{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:CBUMEFA23U4G3AA3QSR6ZWY222","short_pith_number":"pith:CBUMEFA2","schema_version":"1.0","canonical_sha256":"1068c2141add386d801b84a3ecdb1ad699749057604cfcaa2368c7a6c202b9d9","source":{"kind":"arxiv","id":"1510.00782","version":1},"attestation_state":"computed","paper":{"title":"A Spiky Ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"M\\'arton Nasz\\'odi","submitted_at":"2015-10-03T06:33:15Z","abstract_excerpt":"The Illumination Problem may be phrased as the problem of covering a convex body in Euclidean $n$-space by a minimum number of translates of its interior. By a probabilistic argument, we show that, arbitrarily close to the Euclidean ball, there is a centrally symmetric convex body of illumination number exponentially large in the dimension."},"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":"1510.00782","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-10-03T06:33:15Z","cross_cats_sorted":[],"title_canon_sha256":"c6b65032aad0077211f7829184b7f38bd26db26c89dd08038b83c95a104ee62b","abstract_canon_sha256":"044fd97b41d4d3214b51d9b3215f7c1e4ec3b08d8f55a46aeab07cebcbeaae3e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:11.074014Z","signature_b64":"FzvwG2MALqpKCqA9Yn7OvM0qpchyCvs+lYinKXQTa+yBFYrMl7wtsAkQkeMY/p/8sjnUoHjm5i2SYdG1MqSLCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1068c2141add386d801b84a3ecdb1ad699749057604cfcaa2368c7a6c202b9d9","last_reissued_at":"2026-05-18T01:20:11.073566Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:11.073566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Spiky Ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"M\\'arton Nasz\\'odi","submitted_at":"2015-10-03T06:33:15Z","abstract_excerpt":"The Illumination Problem may be phrased as the problem of covering a convex body in Euclidean $n$-space by a minimum number of translates of its interior. By a probabilistic argument, we show that, arbitrarily close to the Euclidean ball, there is a centrally symmetric convex body of illumination number exponentially large in the dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00782","kind":"arxiv","version":1},"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":"1510.00782","created_at":"2026-05-18T01:20:11.073632+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.00782v1","created_at":"2026-05-18T01:20:11.073632+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00782","created_at":"2026-05-18T01:20:11.073632+00:00"},{"alias_kind":"pith_short_12","alias_value":"CBUMEFA23U4G","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"CBUMEFA23U4G3AA3","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"CBUMEFA2","created_at":"2026-05-18T12:29:14.074870+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/CBUMEFA23U4G3AA3QSR6ZWY222","json":"https://pith.science/pith/CBUMEFA23U4G3AA3QSR6ZWY222.json","graph_json":"https://pith.science/api/pith-number/CBUMEFA23U4G3AA3QSR6ZWY222/graph.json","events_json":"https://pith.science/api/pith-number/CBUMEFA23U4G3AA3QSR6ZWY222/events.json","paper":"https://pith.science/paper/CBUMEFA2"},"agent_actions":{"view_html":"https://pith.science/pith/CBUMEFA23U4G3AA3QSR6ZWY222","download_json":"https://pith.science/pith/CBUMEFA23U4G3AA3QSR6ZWY222.json","view_paper":"https://pith.science/paper/CBUMEFA2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.00782&json=true","fetch_graph":"https://pith.science/api/pith-number/CBUMEFA23U4G3AA3QSR6ZWY222/graph.json","fetch_events":"https://pith.science/api/pith-number/CBUMEFA23U4G3AA3QSR6ZWY222/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CBUMEFA23U4G3AA3QSR6ZWY222/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CBUMEFA23U4G3AA3QSR6ZWY222/action/storage_attestation","attest_author":"https://pith.science/pith/CBUMEFA23U4G3AA3QSR6ZWY222/action/author_attestation","sign_citation":"https://pith.science/pith/CBUMEFA23U4G3AA3QSR6ZWY222/action/citation_signature","submit_replication":"https://pith.science/pith/CBUMEFA23U4G3AA3QSR6ZWY222/action/replication_record"}},"created_at":"2026-05-18T01:20:11.073632+00:00","updated_at":"2026-05-18T01:20:11.073632+00:00"}