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That is, the dispersion of this point set is bounded from above by $\\varepsilon$."},"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":"1710.06754","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-09-28T19:45:11Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"c55beb67dbe9efee57974f55c349637bea4650c2817f87e5f935682c3081f84a","abstract_canon_sha256":"c166eeca92de2b094ab542f03c025f5c4c89fdbdf27676d4aaab78e326219ff8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T19:11:06.063727Z","signature_b64":"1am3YfF3gnIkCCD3oEt2uZSNwY16qgfaKdn2uNYVeL58cm3mxoXe9kXcdDwnGtYxwwn1dPG01eNI4HpXz3tuCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33432c052a4fcd8ca6a3b2ee0b1e564c4855b06bfd1dc3e6dc93dbb45a4891cb","last_reissued_at":"2026-06-04T19:11:06.063219Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T19:11:06.063219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An upper bound on the minimal dispersion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.CA","authors_text":"Jan Vyb\\'iral, Mario Ullrich","submitted_at":"2017-09-28T19:45:11Z","abstract_excerpt":"For $\\varepsilon\\in(0,1/2)$ and a natural number $d\\ge 2$, let $N$ be a natural number with \\[ N \\,\\ge\\, 2^9\\,\\log_2(d)\\, \\left(\\frac{\\log_2(1/\\varepsilon)}{\\varepsilon}\\right)^2. \\] We prove that there is a set of $N$ points in the unit cube $[0,1]^d$, which intersects all axis-parallel boxes with volume $\\varepsilon$. 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