{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ZBUOZRZAKAPFDQKTBQ2IBGEXSV","short_pith_number":"pith:ZBUOZRZA","schema_version":"1.0","canonical_sha256":"c868ecc720501e51c1530c34809897957297812713dd136ff0ba4dea09326373","source":{"kind":"arxiv","id":"1306.6502","version":1},"attestation_state":"computed","paper":{"title":"Lipschitz homotopy and density of Lipschitz mappings in Sobolev spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.GT","authors_text":"Armin Schikorra, Piotr Hajlasz","submitted_at":"2013-06-27T14:00:42Z","abstract_excerpt":"We construct a smooth compact n-dimensional manifold Y with one point singularity such that all its Lipschitz homotopy groups are trivial, but Lipschitz mappings Lip(S^n,Y) are not dense in the Sobolev space W^{1,n}(S^n,Y). On the other hand we show that if a metric space Y is Lipschitz (n-1)-connected, then Lipschitz mappings Lip(X,Y) are dense in N^{1,p}(X,Y) whenever the Nagata dimension of X is bounded by n and the space X supports the p-Poincare inequality."},"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":"1306.6502","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-06-27T14:00:42Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"2709f7f47e07fe638a28a3806fb4040f922e9f6ac1ad01658013a7dc586442e8","abstract_canon_sha256":"b926af8c8091eb44b3e33da375ba5b83043960e95e7773e4b29aacd6e1726be0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:44.625183Z","signature_b64":"GJJ/oVvfF/Z8Gc5/HiHAVwgYLrOjtbHSTaf/NJEHAMFBPzZ+LBmOc/Rq4oXp4Kz0DwiZPfjAxFFYgKjVwMcLBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c868ecc720501e51c1530c34809897957297812713dd136ff0ba4dea09326373","last_reissued_at":"2026-05-18T03:19:44.624394Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:44.624394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lipschitz homotopy and density of Lipschitz mappings in Sobolev spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.GT","authors_text":"Armin Schikorra, Piotr Hajlasz","submitted_at":"2013-06-27T14:00:42Z","abstract_excerpt":"We construct a smooth compact n-dimensional manifold Y with one point singularity such that all its Lipschitz homotopy groups are trivial, but Lipschitz mappings Lip(S^n,Y) are not dense in the Sobolev space W^{1,n}(S^n,Y). On the other hand we show that if a metric space Y is Lipschitz (n-1)-connected, then Lipschitz mappings Lip(X,Y) are dense in N^{1,p}(X,Y) whenever the Nagata dimension of X is bounded by n and the space X supports the p-Poincare inequality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6502","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":"1306.6502","created_at":"2026-05-18T03:19:44.624541+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.6502v1","created_at":"2026-05-18T03:19:44.624541+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.6502","created_at":"2026-05-18T03:19:44.624541+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZBUOZRZAKAPF","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZBUOZRZAKAPFDQKT","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZBUOZRZA","created_at":"2026-05-18T12:28:09.283467+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/ZBUOZRZAKAPFDQKTBQ2IBGEXSV","json":"https://pith.science/pith/ZBUOZRZAKAPFDQKTBQ2IBGEXSV.json","graph_json":"https://pith.science/api/pith-number/ZBUOZRZAKAPFDQKTBQ2IBGEXSV/graph.json","events_json":"https://pith.science/api/pith-number/ZBUOZRZAKAPFDQKTBQ2IBGEXSV/events.json","paper":"https://pith.science/paper/ZBUOZRZA"},"agent_actions":{"view_html":"https://pith.science/pith/ZBUOZRZAKAPFDQKTBQ2IBGEXSV","download_json":"https://pith.science/pith/ZBUOZRZAKAPFDQKTBQ2IBGEXSV.json","view_paper":"https://pith.science/paper/ZBUOZRZA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.6502&json=true","fetch_graph":"https://pith.science/api/pith-number/ZBUOZRZAKAPFDQKTBQ2IBGEXSV/graph.json","fetch_events":"https://pith.science/api/pith-number/ZBUOZRZAKAPFDQKTBQ2IBGEXSV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZBUOZRZAKAPFDQKTBQ2IBGEXSV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZBUOZRZAKAPFDQKTBQ2IBGEXSV/action/storage_attestation","attest_author":"https://pith.science/pith/ZBUOZRZAKAPFDQKTBQ2IBGEXSV/action/author_attestation","sign_citation":"https://pith.science/pith/ZBUOZRZAKAPFDQKTBQ2IBGEXSV/action/citation_signature","submit_replication":"https://pith.science/pith/ZBUOZRZAKAPFDQKTBQ2IBGEXSV/action/replication_record"}},"created_at":"2026-05-18T03:19:44.624541+00:00","updated_at":"2026-05-18T03:19:44.624541+00:00"}