{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:GYJ5BOLLNQJFMXCDVSNGA5MFKT","short_pith_number":"pith:GYJ5BOLL","schema_version":"1.0","canonical_sha256":"3613d0b96b6c12565c43ac9a60758554c1b9265453568d07f09f0a71a4da623c","source":{"kind":"arxiv","id":"0812.3525","version":3},"attestation_state":"computed","paper":{"title":"Universal convex coverings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MG"],"primary_cat":"math.NT","authors_text":"Roland Bacher (IF)","submitted_at":"2008-12-18T13:09:56Z","abstract_excerpt":"In every dimension $d\\ge1$, we establish the existence of a constant $v_d>0$ and of a subset $\\mathcal U_d$ of $\\mathbb R^d$ such that the following holds: $\\mathcal C+\\mathcal U_d=\\mathbb R^d$ for every convex set $\\mathcal C\\subset \\mathbb R^d$ of volume at least $v_d$ and $\\mathcal U_d$ contains at most $\\log(r)^{d-1}r^d$ points at distance at most $r$ from the origin, for every large $r$."},"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":"0812.3525","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-12-18T13:09:56Z","cross_cats_sorted":["math.CO","math.MG"],"title_canon_sha256":"231bdb4b01ee0ec93a75d66342083cdff9266bd0e58462f234e30dead42a7878","abstract_canon_sha256":"47f5de104b740a1f18baa31dfb49b755ac46b047255347487d99fa55321d0641"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:10.876031Z","signature_b64":"9MStgebbmKZqL38zVksjxpt3DHzXBH/mi42OmTA+il9K7T0/GFIgNw7wraV7yB+tBeec63XUdaHZhC2x00fLCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3613d0b96b6c12565c43ac9a60758554c1b9265453568d07f09f0a71a4da623c","last_reissued_at":"2026-05-18T02:58:10.875496Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:10.875496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Universal convex coverings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MG"],"primary_cat":"math.NT","authors_text":"Roland Bacher (IF)","submitted_at":"2008-12-18T13:09:56Z","abstract_excerpt":"In every dimension $d\\ge1$, we establish the existence of a constant $v_d>0$ and of a subset $\\mathcal U_d$ of $\\mathbb R^d$ such that the following holds: $\\mathcal C+\\mathcal U_d=\\mathbb R^d$ for every convex set $\\mathcal C\\subset \\mathbb R^d$ of volume at least $v_d$ and $\\mathcal U_d$ contains at most $\\log(r)^{d-1}r^d$ points at distance at most $r$ from the origin, for every large $r$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3525","kind":"arxiv","version":3},"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":"0812.3525","created_at":"2026-05-18T02:58:10.875587+00:00"},{"alias_kind":"arxiv_version","alias_value":"0812.3525v3","created_at":"2026-05-18T02:58:10.875587+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3525","created_at":"2026-05-18T02:58:10.875587+00:00"},{"alias_kind":"pith_short_12","alias_value":"GYJ5BOLLNQJF","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"GYJ5BOLLNQJFMXCD","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"GYJ5BOLL","created_at":"2026-05-18T12:25:57.157939+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/GYJ5BOLLNQJFMXCDVSNGA5MFKT","json":"https://pith.science/pith/GYJ5BOLLNQJFMXCDVSNGA5MFKT.json","graph_json":"https://pith.science/api/pith-number/GYJ5BOLLNQJFMXCDVSNGA5MFKT/graph.json","events_json":"https://pith.science/api/pith-number/GYJ5BOLLNQJFMXCDVSNGA5MFKT/events.json","paper":"https://pith.science/paper/GYJ5BOLL"},"agent_actions":{"view_html":"https://pith.science/pith/GYJ5BOLLNQJFMXCDVSNGA5MFKT","download_json":"https://pith.science/pith/GYJ5BOLLNQJFMXCDVSNGA5MFKT.json","view_paper":"https://pith.science/paper/GYJ5BOLL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0812.3525&json=true","fetch_graph":"https://pith.science/api/pith-number/GYJ5BOLLNQJFMXCDVSNGA5MFKT/graph.json","fetch_events":"https://pith.science/api/pith-number/GYJ5BOLLNQJFMXCDVSNGA5MFKT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GYJ5BOLLNQJFMXCDVSNGA5MFKT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GYJ5BOLLNQJFMXCDVSNGA5MFKT/action/storage_attestation","attest_author":"https://pith.science/pith/GYJ5BOLLNQJFMXCDVSNGA5MFKT/action/author_attestation","sign_citation":"https://pith.science/pith/GYJ5BOLLNQJFMXCDVSNGA5MFKT/action/citation_signature","submit_replication":"https://pith.science/pith/GYJ5BOLLNQJFMXCDVSNGA5MFKT/action/replication_record"}},"created_at":"2026-05-18T02:58:10.875587+00:00","updated_at":"2026-05-18T02:58:10.875587+00:00"}