{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:3B7CR4TFJUFREBFWOGSCAADQR3","short_pith_number":"pith:3B7CR4TF","schema_version":"1.0","canonical_sha256":"d87e28f2654d0b1204b671a42000708ee5ebe651f51750cf19793383b01fd94a","source":{"kind":"arxiv","id":"1208.0975","version":1},"attestation_state":"computed","paper":{"title":"Covering Numbers in Linear Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.HO","authors_text":"Pete L. Clark","submitted_at":"2012-08-05T02:02:40Z","abstract_excerpt":"We compute the minimal cardinality of a covering (resp. an irredundant covering) of a vector space over an arbitrary field by proper linear subspaces. Analogues for affine linear subspaces are also given."},"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":"1208.0975","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2012-08-05T02:02:40Z","cross_cats_sorted":[],"title_canon_sha256":"d4ebc5b9dff0d603d507ba28e28797496c23df6fc84bdbaf609c1cd4b45997a1","abstract_canon_sha256":"13c49a306d9e7c002d2b3713e228fa8600f7cf1565cc1ff9a685324443168643"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:20.945475Z","signature_b64":"VcfAXvrm3/bK7Acb3ZH+RN1iSkDdZccLSzO+PjjlGBXMuKVkltZ0ro9ALDdAyGfC8gcf3AqcNjqpoFmCcp7wBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d87e28f2654d0b1204b671a42000708ee5ebe651f51750cf19793383b01fd94a","last_reissued_at":"2026-05-18T03:49:20.944798Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:20.944798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Covering Numbers in Linear Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.HO","authors_text":"Pete L. Clark","submitted_at":"2012-08-05T02:02:40Z","abstract_excerpt":"We compute the minimal cardinality of a covering (resp. an irredundant covering) of a vector space over an arbitrary field by proper linear subspaces. Analogues for affine linear subspaces are also given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0975","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":"1208.0975","created_at":"2026-05-18T03:49:20.944904+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.0975v1","created_at":"2026-05-18T03:49:20.944904+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.0975","created_at":"2026-05-18T03:49:20.944904+00:00"},{"alias_kind":"pith_short_12","alias_value":"3B7CR4TFJUFR","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"3B7CR4TFJUFREBFW","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"3B7CR4TF","created_at":"2026-05-18T12:26:50.516681+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/3B7CR4TFJUFREBFWOGSCAADQR3","json":"https://pith.science/pith/3B7CR4TFJUFREBFWOGSCAADQR3.json","graph_json":"https://pith.science/api/pith-number/3B7CR4TFJUFREBFWOGSCAADQR3/graph.json","events_json":"https://pith.science/api/pith-number/3B7CR4TFJUFREBFWOGSCAADQR3/events.json","paper":"https://pith.science/paper/3B7CR4TF"},"agent_actions":{"view_html":"https://pith.science/pith/3B7CR4TFJUFREBFWOGSCAADQR3","download_json":"https://pith.science/pith/3B7CR4TFJUFREBFWOGSCAADQR3.json","view_paper":"https://pith.science/paper/3B7CR4TF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.0975&json=true","fetch_graph":"https://pith.science/api/pith-number/3B7CR4TFJUFREBFWOGSCAADQR3/graph.json","fetch_events":"https://pith.science/api/pith-number/3B7CR4TFJUFREBFWOGSCAADQR3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3B7CR4TFJUFREBFWOGSCAADQR3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3B7CR4TFJUFREBFWOGSCAADQR3/action/storage_attestation","attest_author":"https://pith.science/pith/3B7CR4TFJUFREBFWOGSCAADQR3/action/author_attestation","sign_citation":"https://pith.science/pith/3B7CR4TFJUFREBFWOGSCAADQR3/action/citation_signature","submit_replication":"https://pith.science/pith/3B7CR4TFJUFREBFWOGSCAADQR3/action/replication_record"}},"created_at":"2026-05-18T03:49:20.944904+00:00","updated_at":"2026-05-18T03:49:20.944904+00:00"}