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For every coordinate i=1,...,n, there is a lower and an upper bound L,U : R^{n-1} -> R of 1-Lipschitz maps with L \\leq U and the inequalities read\n  L(x_1,...,x_{i-1},x_{i+1},...,x_n) \\leq x_i \\leq U(x_1,...,x_{i-1},x_{i+1},...,x_n)\n  These sets are also exactly the injective subsets; meaning those Q such that every 1-Lipschitz map A -> Q, defined on a subset A of a metric space "},"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":"1510.04181","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-10-14T16:05:11Z","cross_cats_sorted":[],"title_canon_sha256":"58f1c3310f94596e10e101a04786f51bea7b9189e6cc78b9ea0d096f059e2f17","abstract_canon_sha256":"64d323a4c3325f46fe5e55d5d492fb1a9f5b6302c75dcc53cfef5527fe47a918"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:09.002497Z","signature_b64":"3vqdOfPA1xnhSf98KpYwSM4o9CQ/9+clVxSgbteHhm4s3h4y6XxVthRbEY9Yue/ejkJGDs7OTzg1eoxmmubRBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ca216cdabb30a4c3de77ace9a91ff53db2e7a63805e0e278962c73e2df7ad2d","last_reissued_at":"2026-05-18T01:30:09.001865Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:09.001865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A characterization of injective subsets in R^n with maximum norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Dominic Descombes","submitted_at":"2015-10-14T16:05:11Z","abstract_excerpt":"We characterize all (absolute) 1-Lipschitz retracts Q of R^n with the maximum norm. 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