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Klain, Tanya Khovanova","submitted_at":"2011-09-08T03:15:13Z","abstract_excerpt":"For n >= 2 a construction is given for a large family of compact convex sets K and L in n-dimensional Euclidean space such that the orthogonal projection L_u onto the subspace u^\\perp contains a translate of the corresponding projection K_u for every direction u, while the volumes of K and L satisfy V_n(K) > V_n(L).\n  It is subsequently shown that, if the orthogonal projection L_u onto the subspace u^\\perp contains a translate of K_u for every direction u, then the set (n/(n-1))L contains a translate of K. If follows that V_n(K) <= (n/(n-1))^n V_n(L). In particular, we derive a universal const"},"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":"1109.1619","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-09-08T03:15:13Z","cross_cats_sorted":[],"title_canon_sha256":"0ad8892b0186c9e58c4f07455efb2e15a2d046d7bced009e536d45d99080aa0c","abstract_canon_sha256":"764cb562e09563e20ee0031760e8b26cd268108dfa3a4e9cf2bd136255cadea2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:21.520289Z","signature_b64":"AJv2ODKy+cwQEc2sKtl/a2p1tA4A7OyWHj1tYd/9Y3dl3DqGWw/LHk7qqboIVcnmF2t3Rcsl8DKfu80YCz4qCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e70901cfba64e06d13b6f371ac7c96f2cb412d14bbc05f693b3eed93817f766c","last_reissued_at":"2026-05-18T03:03:21.519788Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:21.519788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Volume bounds for shadow covering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Christina Chen, Daniel A. 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