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It is also shown that the following two statements are equivalent: (i) For every polytope Q inside K having at most d+1 vertices, L contains a translate of Q. (ii) For every d-dimensional subspace W, the orthogonal projection of the set L onto W contains a translate of the corresponding projection of the set K onto W.\n  It is then shown that, if K is "},"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":"0905.3514","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2009-05-21T15:59:47Z","cross_cats_sorted":[],"title_canon_sha256":"fcf0e61764a694166e8445cbf0d648e43762689b414c33c8ba5937b0e88fc8d2","abstract_canon_sha256":"bbc7758665dff3ff9bce0e9c3f848603e036d25304cdd84042e46c7ff7db7900"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:58.337197Z","signature_b64":"TpVhM/gOLcPDGt0hZgBC4VioKWDg6oIXlSOxMwCE+YI0oXCpiVz37rj8RsTotJrTegM2zbCfgmmB4USJOUfhCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5354feb3998498b7323ae1ccf77ef0fdee85b6bb2993e72fc2de8e24b4c0a323","last_reissued_at":"2026-05-18T04:38:58.336656Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:58.336656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Containment and inscribed simplices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Daniel A. 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(ii) For every d-dimensional subspace W, the orthogonal projection of the set L onto W contains a translate of the corresponding projection of the set K onto W.\n  It is then shown that, if K is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3514","kind":"arxiv","version":2},"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":"0905.3514","created_at":"2026-05-18T04:38:58.336725+00:00"},{"alias_kind":"arxiv_version","alias_value":"0905.3514v2","created_at":"2026-05-18T04:38:58.336725+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.3514","created_at":"2026-05-18T04:38:58.336725+00:00"},{"alias_kind":"pith_short_12","alias_value":"KNKP5M4ZQSML","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"KNKP5M4ZQSMLOMR2","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"KNKP5M4Z","created_at":"2026-05-18T12:26:00.592388+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/KNKP5M4ZQSMLOMR24HGPO7XQ7X","json":"https://pith.science/pith/KNKP5M4ZQSMLOMR24HGPO7XQ7X.json","graph_json":"https://pith.science/api/pith-number/KNKP5M4ZQSMLOMR24HGPO7XQ7X/graph.json","events_json":"https://pith.science/api/pith-number/KNKP5M4ZQSMLOMR24HGPO7XQ7X/events.json","paper":"https://pith.science/paper/KNKP5M4Z"},"agent_actions":{"view_html":"https://pith.science/pith/KNKP5M4ZQSMLOMR24HGPO7XQ7X","download_json":"https://pith.science/pith/KNKP5M4ZQSMLOMR24HGPO7XQ7X.json","view_paper":"https://pith.science/paper/KNKP5M4Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0905.3514&json=true","fetch_graph":"https://pith.science/api/pith-number/KNKP5M4ZQSMLOMR24HGPO7XQ7X/graph.json","fetch_events":"https://pith.science/api/pith-number/KNKP5M4ZQSMLOMR24HGPO7XQ7X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KNKP5M4ZQSMLOMR24HGPO7XQ7X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KNKP5M4ZQSMLOMR24HGPO7XQ7X/action/storage_attestation","attest_author":"https://pith.science/pith/KNKP5M4ZQSMLOMR24HGPO7XQ7X/action/author_attestation","sign_citation":"https://pith.science/pith/KNKP5M4ZQSMLOMR24HGPO7XQ7X/action/citation_signature","submit_replication":"https://pith.science/pith/KNKP5M4ZQSMLOMR24HGPO7XQ7X/action/replication_record"}},"created_at":"2026-05-18T04:38:58.336725+00:00","updated_at":"2026-05-18T04:38:58.336725+00:00"}