{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:F3QEEAMTSRKK7A6NU4W6OB7ASC","short_pith_number":"pith:F3QEEAMT","schema_version":"1.0","canonical_sha256":"2ee04201939454af83cda72de707e09088bf6c5501e39b8a163134bcf00128af","source":{"kind":"arxiv","id":"1605.08538","version":1},"attestation_state":"computed","paper":{"title":"Maximum Semidefinite and Linear Extension Complexity of Families of Polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"math.OC","authors_text":"Gennadiy Averkov, Stefan Weltge, Volker Kaibel","submitted_at":"2016-05-27T08:37:17Z","abstract_excerpt":"We relate the maximum semidefinite and linear extension complexity of a family of polytopes to the cardinality of this family and the minimum pairwise Hausdorff distance of its members. This result directly implies a known lower bound on the maximum semidefinite extension complexity of 0/1-polytopes. We further show how our result can be used to improve on the corresponding bounds known for polygons with integer vertices.\n  Our geometric proof builds upon nothing else than a simple well-known property of maximum volume inscribed ellipsoids of convex bodies. In particular, it does not rely on f"},"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":"1605.08538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-27T08:37:17Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"198330bc04cd871d02e3def6ba3754958e3462396a295be23ef5773c847a7b43","abstract_canon_sha256":"f237fdc1b7f3d4b0df7c22ef4269489a9ccba8c49e2218aba7719e665cb81d8a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:29.683014Z","signature_b64":"IcRJRxCGKJXTMIJ12NxhUzIiQsAOmdbiLWgkoZPfYTh6JQrIS6/UeWzzJsuR7bv7ITdYl7j+aKNPThkvF04eBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ee04201939454af83cda72de707e09088bf6c5501e39b8a163134bcf00128af","last_reissued_at":"2026-05-18T01:13:29.682453Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:29.682453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximum Semidefinite and Linear Extension Complexity of Families of Polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"math.OC","authors_text":"Gennadiy Averkov, Stefan Weltge, Volker Kaibel","submitted_at":"2016-05-27T08:37:17Z","abstract_excerpt":"We relate the maximum semidefinite and linear extension complexity of a family of polytopes to the cardinality of this family and the minimum pairwise Hausdorff distance of its members. This result directly implies a known lower bound on the maximum semidefinite extension complexity of 0/1-polytopes. We further show how our result can be used to improve on the corresponding bounds known for polygons with integer vertices.\n  Our geometric proof builds upon nothing else than a simple well-known property of maximum volume inscribed ellipsoids of convex bodies. In particular, it does not rely on f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08538","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":"1605.08538","created_at":"2026-05-18T01:13:29.682545+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.08538v1","created_at":"2026-05-18T01:13:29.682545+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08538","created_at":"2026-05-18T01:13:29.682545+00:00"},{"alias_kind":"pith_short_12","alias_value":"F3QEEAMTSRKK","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"F3QEEAMTSRKK7A6N","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"F3QEEAMT","created_at":"2026-05-18T12:30:15.759754+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/F3QEEAMTSRKK7A6NU4W6OB7ASC","json":"https://pith.science/pith/F3QEEAMTSRKK7A6NU4W6OB7ASC.json","graph_json":"https://pith.science/api/pith-number/F3QEEAMTSRKK7A6NU4W6OB7ASC/graph.json","events_json":"https://pith.science/api/pith-number/F3QEEAMTSRKK7A6NU4W6OB7ASC/events.json","paper":"https://pith.science/paper/F3QEEAMT"},"agent_actions":{"view_html":"https://pith.science/pith/F3QEEAMTSRKK7A6NU4W6OB7ASC","download_json":"https://pith.science/pith/F3QEEAMTSRKK7A6NU4W6OB7ASC.json","view_paper":"https://pith.science/paper/F3QEEAMT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.08538&json=true","fetch_graph":"https://pith.science/api/pith-number/F3QEEAMTSRKK7A6NU4W6OB7ASC/graph.json","fetch_events":"https://pith.science/api/pith-number/F3QEEAMTSRKK7A6NU4W6OB7ASC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F3QEEAMTSRKK7A6NU4W6OB7ASC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F3QEEAMTSRKK7A6NU4W6OB7ASC/action/storage_attestation","attest_author":"https://pith.science/pith/F3QEEAMTSRKK7A6NU4W6OB7ASC/action/author_attestation","sign_citation":"https://pith.science/pith/F3QEEAMTSRKK7A6NU4W6OB7ASC/action/citation_signature","submit_replication":"https://pith.science/pith/F3QEEAMTSRKK7A6NU4W6OB7ASC/action/replication_record"}},"created_at":"2026-05-18T01:13:29.682545+00:00","updated_at":"2026-05-18T01:13:29.682545+00:00"}