{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:AZGNNQQ3JTLRXTPOMAJS57MLTG","short_pith_number":"pith:AZGNNQQ3","schema_version":"1.0","canonical_sha256":"064cd6c21b4cd71bcdee60132efd8b99a1dc14d34c71f61fbcffd93030b0e9ba","source":{"kind":"arxiv","id":"1007.1375","version":2},"attestation_state":"computed","paper":{"title":"Simple wedge points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shimon Garti","submitted_at":"2010-07-08T13:47:27Z","abstract_excerpt":"Let V be a finite set of points in the plane, not contained in a line. Assume |V| = n is an odd number, and |L \\cap V| \\leq 3 for every line L which is spanned by V. We prove that every simple line L_{a,b} in V creates a simple wedge (i.e., a triple {a, b, c} \\subseteq V such that L_{a,b} and L_{a,c} are simple lines). We also show that both restrictions on V (namely |V| is odd and |L \\cap V| \\leq 3) are needed.\nWe conjecture, further, that if |V | = n is an odd number then V contains a simple wedge, even if V is not 3-bounded. We introduce a method for proving this, which gives (in this paper"},"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":"1007.1375","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-07-08T13:47:27Z","cross_cats_sorted":[],"title_canon_sha256":"96a564812dba6b9c675d928f40f1e6f76fcf0c45b0100a921a501690d77d902c","abstract_canon_sha256":"7fb7f1e9d6e51153e65e394b90e9118aa28d7d3ebee451a47fa950cc31e67efc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:05.549895Z","signature_b64":"3sfQEWbUyDmgiH9TkVfTH5uFVSvYPFwBrBcWyUOICeFs6u81t5aDsFzRJT1vZhACtQIV/EoyK04cEpeTUhFSAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"064cd6c21b4cd71bcdee60132efd8b99a1dc14d34c71f61fbcffd93030b0e9ba","last_reissued_at":"2026-05-18T03:46:05.549443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:05.549443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simple wedge points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shimon Garti","submitted_at":"2010-07-08T13:47:27Z","abstract_excerpt":"Let V be a finite set of points in the plane, not contained in a line. Assume |V| = n is an odd number, and |L \\cap V| \\leq 3 for every line L which is spanned by V. We prove that every simple line L_{a,b} in V creates a simple wedge (i.e., a triple {a, b, c} \\subseteq V such that L_{a,b} and L_{a,c} are simple lines). We also show that both restrictions on V (namely |V| is odd and |L \\cap V| \\leq 3) are needed.\nWe conjecture, further, that if |V | = n is an odd number then V contains a simple wedge, even if V is not 3-bounded. We introduce a method for proving this, which gives (in this paper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1375","kind":"arxiv","version":2},"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":"1007.1375","created_at":"2026-05-18T03:46:05.549516+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.1375v2","created_at":"2026-05-18T03:46:05.549516+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.1375","created_at":"2026-05-18T03:46:05.549516+00:00"},{"alias_kind":"pith_short_12","alias_value":"AZGNNQQ3JTLR","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"AZGNNQQ3JTLRXTPO","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"AZGNNQQ3","created_at":"2026-05-18T12:26:05.355336+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/AZGNNQQ3JTLRXTPOMAJS57MLTG","json":"https://pith.science/pith/AZGNNQQ3JTLRXTPOMAJS57MLTG.json","graph_json":"https://pith.science/api/pith-number/AZGNNQQ3JTLRXTPOMAJS57MLTG/graph.json","events_json":"https://pith.science/api/pith-number/AZGNNQQ3JTLRXTPOMAJS57MLTG/events.json","paper":"https://pith.science/paper/AZGNNQQ3"},"agent_actions":{"view_html":"https://pith.science/pith/AZGNNQQ3JTLRXTPOMAJS57MLTG","download_json":"https://pith.science/pith/AZGNNQQ3JTLRXTPOMAJS57MLTG.json","view_paper":"https://pith.science/paper/AZGNNQQ3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.1375&json=true","fetch_graph":"https://pith.science/api/pith-number/AZGNNQQ3JTLRXTPOMAJS57MLTG/graph.json","fetch_events":"https://pith.science/api/pith-number/AZGNNQQ3JTLRXTPOMAJS57MLTG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AZGNNQQ3JTLRXTPOMAJS57MLTG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AZGNNQQ3JTLRXTPOMAJS57MLTG/action/storage_attestation","attest_author":"https://pith.science/pith/AZGNNQQ3JTLRXTPOMAJS57MLTG/action/author_attestation","sign_citation":"https://pith.science/pith/AZGNNQQ3JTLRXTPOMAJS57MLTG/action/citation_signature","submit_replication":"https://pith.science/pith/AZGNNQQ3JTLRXTPOMAJS57MLTG/action/replication_record"}},"created_at":"2026-05-18T03:46:05.549516+00:00","updated_at":"2026-05-18T03:46:05.549516+00:00"}