{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JSX47SASBMAC4X4IJKSM35UUAT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fa3bb05e0c3b94be18ddc1b4ed24f902d6c235fe39a16db864f523e327436663","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-10T09:34:40Z","title_canon_sha256":"8dc2e6e83e26d1f59841452f421e88d3b912208d54ddca9f2d5b17e9250a1036"},"schema_version":"1.0","source":{"id":"1404.2752","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2752","created_at":"2026-05-18T02:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2752v2","created_at":"2026-05-18T02:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2752","created_at":"2026-05-18T02:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"JSX47SASBMAC","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JSX47SASBMAC4X4I","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JSX47SAS","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:1c460464a66d796b0a9549ac6137609c49b4c6bde995ad040bec99954b1df502","target":"graph","created_at":"2026-05-18T02:29:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Kanstantsin Pashkovich, Stefan Weltge","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-10T09:34:40Z","title":"Hidden Vertices in Extensions of Polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2752","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2378fb8c7121e28df13d3ce305bc6c24244d95a181fd0dac3c36d22e8fcf2385","target":"record","created_at":"2026-05-18T02:29:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fa3bb05e0c3b94be18ddc1b4ed24f902d6c235fe39a16db864f523e327436663","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-10T09:34:40Z","title_canon_sha256":"8dc2e6e83e26d1f59841452f421e88d3b912208d54ddca9f2d5b17e9250a1036"},"schema_version":"1.0","source":{"id":"1404.2752","kind":"arxiv","version":2}},"canonical_sha256":"4cafcfc8120b002e5f884aa4cdf69404ee6e4ee55870422d5e5e55c19724e68c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4cafcfc8120b002e5f884aa4cdf69404ee6e4ee55870422d5e5e55c19724e68c","first_computed_at":"2026-05-18T02:29:39.018645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:39.018645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hTDxFulPpYtFUKC5gK9CRr9QoZUoDkBHjPd6b4KUbJsCqTDWvHsPkbDscyE0N0CRaJyPd/pNu/FQsAPwJyQ6Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:39.019086Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.2752","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2378fb8c7121e28df13d3ce305bc6c24244d95a181fd0dac3c36d22e8fcf2385","sha256:1c460464a66d796b0a9549ac6137609c49b4c6bde995ad040bec99954b1df502"],"state_sha256":"8a2737afa9f5f3c06579b047d98cd0ac62335f6b95c0d5b5b8dd5b533efbac14"}