{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:RTLN2H24XJCZJGCGR6GD727E75","short_pith_number":"pith:RTLN2H24","schema_version":"1.0","canonical_sha256":"8cd6dd1f5cba459498468f8c3febe4ff74b04d629d5468691b1d770f234e47b9","source":{"kind":"arxiv","id":"1811.03983","version":1},"attestation_state":"computed","paper":{"title":"On a relation between packing and covering densities of convex bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Roman Prosanov","submitted_at":"2018-11-09T15:58:46Z","abstract_excerpt":"We show that a convex body admits a translative dense packing in $\\mathbb{R}^d$ if and only if it admits a translative economical covering."},"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":"1811.03983","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-11-09T15:58:46Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"0e1958b3055423903be4ec7bb1c15e2c4bfd1d72481e3b7ec83a25c51dd9b786","abstract_canon_sha256":"925b33c18f9e7da8a0e956b78d29c801a45966c797159c0eac4a0acf55bd0f58"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:11.373894Z","signature_b64":"vOlYIZyKa/t1gQiLhvUGrnu0I3uAH+5gTOb68avwKNE1Nk0aMr3reQHAoeQEciyc9xG0mWbB2pLPekR9mqc0Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8cd6dd1f5cba459498468f8c3febe4ff74b04d629d5468691b1d770f234e47b9","last_reissued_at":"2026-05-18T00:01:11.373252Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:11.373252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a relation between packing and covering densities of convex bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Roman Prosanov","submitted_at":"2018-11-09T15:58:46Z","abstract_excerpt":"We show that a convex body admits a translative dense packing in $\\mathbb{R}^d$ if and only if it admits a translative economical covering."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03983","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":"1811.03983","created_at":"2026-05-18T00:01:11.373363+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.03983v1","created_at":"2026-05-18T00:01:11.373363+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.03983","created_at":"2026-05-18T00:01:11.373363+00:00"},{"alias_kind":"pith_short_12","alias_value":"RTLN2H24XJCZ","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"RTLN2H24XJCZJGCG","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"RTLN2H24","created_at":"2026-05-18T12:32:50.500415+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/RTLN2H24XJCZJGCGR6GD727E75","json":"https://pith.science/pith/RTLN2H24XJCZJGCGR6GD727E75.json","graph_json":"https://pith.science/api/pith-number/RTLN2H24XJCZJGCGR6GD727E75/graph.json","events_json":"https://pith.science/api/pith-number/RTLN2H24XJCZJGCGR6GD727E75/events.json","paper":"https://pith.science/paper/RTLN2H24"},"agent_actions":{"view_html":"https://pith.science/pith/RTLN2H24XJCZJGCGR6GD727E75","download_json":"https://pith.science/pith/RTLN2H24XJCZJGCGR6GD727E75.json","view_paper":"https://pith.science/paper/RTLN2H24","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.03983&json=true","fetch_graph":"https://pith.science/api/pith-number/RTLN2H24XJCZJGCGR6GD727E75/graph.json","fetch_events":"https://pith.science/api/pith-number/RTLN2H24XJCZJGCGR6GD727E75/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RTLN2H24XJCZJGCGR6GD727E75/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RTLN2H24XJCZJGCGR6GD727E75/action/storage_attestation","attest_author":"https://pith.science/pith/RTLN2H24XJCZJGCGR6GD727E75/action/author_attestation","sign_citation":"https://pith.science/pith/RTLN2H24XJCZJGCGR6GD727E75/action/citation_signature","submit_replication":"https://pith.science/pith/RTLN2H24XJCZJGCGR6GD727E75/action/replication_record"}},"created_at":"2026-05-18T00:01:11.373363+00:00","updated_at":"2026-05-18T00:01:11.373363+00:00"}