{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:44ERRALMWNBQVBKAYRICXCS4QO","short_pith_number":"pith:44ERRALM","schema_version":"1.0","canonical_sha256":"e70918816cb3430a8540c4502b8a5c8381fc10d9591c26a45f3a38eea8e3852d","source":{"kind":"arxiv","id":"0806.4473","version":1},"attestation_state":"computed","paper":{"title":"Simultaneous packing and covering in sequence spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Konrad J. Swanepoel","submitted_at":"2008-06-27T09:49:37Z","abstract_excerpt":"We adapt a construction of Klee (1981) to find a packing of unit balls in $\\ell_p$ ($1\\leq p<\\infty$) which is efficient in the sense that enlarging the radius of each ball to any $R>2^{1-1/p}$ covers the whole space. We show that the value $2^{1-1/p}$ is optimal."},"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":"0806.4473","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2008-06-27T09:49:37Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"98995e5f7082e5023f2099ba8f79e57ff40dfd50e2e341c11be0cfe1fc830b60","abstract_canon_sha256":"e262b4700c5cca2383bd49976dbeadd04002763dc7b73799f7b16cfd1f60d73f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:21.500901Z","signature_b64":"LpRoKHnDCssg+YKrP6PWMXDSSmL1Ox4G54jt61r0gSjdH6bdF8bTL63eYyZ8O3HeYwFDG97qAjh2oPFTMvdDAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e70918816cb3430a8540c4502b8a5c8381fc10d9591c26a45f3a38eea8e3852d","last_reissued_at":"2026-05-18T02:28:21.500301Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:21.500301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simultaneous packing and covering in sequence spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Konrad J. Swanepoel","submitted_at":"2008-06-27T09:49:37Z","abstract_excerpt":"We adapt a construction of Klee (1981) to find a packing of unit balls in $\\ell_p$ ($1\\leq p<\\infty$) which is efficient in the sense that enlarging the radius of each ball to any $R>2^{1-1/p}$ covers the whole space. We show that the value $2^{1-1/p}$ is optimal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.4473","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":"0806.4473","created_at":"2026-05-18T02:28:21.500420+00:00"},{"alias_kind":"arxiv_version","alias_value":"0806.4473v1","created_at":"2026-05-18T02:28:21.500420+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.4473","created_at":"2026-05-18T02:28:21.500420+00:00"},{"alias_kind":"pith_short_12","alias_value":"44ERRALMWNBQ","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"44ERRALMWNBQVBKA","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"44ERRALM","created_at":"2026-05-18T12:25:56.245647+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/44ERRALMWNBQVBKAYRICXCS4QO","json":"https://pith.science/pith/44ERRALMWNBQVBKAYRICXCS4QO.json","graph_json":"https://pith.science/api/pith-number/44ERRALMWNBQVBKAYRICXCS4QO/graph.json","events_json":"https://pith.science/api/pith-number/44ERRALMWNBQVBKAYRICXCS4QO/events.json","paper":"https://pith.science/paper/44ERRALM"},"agent_actions":{"view_html":"https://pith.science/pith/44ERRALMWNBQVBKAYRICXCS4QO","download_json":"https://pith.science/pith/44ERRALMWNBQVBKAYRICXCS4QO.json","view_paper":"https://pith.science/paper/44ERRALM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0806.4473&json=true","fetch_graph":"https://pith.science/api/pith-number/44ERRALMWNBQVBKAYRICXCS4QO/graph.json","fetch_events":"https://pith.science/api/pith-number/44ERRALMWNBQVBKAYRICXCS4QO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/44ERRALMWNBQVBKAYRICXCS4QO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/44ERRALMWNBQVBKAYRICXCS4QO/action/storage_attestation","attest_author":"https://pith.science/pith/44ERRALMWNBQVBKAYRICXCS4QO/action/author_attestation","sign_citation":"https://pith.science/pith/44ERRALMWNBQVBKAYRICXCS4QO/action/citation_signature","submit_replication":"https://pith.science/pith/44ERRALMWNBQVBKAYRICXCS4QO/action/replication_record"}},"created_at":"2026-05-18T02:28:21.500420+00:00","updated_at":"2026-05-18T02:28:21.500420+00:00"}