{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:QL3RLT5XA64VFQOGLVIICYYZS7","short_pith_number":"pith:QL3RLT5X","schema_version":"1.0","canonical_sha256":"82f715cfb707b952c1c65d5081631997ef2d4ddad43fc6e2c59020b44b1725cd","source":{"kind":"arxiv","id":"2412.14287","version":1},"attestation_state":"computed","paper":{"title":"Subset Selection Problems in Planar Point Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"Adrian Dumitrescu, Dingyuan Liu, Felix Christian Clemen, J\\'ozsef Balogh","submitted_at":"2024-12-18T19:30:27Z","abstract_excerpt":"Given a finite set satisfying condition $\\mathcal{A}$, the subset selection problem asks, how large of a subset satisfying condition $\\mathcal{B}$ can we find? We make progress on three instances of subset selection problems in planar point sets. Let $n,s\\in\\mathbb{N}$ with $n\\geq s$, and let $P\\subseteq\\mathbb{R}^2$ be a set of $n$ points, where at most $s$ points lie on the same line.\n  Firstly, we select a general position subset of $P$, i.e., a subset containing no $3$ points on the same line. This problem was proposed by Erd\\H{o}s under the regime when $s$ is a constant. For $s$ being non"},"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":"2412.14287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-12-18T19:30:27Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"de764e00e675c5a696907d92ea4d6847c715ebf10d36b69d0c43d85cc5aa69e1","abstract_canon_sha256":"b5b215e14555a3d04b009f01a6c8917402135883a5beec34cf73364ec2202bee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:51:45.200954Z","signature_b64":"gXCPKwj4I71Oskd2hHhD9BCRlRMVCAwCfWZF0Mvp7fZnMHWcxMCOWr519TH4pzmha5A//ZDgUl8waiKQicafDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82f715cfb707b952c1c65d5081631997ef2d4ddad43fc6e2c59020b44b1725cd","last_reissued_at":"2026-07-05T09:51:45.200364Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:51:45.200364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subset Selection Problems in Planar Point Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"Adrian Dumitrescu, Dingyuan Liu, Felix Christian Clemen, J\\'ozsef Balogh","submitted_at":"2024-12-18T19:30:27Z","abstract_excerpt":"Given a finite set satisfying condition $\\mathcal{A}$, the subset selection problem asks, how large of a subset satisfying condition $\\mathcal{B}$ can we find? We make progress on three instances of subset selection problems in planar point sets. Let $n,s\\in\\mathbb{N}$ with $n\\geq s$, and let $P\\subseteq\\mathbb{R}^2$ be a set of $n$ points, where at most $s$ points lie on the same line.\n  Firstly, we select a general position subset of $P$, i.e., a subset containing no $3$ points on the same line. This problem was proposed by Erd\\H{o}s under the regime when $s$ is a constant. For $s$ being non"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.14287","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.14287/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2412.14287","created_at":"2026-07-05T09:51:45.200427+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.14287v1","created_at":"2026-07-05T09:51:45.200427+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.14287","created_at":"2026-07-05T09:51:45.200427+00:00"},{"alias_kind":"pith_short_12","alias_value":"QL3RLT5XA64V","created_at":"2026-07-05T09:51:45.200427+00:00"},{"alias_kind":"pith_short_16","alias_value":"QL3RLT5XA64VFQOG","created_at":"2026-07-05T09:51:45.200427+00:00"},{"alias_kind":"pith_short_8","alias_value":"QL3RLT5X","created_at":"2026-07-05T09:51:45.200427+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.05841","citing_title":"Geometric Sidon Problems","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2605.22752","citing_title":"Lines in the prime number graph","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2605.09215","citing_title":"No-three-in-line sets on the checkerboard grid","ref_index":4,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QL3RLT5XA64VFQOGLVIICYYZS7","json":"https://pith.science/pith/QL3RLT5XA64VFQOGLVIICYYZS7.json","graph_json":"https://pith.science/api/pith-number/QL3RLT5XA64VFQOGLVIICYYZS7/graph.json","events_json":"https://pith.science/api/pith-number/QL3RLT5XA64VFQOGLVIICYYZS7/events.json","paper":"https://pith.science/paper/QL3RLT5X"},"agent_actions":{"view_html":"https://pith.science/pith/QL3RLT5XA64VFQOGLVIICYYZS7","download_json":"https://pith.science/pith/QL3RLT5XA64VFQOGLVIICYYZS7.json","view_paper":"https://pith.science/paper/QL3RLT5X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.14287&json=true","fetch_graph":"https://pith.science/api/pith-number/QL3RLT5XA64VFQOGLVIICYYZS7/graph.json","fetch_events":"https://pith.science/api/pith-number/QL3RLT5XA64VFQOGLVIICYYZS7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QL3RLT5XA64VFQOGLVIICYYZS7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QL3RLT5XA64VFQOGLVIICYYZS7/action/storage_attestation","attest_author":"https://pith.science/pith/QL3RLT5XA64VFQOGLVIICYYZS7/action/author_attestation","sign_citation":"https://pith.science/pith/QL3RLT5XA64VFQOGLVIICYYZS7/action/citation_signature","submit_replication":"https://pith.science/pith/QL3RLT5XA64VFQOGLVIICYYZS7/action/replication_record"}},"created_at":"2026-07-05T09:51:45.200427+00:00","updated_at":"2026-07-05T09:51:45.200427+00:00"}