOJRAKBWSCCY2KADK6H4WF2KT/action/citation_signature","submit_replication":"https://pith.science/pith/PXOJRAKBWSCCY2KADK6H4WF2KT/action/replication_record"}},"created_at":"2026-05-18T02:54:06.669991+00:00","updated_at":"2026-05-18T02:54:06.669991+00:00"}