{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:EJQRIK4U3KGOQHRS6P32PLNLMV","short_pith_number":"pith:EJQRIK4U","schema_version":"1.0","canonical_sha256":"2261142b94da8ce81e32f3f7a7adab65701ad8f587b730c3b63ba81371c087c9","source":{"kind":"arxiv","id":"1707.08794","version":2},"attestation_state":"computed","paper":{"title":"A note on minimal dispersion of point sets in the unit cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CG","authors_text":"Jakub Sosnovec","submitted_at":"2017-07-27T09:35:31Z","abstract_excerpt":"We study the dispersion of a point set, a notion closely related to the discrepancy. Given a real $r\\in (0,1)$ and an integer $d\\geq 2$, let $N(r,d)$ denote the minimum number of points inside the $d$-dimensional unit cube $[0,1]^d$ such that they intersect every axis-aligned box inside $[0,1]^d$ of volume greater than $r$. We prove an upper bound on $N(r,d)$, matching a lower bound of Aistleitner et al. up to a multiplicative constant depending only on $r$. This fully determines the rate of growth of $N(r,d)$ if $r\\in(0,1)$ is fixed."},"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":"1707.08794","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-07-27T09:35:31Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"057aa0d7b62622e4765e9e93d10a73658f257a10bbb4bcb5d79897cd584b1c39","abstract_canon_sha256":"39625651ebfb60d916205af289f0010c2b82694fae67b75305bac535e3bbdc74"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:33.968943Z","signature_b64":"0ERcPH8X3Ixu5wwaldtUeoNup1Dm8t4dsrRT93xk4dBVv9Ut0tbP3Zd76+ave6ms+jJioEmPOlPvMf8J7RO/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2261142b94da8ce81e32f3f7a7adab65701ad8f587b730c3b63ba81371c087c9","last_reissued_at":"2026-05-18T00:30:33.968364Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:33.968364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on minimal dispersion of point sets in the unit cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CG","authors_text":"Jakub Sosnovec","submitted_at":"2017-07-27T09:35:31Z","abstract_excerpt":"We study the dispersion of a point set, a notion closely related to the discrepancy. Given a real $r\\in (0,1)$ and an integer $d\\geq 2$, let $N(r,d)$ denote the minimum number of points inside the $d$-dimensional unit cube $[0,1]^d$ such that they intersect every axis-aligned box inside $[0,1]^d$ of volume greater than $r$. We prove an upper bound on $N(r,d)$, matching a lower bound of Aistleitner et al. up to a multiplicative constant depending only on $r$. This fully determines the rate of growth of $N(r,d)$ if $r\\in(0,1)$ is fixed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08794","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":"1707.08794","created_at":"2026-05-18T00:30:33.968470+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.08794v2","created_at":"2026-05-18T00:30:33.968470+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.08794","created_at":"2026-05-18T00:30:33.968470+00:00"},{"alias_kind":"pith_short_12","alias_value":"EJQRIK4U3KGO","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"EJQRIK4U3KGOQHRS","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"EJQRIK4U","created_at":"2026-05-18T12:31:12.930513+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/EJQRIK4U3KGOQHRS6P32PLNLMV","json":"https://pith.science/pith/EJQRIK4U3KGOQHRS6P32PLNLMV.json","graph_json":"https://pith.science/api/pith-number/EJQRIK4U3KGOQHRS6P32PLNLMV/graph.json","events_json":"https://pith.science/api/pith-number/EJQRIK4U3KGOQHRS6P32PLNLMV/events.json","paper":"https://pith.science/paper/EJQRIK4U"},"agent_actions":{"view_html":"https://pith.science/pith/EJQRIK4U3KGOQHRS6P32PLNLMV","download_json":"https://pith.science/pith/EJQRIK4U3KGOQHRS6P32PLNLMV.json","view_paper":"https://pith.science/paper/EJQRIK4U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.08794&json=true","fetch_graph":"https://pith.science/api/pith-number/EJQRIK4U3KGOQHRS6P32PLNLMV/graph.json","fetch_events":"https://pith.science/api/pith-number/EJQRIK4U3KGOQHRS6P32PLNLMV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EJQRIK4U3KGOQHRS6P32PLNLMV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EJQRIK4U3KGOQHRS6P32PLNLMV/action/storage_attestation","attest_author":"https://pith.science/pith/EJQRIK4U3KGOQHRS6P32PLNLMV/action/author_attestation","sign_citation":"https://pith.science/pith/EJQRIK4U3KGOQHRS6P32PLNLMV/action/citation_signature","submit_replication":"https://pith.science/pith/EJQRIK4U3KGOQHRS6P32PLNLMV/action/replication_record"}},"created_at":"2026-05-18T00:30:33.968470+00:00","updated_at":"2026-05-18T00:30:33.968470+00:00"}