{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:IZKEQLJETZD2JXRASDVYNYHBAE","short_pith_number":"pith:IZKEQLJE","schema_version":"1.0","canonical_sha256":"4654482d249e47a4de2090eb86e0e101345ce48f2f098eeb1833f297214cffd4","source":{"kind":"arxiv","id":"1002.0948","version":2},"attestation_state":"computed","paper":{"title":"Transversal numbers over subsets of linear spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.OC","authors_text":"Gennadiy Averkov, Robert Weismantel","submitted_at":"2010-02-04T10:04:18Z","abstract_excerpt":"Let $M$ be a subset of $\\mathbb{R}^k$. It is an important question in the theory of linear inequalities to estimate the minimal number $h=h(M)$ such that every system of linear inequalities which is infeasible over $M$ has a subsystem of at most $h$ inequalities which is already infeasible over $M.$ This number $h(M)$ is said to be the Helly number of $M.$ In view of Helly's theorem, $h(\\mathbb{R}^n)=n+1$ and, by the theorem due to Doignon, Bell and Scarf, $h(\\mathbb{Z}^d)=2^d.$ We give a common extension of these equalities showing that $h(\\mathbb{R}^n \\times \\mathbb{Z}^d) = (n+1) 2^d.$ We sh"},"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":"1002.0948","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-02-04T10:04:18Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"3c1c7cfe7baaa2464b4a691a0880a66068a269263d5d2f4574f1c104fb867405","abstract_canon_sha256":"3bce723bb1be0121515c18b7093ef11d76bf82a0c2c4cf9621ff6ebd4269a26a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:50.305732Z","signature_b64":"VkMK6nauZ8D4QoJG0XptwI1FOEaF/luVIe7V25cf85sZkPVHWwNyK4X1HZJoz7jnRqTS4mXU14NgVrbl+aTZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4654482d249e47a4de2090eb86e0e101345ce48f2f098eeb1833f297214cffd4","last_reissued_at":"2026-05-18T04:39:50.305051Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:50.305051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transversal numbers over subsets of linear spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.OC","authors_text":"Gennadiy Averkov, Robert Weismantel","submitted_at":"2010-02-04T10:04:18Z","abstract_excerpt":"Let $M$ be a subset of $\\mathbb{R}^k$. It is an important question in the theory of linear inequalities to estimate the minimal number $h=h(M)$ such that every system of linear inequalities which is infeasible over $M$ has a subsystem of at most $h$ inequalities which is already infeasible over $M.$ This number $h(M)$ is said to be the Helly number of $M.$ In view of Helly's theorem, $h(\\mathbb{R}^n)=n+1$ and, by the theorem due to Doignon, Bell and Scarf, $h(\\mathbb{Z}^d)=2^d.$ We give a common extension of these equalities showing that $h(\\mathbb{R}^n \\times \\mathbb{Z}^d) = (n+1) 2^d.$ We sh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0948","kind":"arxiv","version":2},"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":"1002.0948","created_at":"2026-05-18T04:39:50.305159+00:00"},{"alias_kind":"arxiv_version","alias_value":"1002.0948v2","created_at":"2026-05-18T04:39:50.305159+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0948","created_at":"2026-05-18T04:39:50.305159+00:00"},{"alias_kind":"pith_short_12","alias_value":"IZKEQLJETZD2","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"IZKEQLJETZD2JXRA","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"IZKEQLJE","created_at":"2026-05-18T12:26:09.077623+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/IZKEQLJETZD2JXRASDVYNYHBAE","json":"https://pith.science/pith/IZKEQLJETZD2JXRASDVYNYHBAE.json","graph_json":"https://pith.science/api/pith-number/IZKEQLJETZD2JXRASDVYNYHBAE/graph.json","events_json":"https://pith.science/api/pith-number/IZKEQLJETZD2JXRASDVYNYHBAE/events.json","paper":"https://pith.science/paper/IZKEQLJE"},"agent_actions":{"view_html":"https://pith.science/pith/IZKEQLJETZD2JXRASDVYNYHBAE","download_json":"https://pith.science/pith/IZKEQLJETZD2JXRASDVYNYHBAE.json","view_paper":"https://pith.science/paper/IZKEQLJE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1002.0948&json=true","fetch_graph":"https://pith.science/api/pith-number/IZKEQLJETZD2JXRASDVYNYHBAE/graph.json","fetch_events":"https://pith.science/api/pith-number/IZKEQLJETZD2JXRASDVYNYHBAE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IZKEQLJETZD2JXRASDVYNYHBAE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IZKEQLJETZD2JXRASDVYNYHBAE/action/storage_attestation","attest_author":"https://pith.science/pith/IZKEQLJETZD2JXRASDVYNYHBAE/action/author_attestation","sign_citation":"https://pith.science/pith/IZKEQLJETZD2JXRASDVYNYHBAE/action/citation_signature","submit_replication":"https://pith.science/pith/IZKEQLJETZD2JXRASDVYNYHBAE/action/replication_record"}},"created_at":"2026-05-18T04:39:50.305159+00:00","updated_at":"2026-05-18T04:39:50.305159+00:00"}