{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:WDQIBFQ6QWAGTMLWWPT6LNMENS","short_pith_number":"pith:WDQIBFQ6","schema_version":"1.0","canonical_sha256":"b0e080961e858069b176b3e7e5b5846cbf4d08c56fa472d7b9b9939d0ee07c92","source":{"kind":"arxiv","id":"1103.4456","version":1},"attestation_state":"computed","paper":{"title":"Finding largest small polygons with GloptiPoly","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"CTU/FEE), Didier Henrion (LAAS, Frederic Messine (ENSEEIHT, IRIT)","submitted_at":"2011-03-23T06:21:28Z","abstract_excerpt":"A small polygon is a convex polygon of unit diameter. We are interested in small polygons which have the largest area for a given number of vertices $n$. Many instances are already solved in the literature, namely for all odd $n$, and for $n=4, 6$ and 8. Thus, for even $n\\geq 10$, instances of this problem remain open. Finding those largest small polygons can be formulated as nonconvex quadratic programming problems which can challenge state-of-the-art global optimization algorithms. We show that a recently developed technique for global polynomial optimization, based on a semidefinite program"},"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":"1103.4456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-03-23T06:21:28Z","cross_cats_sorted":[],"title_canon_sha256":"5f0a3bd29cf39f46ac47a1cc65a80b8892dfe0bf0107e2cad460cbfed1db252a","abstract_canon_sha256":"af383f1d358bee8d92adc50c1f6d114ed981859ad4763213a78e668a9ef71a2f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:02.012260Z","signature_b64":"GOejb6iqoBq69oKT8U5UcIlfm+bBwlMAVYhW2Rto1v5SUJAkCkyqAGQQOVRzTP1Zslakiyk1KFI88QAWa3nbCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0e080961e858069b176b3e7e5b5846cbf4d08c56fa472d7b9b9939d0ee07c92","last_reissued_at":"2026-05-18T04:26:02.011811Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:02.011811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finding largest small polygons with GloptiPoly","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"CTU/FEE), Didier Henrion (LAAS, Frederic Messine (ENSEEIHT, IRIT)","submitted_at":"2011-03-23T06:21:28Z","abstract_excerpt":"A small polygon is a convex polygon of unit diameter. We are interested in small polygons which have the largest area for a given number of vertices $n$. Many instances are already solved in the literature, namely for all odd $n$, and for $n=4, 6$ and 8. Thus, for even $n\\geq 10$, instances of this problem remain open. Finding those largest small polygons can be formulated as nonconvex quadratic programming problems which can challenge state-of-the-art global optimization algorithms. We show that a recently developed technique for global polynomial optimization, based on a semidefinite program"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4456","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":"1103.4456","created_at":"2026-05-18T04:26:02.011881+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.4456v1","created_at":"2026-05-18T04:26:02.011881+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4456","created_at":"2026-05-18T04:26:02.011881+00:00"},{"alias_kind":"pith_short_12","alias_value":"WDQIBFQ6QWAG","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"WDQIBFQ6QWAGTMLW","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"WDQIBFQ6","created_at":"2026-05-18T12:26:44.992195+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/WDQIBFQ6QWAGTMLWWPT6LNMENS","json":"https://pith.science/pith/WDQIBFQ6QWAGTMLWWPT6LNMENS.json","graph_json":"https://pith.science/api/pith-number/WDQIBFQ6QWAGTMLWWPT6LNMENS/graph.json","events_json":"https://pith.science/api/pith-number/WDQIBFQ6QWAGTMLWWPT6LNMENS/events.json","paper":"https://pith.science/paper/WDQIBFQ6"},"agent_actions":{"view_html":"https://pith.science/pith/WDQIBFQ6QWAGTMLWWPT6LNMENS","download_json":"https://pith.science/pith/WDQIBFQ6QWAGTMLWWPT6LNMENS.json","view_paper":"https://pith.science/paper/WDQIBFQ6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.4456&json=true","fetch_graph":"https://pith.science/api/pith-number/WDQIBFQ6QWAGTMLWWPT6LNMENS/graph.json","fetch_events":"https://pith.science/api/pith-number/WDQIBFQ6QWAGTMLWWPT6LNMENS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WDQIBFQ6QWAGTMLWWPT6LNMENS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WDQIBFQ6QWAGTMLWWPT6LNMENS/action/storage_attestation","attest_author":"https://pith.science/pith/WDQIBFQ6QWAGTMLWWPT6LNMENS/action/author_attestation","sign_citation":"https://pith.science/pith/WDQIBFQ6QWAGTMLWWPT6LNMENS/action/citation_signature","submit_replication":"https://pith.science/pith/WDQIBFQ6QWAGTMLWWPT6LNMENS/action/replication_record"}},"created_at":"2026-05-18T04:26:02.011881+00:00","updated_at":"2026-05-18T04:26:02.011881+00:00"}