{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:4KEFUAE4GBMYCKHRQ7MB3PBQGZ","short_pith_number":"pith:4KEFUAE4","schema_version":"1.0","canonical_sha256":"e2885a009c30598128f187d81dbc303661f6b7e1806243dc4edc4794d9c1678e","source":{"kind":"arxiv","id":"1410.4126","version":3},"attestation_state":"computed","paper":{"title":"The intersection graph of the disks with diameters the sides of a convex $n$-gon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.MG","authors_text":"Clemens Huemer, Pablo P\\'erez-Lantero","submitted_at":"2014-10-14T19:08:15Z","abstract_excerpt":"Given a convex polygon of $n$ sides, one can draw $n$ disks (called side disks) where each disk has a different side of the polygon as diameter and the midpoint of the side as its center. The intersection graph of such disks is the undirected graph with vertices the $n$ disks and two disks are adjacent if and only if they have a point in common. We prove that for every convex polygon this graph is planar. Particularly, for $n=5$, this shows that for any convex pentagon there are two disks among the five side disks that do not intersect, which means that $K_5$ is never the intersection graph of"},"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":"1410.4126","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-10-14T19:08:15Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"8077447e3dd5bba034132a649e6df0b58dd7f33fa5a58fb1565b74e19a389dae","abstract_canon_sha256":"913f5513ce5bf496145138a77515fcc86504aa214057ac309683ffc1011e4c64"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:22.964813Z","signature_b64":"x1W/mhClP0w//8tLzm9yOxtZ0DtSFl7SlitBTC4+IeGq2Gkj8XGw56eT4OxJy3Qdy9/OTkb2Xcim0CuYmXWeAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2885a009c30598128f187d81dbc303661f6b7e1806243dc4edc4794d9c1678e","last_reissued_at":"2026-05-18T01:12:22.964392Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:22.964392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The intersection graph of the disks with diameters the sides of a convex $n$-gon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.MG","authors_text":"Clemens Huemer, Pablo P\\'erez-Lantero","submitted_at":"2014-10-14T19:08:15Z","abstract_excerpt":"Given a convex polygon of $n$ sides, one can draw $n$ disks (called side disks) where each disk has a different side of the polygon as diameter and the midpoint of the side as its center. The intersection graph of such disks is the undirected graph with vertices the $n$ disks and two disks are adjacent if and only if they have a point in common. We prove that for every convex polygon this graph is planar. Particularly, for $n=5$, this shows that for any convex pentagon there are two disks among the five side disks that do not intersect, which means that $K_5$ is never the intersection graph of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4126","kind":"arxiv","version":3},"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":"1410.4126","created_at":"2026-05-18T01:12:22.964450+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.4126v3","created_at":"2026-05-18T01:12:22.964450+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.4126","created_at":"2026-05-18T01:12:22.964450+00:00"},{"alias_kind":"pith_short_12","alias_value":"4KEFUAE4GBMY","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"4KEFUAE4GBMYCKHR","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"4KEFUAE4","created_at":"2026-05-18T12:28:14.216126+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/4KEFUAE4GBMYCKHRQ7MB3PBQGZ","json":"https://pith.science/pith/4KEFUAE4GBMYCKHRQ7MB3PBQGZ.json","graph_json":"https://pith.science/api/pith-number/4KEFUAE4GBMYCKHRQ7MB3PBQGZ/graph.json","events_json":"https://pith.science/api/pith-number/4KEFUAE4GBMYCKHRQ7MB3PBQGZ/events.json","paper":"https://pith.science/paper/4KEFUAE4"},"agent_actions":{"view_html":"https://pith.science/pith/4KEFUAE4GBMYCKHRQ7MB3PBQGZ","download_json":"https://pith.science/pith/4KEFUAE4GBMYCKHRQ7MB3PBQGZ.json","view_paper":"https://pith.science/paper/4KEFUAE4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.4126&json=true","fetch_graph":"https://pith.science/api/pith-number/4KEFUAE4GBMYCKHRQ7MB3PBQGZ/graph.json","fetch_events":"https://pith.science/api/pith-number/4KEFUAE4GBMYCKHRQ7MB3PBQGZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4KEFUAE4GBMYCKHRQ7MB3PBQGZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4KEFUAE4GBMYCKHRQ7MB3PBQGZ/action/storage_attestation","attest_author":"https://pith.science/pith/4KEFUAE4GBMYCKHRQ7MB3PBQGZ/action/author_attestation","sign_citation":"https://pith.science/pith/4KEFUAE4GBMYCKHRQ7MB3PBQGZ/action/citation_signature","submit_replication":"https://pith.science/pith/4KEFUAE4GBMYCKHRQ7MB3PBQGZ/action/replication_record"}},"created_at":"2026-05-18T01:12:22.964450+00:00","updated_at":"2026-05-18T01:12:22.964450+00:00"}