{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:JSX47SASBMAC4X4IJKSM35UUAT","short_pith_number":"pith:JSX47SAS","schema_version":"1.0","canonical_sha256":"4cafcfc8120b002e5f884aa4cdf69404ee6e4ee55870422d5e5e55c19724e68c","source":{"kind":"arxiv","id":"1404.2752","version":2},"attestation_state":"computed","paper":{"title":"Hidden Vertices in Extensions of Polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kanstantsin Pashkovich, Stefan Weltge","submitted_at":"2014-04-10T09:34:40Z","abstract_excerpt":"Some widely known compact extended formulations have the property that each vertex of the corresponding extension polytope is projected onto a vertex of the target polytope. In this paper, we prove that for heptagons with vertices in general position none of the minimum size extensions has this property. Additionally, for any d >= 2 we construct a family of d-polytopes such that at least 1/9 of all vertices of any of their minimum size extensions is not projected onto vertices."},"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":"1404.2752","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-10T09:34:40Z","cross_cats_sorted":[],"title_canon_sha256":"8dc2e6e83e26d1f59841452f421e88d3b912208d54ddca9f2d5b17e9250a1036","abstract_canon_sha256":"fa3bb05e0c3b94be18ddc1b4ed24f902d6c235fe39a16db864f523e327436663"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:39.019086Z","signature_b64":"hTDxFulPpYtFUKC5gK9CRr9QoZUoDkBHjPd6b4KUbJsCqTDWvHsPkbDscyE0N0CRaJyPd/pNu/FQsAPwJyQ6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4cafcfc8120b002e5f884aa4cdf69404ee6e4ee55870422d5e5e55c19724e68c","last_reissued_at":"2026-05-18T02:29:39.018645Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:39.018645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hidden Vertices in Extensions of Polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kanstantsin Pashkovich, Stefan Weltge","submitted_at":"2014-04-10T09:34:40Z","abstract_excerpt":"Some widely known compact extended formulations have the property that each vertex of the corresponding extension polytope is projected onto a vertex of the target polytope. In this paper, we prove that for heptagons with vertices in general position none of the minimum size extensions has this property. Additionally, for any d >= 2 we construct a family of d-polytopes such that at least 1/9 of all vertices of any of their minimum size extensions is not projected onto vertices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2752","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":"1404.2752","created_at":"2026-05-18T02:29:39.018712+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.2752v2","created_at":"2026-05-18T02:29:39.018712+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2752","created_at":"2026-05-18T02:29:39.018712+00:00"},{"alias_kind":"pith_short_12","alias_value":"JSX47SASBMAC","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"JSX47SASBMAC4X4I","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"JSX47SAS","created_at":"2026-05-18T12:28:35.611951+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/JSX47SASBMAC4X4IJKSM35UUAT","json":"https://pith.science/pith/JSX47SASBMAC4X4IJKSM35UUAT.json","graph_json":"https://pith.science/api/pith-number/JSX47SASBMAC4X4IJKSM35UUAT/graph.json","events_json":"https://pith.science/api/pith-number/JSX47SASBMAC4X4IJKSM35UUAT/events.json","paper":"https://pith.science/paper/JSX47SAS"},"agent_actions":{"view_html":"https://pith.science/pith/JSX47SASBMAC4X4IJKSM35UUAT","download_json":"https://pith.science/pith/JSX47SASBMAC4X4IJKSM35UUAT.json","view_paper":"https://pith.science/paper/JSX47SAS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.2752&json=true","fetch_graph":"https://pith.science/api/pith-number/JSX47SASBMAC4X4IJKSM35UUAT/graph.json","fetch_events":"https://pith.science/api/pith-number/JSX47SASBMAC4X4IJKSM35UUAT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JSX47SASBMAC4X4IJKSM35UUAT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JSX47SASBMAC4X4IJKSM35UUAT/action/storage_attestation","attest_author":"https://pith.science/pith/JSX47SASBMAC4X4IJKSM35UUAT/action/author_attestation","sign_citation":"https://pith.science/pith/JSX47SASBMAC4X4IJKSM35UUAT/action/citation_signature","submit_replication":"https://pith.science/pith/JSX47SASBMAC4X4IJKSM35UUAT/action/replication_record"}},"created_at":"2026-05-18T02:29:39.018712+00:00","updated_at":"2026-05-18T02:29:39.018712+00:00"}