{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:O5O5H4OTVL5MJF6K322BWPICBJ","short_pith_number":"pith:O5O5H4OT","schema_version":"1.0","canonical_sha256":"775dd3f1d3aafac497cadeb41b3d020a4d3d4494b97f2144439c4b8ac0a9785d","source":{"kind":"arxiv","id":"0912.3929","version":4},"attestation_state":"computed","paper":{"title":"Metric inequalities for polygons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.MG","authors_text":"Adrian Dumitrescu","submitted_at":"2009-12-19T19:33:55Z","abstract_excerpt":"Let $A_1,A_2,...,A_n$ be the vertices of a polygon with unit perimeter, that is $\\sum_{i=1}^n |A_i A_{i+1}|=1$. We derive various tight estimates on the minimum and maximum values of the sum of pairwise distances, and respectively sum of pairwise squared distances among its vertices. In most cases such estimates on these sums in the literature were known only for convex polygons.\n  In the second part, we turn to a problem of Bra\\ss\\ regarding the maximum perimeter of a simple $n$-gon ($n$ odd) contained in a disk of unit radius. The problem was solved by Audet et al. \\cite{AHM09b}, who gave an"},"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":"0912.3929","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2009-12-19T19:33:55Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"51a7da24c9430550ff691699afc3b6866a8c2e37ccb69f1b37b07bcfae7257b2","abstract_canon_sha256":"cdaca24da490dcdc60b5024bad19fb6e6bde9a429f1465a16f9bb5433b3beffe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:03.553792Z","signature_b64":"RMVT2M3+QAsgKeGLzz0LZvsiAOPX8advXGEuUObiF0PsyBKXMaEWcEHalfKwudPQVucHG8QnvNqGkrbIqKqkBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"775dd3f1d3aafac497cadeb41b3d020a4d3d4494b97f2144439c4b8ac0a9785d","last_reissued_at":"2026-05-18T03:53:03.553070Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:03.553070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Metric inequalities for polygons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.MG","authors_text":"Adrian Dumitrescu","submitted_at":"2009-12-19T19:33:55Z","abstract_excerpt":"Let $A_1,A_2,...,A_n$ be the vertices of a polygon with unit perimeter, that is $\\sum_{i=1}^n |A_i A_{i+1}|=1$. We derive various tight estimates on the minimum and maximum values of the sum of pairwise distances, and respectively sum of pairwise squared distances among its vertices. In most cases such estimates on these sums in the literature were known only for convex polygons.\n  In the second part, we turn to a problem of Bra\\ss\\ regarding the maximum perimeter of a simple $n$-gon ($n$ odd) contained in a disk of unit radius. The problem was solved by Audet et al. \\cite{AHM09b}, who gave an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.3929","kind":"arxiv","version":4},"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":"0912.3929","created_at":"2026-05-18T03:53:03.553196+00:00"},{"alias_kind":"arxiv_version","alias_value":"0912.3929v4","created_at":"2026-05-18T03:53:03.553196+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.3929","created_at":"2026-05-18T03:53:03.553196+00:00"},{"alias_kind":"pith_short_12","alias_value":"O5O5H4OTVL5M","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"O5O5H4OTVL5MJF6K","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"O5O5H4OT","created_at":"2026-05-18T12:26:01.383474+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/O5O5H4OTVL5MJF6K322BWPICBJ","json":"https://pith.science/pith/O5O5H4OTVL5MJF6K322BWPICBJ.json","graph_json":"https://pith.science/api/pith-number/O5O5H4OTVL5MJF6K322BWPICBJ/graph.json","events_json":"https://pith.science/api/pith-number/O5O5H4OTVL5MJF6K322BWPICBJ/events.json","paper":"https://pith.science/paper/O5O5H4OT"},"agent_actions":{"view_html":"https://pith.science/pith/O5O5H4OTVL5MJF6K322BWPICBJ","download_json":"https://pith.science/pith/O5O5H4OTVL5MJF6K322BWPICBJ.json","view_paper":"https://pith.science/paper/O5O5H4OT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0912.3929&json=true","fetch_graph":"https://pith.science/api/pith-number/O5O5H4OTVL5MJF6K322BWPICBJ/graph.json","fetch_events":"https://pith.science/api/pith-number/O5O5H4OTVL5MJF6K322BWPICBJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O5O5H4OTVL5MJF6K322BWPICBJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O5O5H4OTVL5MJF6K322BWPICBJ/action/storage_attestation","attest_author":"https://pith.science/pith/O5O5H4OTVL5MJF6K322BWPICBJ/action/author_attestation","sign_citation":"https://pith.science/pith/O5O5H4OTVL5MJF6K322BWPICBJ/action/citation_signature","submit_replication":"https://pith.science/pith/O5O5H4OTVL5MJF6K322BWPICBJ/action/replication_record"}},"created_at":"2026-05-18T03:53:03.553196+00:00","updated_at":"2026-05-18T03:53:03.553196+00:00"}