{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:U3RKKZZQ6QQKKPX75425SUO7DA","short_pith_number":"pith:U3RKKZZQ","schema_version":"1.0","canonical_sha256":"a6e2a56730f420a53effef35d951df183cf0e8426db1614b04327336b8db1b28","source":{"kind":"arxiv","id":"1611.09331","version":4},"attestation_state":"computed","paper":{"title":"Characterizing circles by a convex combinatorial property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"G\\'abor Cz\\'edli","submitted_at":"2016-11-28T20:37:03Z","abstract_excerpt":"Let $K_0$ be a compact convex subset of the plane $\\mathbb R^2$, and assume that $K_1\\subseteq \\mathbb R^2$ is similar to $K_0$, that is, $K_1$ is the image of $K_0$ with respect to a similarity transformation $\\mathbb R^2\\to\\mathbb R^2$. Kira Adaricheva and Madina Bolat have recently proved that if $K_0$ is a disk and both $K_0$ and $K_1$ are included in a triangle with vertices $A_0$, $A_1$, and $A_2$, then there exist a $j\\in \\{0,1,2\\}$ and a $k\\in\\{0,1\\}$ such that $K_{1-k}$ is included in the convex hull of $K_k\\cup(\\{A_0,A_1, A_2\\}\\setminus\\{A_j\\})$. Here we prove that this property char"},"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":"1611.09331","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-11-28T20:37:03Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"d91834d97f5663758b857cd64f824c06b937885a70442dbdab46d825dabc90b2","abstract_canon_sha256":"93fb0b046f43b925c2d47981d89cc6fe2cc9892c512993ed5b057ad15cfa5034"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:47.134618Z","signature_b64":"pMJn8YSOSdP/pIZm4vbk9q3py/ouiGKSNXE/T+6R+RqE2DPrdS3TNzb28pPLxcyYgGl5BjNpOjzS3KeT/RdKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6e2a56730f420a53effef35d951df183cf0e8426db1614b04327336b8db1b28","last_reissued_at":"2026-05-18T00:39:47.133870Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:47.133870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterizing circles by a convex combinatorial property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"G\\'abor Cz\\'edli","submitted_at":"2016-11-28T20:37:03Z","abstract_excerpt":"Let $K_0$ be a compact convex subset of the plane $\\mathbb R^2$, and assume that $K_1\\subseteq \\mathbb R^2$ is similar to $K_0$, that is, $K_1$ is the image of $K_0$ with respect to a similarity transformation $\\mathbb R^2\\to\\mathbb R^2$. Kira Adaricheva and Madina Bolat have recently proved that if $K_0$ is a disk and both $K_0$ and $K_1$ are included in a triangle with vertices $A_0$, $A_1$, and $A_2$, then there exist a $j\\in \\{0,1,2\\}$ and a $k\\in\\{0,1\\}$ such that $K_{1-k}$ is included in the convex hull of $K_k\\cup(\\{A_0,A_1, A_2\\}\\setminus\\{A_j\\})$. Here we prove that this property char"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09331","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":"1611.09331","created_at":"2026-05-18T00:39:47.133995+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.09331v4","created_at":"2026-05-18T00:39:47.133995+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09331","created_at":"2026-05-18T00:39:47.133995+00:00"},{"alias_kind":"pith_short_12","alias_value":"U3RKKZZQ6QQK","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"U3RKKZZQ6QQKKPX7","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"U3RKKZZQ","created_at":"2026-05-18T12:30:46.583412+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/U3RKKZZQ6QQKKPX75425SUO7DA","json":"https://pith.science/pith/U3RKKZZQ6QQKKPX75425SUO7DA.json","graph_json":"https://pith.science/api/pith-number/U3RKKZZQ6QQKKPX75425SUO7DA/graph.json","events_json":"https://pith.science/api/pith-number/U3RKKZZQ6QQKKPX75425SUO7DA/events.json","paper":"https://pith.science/paper/U3RKKZZQ"},"agent_actions":{"view_html":"https://pith.science/pith/U3RKKZZQ6QQKKPX75425SUO7DA","download_json":"https://pith.science/pith/U3RKKZZQ6QQKKPX75425SUO7DA.json","view_paper":"https://pith.science/paper/U3RKKZZQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.09331&json=true","fetch_graph":"https://pith.science/api/pith-number/U3RKKZZQ6QQKKPX75425SUO7DA/graph.json","fetch_events":"https://pith.science/api/pith-number/U3RKKZZQ6QQKKPX75425SUO7DA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U3RKKZZQ6QQKKPX75425SUO7DA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U3RKKZZQ6QQKKPX75425SUO7DA/action/storage_attestation","attest_author":"https://pith.science/pith/U3RKKZZQ6QQKKPX75425SUO7DA/action/author_attestation","sign_citation":"https://pith.science/pith/U3RKKZZQ6QQKKPX75425SUO7DA/action/citation_signature","submit_replication":"https://pith.science/pith/U3RKKZZQ6QQKKPX75425SUO7DA/action/replication_record"}},"created_at":"2026-05-18T00:39:47.133995+00:00","updated_at":"2026-05-18T00:39:47.133995+00:00"}