{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:UTNRXCHCNRHEVALWJ4H7K6WZBA","short_pith_number":"pith:UTNRXCHC","schema_version":"1.0","canonical_sha256":"a4db1b88e26c4e4a81764f0ff57ad9081e8d4d71af7579a0e1d50513decc51ea","source":{"kind":"arxiv","id":"1704.01940","version":4},"attestation_state":"computed","paper":{"title":"Mapping $n$ grid points onto a square forces an arbitrarily large Lipschitz constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.FA"],"primary_cat":"math.MG","authors_text":"Eva Kopeck\\'a, Michael Dymond, Vojt\\v{e}ch Kalu\\v{z}a","submitted_at":"2017-04-06T17:10:07Z","abstract_excerpt":"We prove that the regular $n\\times n$ square grid of points in the integer lattice $\\mathbb{Z}^{2}$ cannot be recovered from an arbitrary $n^{2}$-element subset of $\\mathbb{Z}^{2}$ via a mapping with prescribed Lipschitz constant (independent of $n$). This answers negatively a question of Feige from 2002. Our resolution of Feige's question takes place largely in a continuous setting and is based on some new results for Lipschitz mappings falling into two broad areas of interest, which we study independently. Firstly the present work contains a detailed investigation of Lipschitz regular mappin"},"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":"1704.01940","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-04-06T17:10:07Z","cross_cats_sorted":["cs.DM","math.FA"],"title_canon_sha256":"fa6db7338cb56131e79a94df2adb33f7f1e2ecbf1c262d2e65f9ba25be50dae9","abstract_canon_sha256":"bb85daab72960b93086d80cf1c1301039a2b08346dba75d2550770fbc5821cac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:18.738554Z","signature_b64":"BgGkz+1cJhQ0V3vcbMK03YgjOiKJPgaWqLjjn6WW3pq+eHUqZNVDU8gWArYU82rxkZXPVCkLzbirBICP00AsCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4db1b88e26c4e4a81764f0ff57ad9081e8d4d71af7579a0e1d50513decc51ea","last_reissued_at":"2026-05-18T00:07:18.737803Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:18.737803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mapping $n$ grid points onto a square forces an arbitrarily large Lipschitz constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.FA"],"primary_cat":"math.MG","authors_text":"Eva Kopeck\\'a, Michael Dymond, Vojt\\v{e}ch Kalu\\v{z}a","submitted_at":"2017-04-06T17:10:07Z","abstract_excerpt":"We prove that the regular $n\\times n$ square grid of points in the integer lattice $\\mathbb{Z}^{2}$ cannot be recovered from an arbitrary $n^{2}$-element subset of $\\mathbb{Z}^{2}$ via a mapping with prescribed Lipschitz constant (independent of $n$). This answers negatively a question of Feige from 2002. Our resolution of Feige's question takes place largely in a continuous setting and is based on some new results for Lipschitz mappings falling into two broad areas of interest, which we study independently. Firstly the present work contains a detailed investigation of Lipschitz regular mappin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01940","kind":"arxiv","version":4},"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":"1704.01940","created_at":"2026-05-18T00:07:18.737912+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.01940v4","created_at":"2026-05-18T00:07:18.737912+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01940","created_at":"2026-05-18T00:07:18.737912+00:00"},{"alias_kind":"pith_short_12","alias_value":"UTNRXCHCNRHE","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"UTNRXCHCNRHEVALW","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"UTNRXCHC","created_at":"2026-05-18T12:31:49.984773+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/UTNRXCHCNRHEVALWJ4H7K6WZBA","json":"https://pith.science/pith/UTNRXCHCNRHEVALWJ4H7K6WZBA.json","graph_json":"https://pith.science/api/pith-number/UTNRXCHCNRHEVALWJ4H7K6WZBA/graph.json","events_json":"https://pith.science/api/pith-number/UTNRXCHCNRHEVALWJ4H7K6WZBA/events.json","paper":"https://pith.science/paper/UTNRXCHC"},"agent_actions":{"view_html":"https://pith.science/pith/UTNRXCHCNRHEVALWJ4H7K6WZBA","download_json":"https://pith.science/pith/UTNRXCHCNRHEVALWJ4H7K6WZBA.json","view_paper":"https://pith.science/paper/UTNRXCHC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.01940&json=true","fetch_graph":"https://pith.science/api/pith-number/UTNRXCHCNRHEVALWJ4H7K6WZBA/graph.json","fetch_events":"https://pith.science/api/pith-number/UTNRXCHCNRHEVALWJ4H7K6WZBA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UTNRXCHCNRHEVALWJ4H7K6WZBA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UTNRXCHCNRHEVALWJ4H7K6WZBA/action/storage_attestation","attest_author":"https://pith.science/pith/UTNRXCHCNRHEVALWJ4H7K6WZBA/action/author_attestation","sign_citation":"https://pith.science/pith/UTNRXCHCNRHEVALWJ4H7K6WZBA/action/citation_signature","submit_replication":"https://pith.science/pith/UTNRXCHCNRHEVALWJ4H7K6WZBA/action/replication_record"}},"created_at":"2026-05-18T00:07:18.737912+00:00","updated_at":"2026-05-18T00:07:18.737912+00:00"}