{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:44EQDT52MTQG2E5W6NY2Y7EW6L","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"764cb562e09563e20ee0031760e8b26cd268108dfa3a4e9cf2bd136255cadea2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-09-08T03:15:13Z","title_canon_sha256":"0ad8892b0186c9e58c4f07455efb2e15a2d046d7bced009e536d45d99080aa0c"},"schema_version":"1.0","source":{"id":"1109.1619","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1619","created_at":"2026-05-18T03:03:21Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1619v1","created_at":"2026-05-18T03:03:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1619","created_at":"2026-05-18T03:03:21Z"},{"alias_kind":"pith_short_12","alias_value":"44EQDT52MTQG","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"44EQDT52MTQG2E5W","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"44EQDT52","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:4d137ce3c8d3dd0fa2c3c602c0441c8e9b2e13c79ef6a2ceaabde3705af9d7f8","target":"graph","created_at":"2026-05-18T03:03:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Christina Chen, Daniel A. Klain, Tanya Khovanova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-09-08T03:15:13Z","title":"Volume bounds for shadow covering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1619","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:33de78fa8bee7a8e5486545d82bda26b80d30a5f9fee7fd9371a5f0b9c5dd6ce","target":"record","created_at":"2026-05-18T03:03:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"764cb562e09563e20ee0031760e8b26cd268108dfa3a4e9cf2bd136255cadea2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-09-08T03:15:13Z","title_canon_sha256":"0ad8892b0186c9e58c4f07455efb2e15a2d046d7bced009e536d45d99080aa0c"},"schema_version":"1.0","source":{"id":"1109.1619","kind":"arxiv","version":1}},"canonical_sha256":"e70901cfba64e06d13b6f371ac7c96f2cb412d14bbc05f693b3eed93817f766c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e70901cfba64e06d13b6f371ac7c96f2cb412d14bbc05f693b3eed93817f766c","first_computed_at":"2026-05-18T03:03:21.519788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:21.519788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AJv2ODKy+cwQEc2sKtl/a2p1tA4A7OyWHj1tYd/9Y3dl3DqGWw/LHk7qqboIVcnmF2t3Rcsl8DKfu80YCz4qCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:21.520289Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.1619","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33de78fa8bee7a8e5486545d82bda26b80d30a5f9fee7fd9371a5f0b9c5dd6ce","sha256:4d137ce3c8d3dd0fa2c3c602c0441c8e9b2e13c79ef6a2ceaabde3705af9d7f8"],"state_sha256":"6f76382dffcbc6060a067ddc3d1fa9ae4bc26dcbb8cb7c3cfc8c05724993a2ea"}