{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:ISG75LN5N6JFED4Y7BDG5IPT2Y","short_pith_number":"pith:ISG75LN5","schema_version":"1.0","canonical_sha256":"448dfeadbd6f92520f98f8466ea1f3d6046ddb8f19371e9e28800eec4261684e","source":{"kind":"arxiv","id":"1011.0517","version":3},"attestation_state":"computed","paper":{"title":"Holes or Empty Pseudo-Triangles in Planar Point Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Bhaswar B. Bhattacharya, Sandip Das","submitted_at":"2010-11-02T05:52:05Z","abstract_excerpt":"Let $E(k, \\ell)$ denote the smallest integer such that any set of at least $E(k, \\ell)$ points in the plane, no three on a line, contains either an empty convex polygon with $k$ vertices or an empty pseudo-triangle with $\\ell$ vertices. The existence of $E(k, \\ell)$ for positive integers $k, \\ell\\geq 3$, is the consequence of a result proved by Valtr [Discrete and Computational Geometry, Vol. 37, 565--576, 2007]. In this paper, following a series of new results about the existence of empty pseudo-triangles in point sets with triangular convex hulls, we determine the exact values of $E(k, 5)$ a"},"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":"1011.0517","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-11-02T05:52:05Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"5e368f4fe49ec0157734131d1e359ae900e26f6d33edbb951f31ab4e3f8a9c3d","abstract_canon_sha256":"75a2a92092de178dc5b8d910d0c7cf46f08af4d27ad4a5217f5ec5287d996114"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:05.433592Z","signature_b64":"cjrfOoxgN/ej+n9Dr2KJYR6qoxm5mddExrrqJ1e/vWut1ji7Dv/kKhdfb730jGsu98j7T3dmOLdITzLSfGoQBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"448dfeadbd6f92520f98f8466ea1f3d6046ddb8f19371e9e28800eec4261684e","last_reissued_at":"2026-05-18T03:43:05.432897Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:05.432897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Holes or Empty Pseudo-Triangles in Planar Point Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Bhaswar B. Bhattacharya, Sandip Das","submitted_at":"2010-11-02T05:52:05Z","abstract_excerpt":"Let $E(k, \\ell)$ denote the smallest integer such that any set of at least $E(k, \\ell)$ points in the plane, no three on a line, contains either an empty convex polygon with $k$ vertices or an empty pseudo-triangle with $\\ell$ vertices. The existence of $E(k, \\ell)$ for positive integers $k, \\ell\\geq 3$, is the consequence of a result proved by Valtr [Discrete and Computational Geometry, Vol. 37, 565--576, 2007]. In this paper, following a series of new results about the existence of empty pseudo-triangles in point sets with triangular convex hulls, we determine the exact values of $E(k, 5)$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0517","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":"1011.0517","created_at":"2026-05-18T03:43:05.433007+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.0517v3","created_at":"2026-05-18T03:43:05.433007+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.0517","created_at":"2026-05-18T03:43:05.433007+00:00"},{"alias_kind":"pith_short_12","alias_value":"ISG75LN5N6JF","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"ISG75LN5N6JFED4Y","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"ISG75LN5","created_at":"2026-05-18T12:26:09.077623+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/ISG75LN5N6JFED4Y7BDG5IPT2Y","json":"https://pith.science/pith/ISG75LN5N6JFED4Y7BDG5IPT2Y.json","graph_json":"https://pith.science/api/pith-number/ISG75LN5N6JFED4Y7BDG5IPT2Y/graph.json","events_json":"https://pith.science/api/pith-number/ISG75LN5N6JFED4Y7BDG5IPT2Y/events.json","paper":"https://pith.science/paper/ISG75LN5"},"agent_actions":{"view_html":"https://pith.science/pith/ISG75LN5N6JFED4Y7BDG5IPT2Y","download_json":"https://pith.science/pith/ISG75LN5N6JFED4Y7BDG5IPT2Y.json","view_paper":"https://pith.science/paper/ISG75LN5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.0517&json=true","fetch_graph":"https://pith.science/api/pith-number/ISG75LN5N6JFED4Y7BDG5IPT2Y/graph.json","fetch_events":"https://pith.science/api/pith-number/ISG75LN5N6JFED4Y7BDG5IPT2Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ISG75LN5N6JFED4Y7BDG5IPT2Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ISG75LN5N6JFED4Y7BDG5IPT2Y/action/storage_attestation","attest_author":"https://pith.science/pith/ISG75LN5N6JFED4Y7BDG5IPT2Y/action/author_attestation","sign_citation":"https://pith.science/pith/ISG75LN5N6JFED4Y7BDG5IPT2Y/action/citation_signature","submit_replication":"https://pith.science/pith/ISG75LN5N6JFED4Y7BDG5IPT2Y/action/replication_record"}},"created_at":"2026-05-18T03:43:05.433007+00:00","updated_at":"2026-05-18T03:43:05.433007+00:00"}