{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:I4TKF453YZ7R3BWW6XMGAT324X","short_pith_number":"pith:I4TKF453","schema_version":"1.0","canonical_sha256":"4726a2f3bbc67f1d86d6f5d8604f7ae5ffa099f74cc11ba981b7e9431d4eae91","source":{"kind":"arxiv","id":"2409.14213","version":1},"attestation_state":"computed","paper":{"title":"Avoiding secants of given size in finite projective planes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tam\\'as H\\'eger, Zolt\\'an L\\'or\\'ant Nagy","submitted_at":"2024-09-21T18:17:05Z","abstract_excerpt":"Let $q$ be a prime power and $k$ be a natural number. What are the possible cardinalities of point sets ${S}$ in a projective plane of order $q$, which do not intersect any line at exactly $k$ points? This problem and its variants have been investigated before, in relation with blocking sets, untouchable sets or sets of even type, among others. In this paper we show a series of results which point out the existence of all or almost all possible values $m\\in [0, q^2+q+1]$ for $|S|=m$, provided that $k$ is not close to the extremal values $0$ or $q+1$. Moreover, using polynomial techniques we sh"},"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":"2409.14213","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-09-21T18:17:05Z","cross_cats_sorted":[],"title_canon_sha256":"9c329fe41c7aa9b6d04acfa0cb16fddbef05b7bf274684dd1e185faa3c6f9f4a","abstract_canon_sha256":"2ed4089fd8cddd06a0d04d7ef5f6af04bb99c08914f85e236f1f2ea0f9bf8d22"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:10:13.396284Z","signature_b64":"OyNWGqBYYvNFeXYZjlu18lJoAxm9tMFEP73IkWywGDz/gzbenBF3j6+rHgDEh+BBpxmcAr6Hz6DXzdnlKeX+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4726a2f3bbc67f1d86d6f5d8604f7ae5ffa099f74cc11ba981b7e9431d4eae91","last_reissued_at":"2026-07-05T09:10:13.395796Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:10:13.395796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Avoiding secants of given size in finite projective planes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tam\\'as H\\'eger, Zolt\\'an L\\'or\\'ant Nagy","submitted_at":"2024-09-21T18:17:05Z","abstract_excerpt":"Let $q$ be a prime power and $k$ be a natural number. What are the possible cardinalities of point sets ${S}$ in a projective plane of order $q$, which do not intersect any line at exactly $k$ points? This problem and its variants have been investigated before, in relation with blocking sets, untouchable sets or sets of even type, among others. In this paper we show a series of results which point out the existence of all or almost all possible values $m\\in [0, q^2+q+1]$ for $|S|=m$, provided that $k$ is not close to the extremal values $0$ or $q+1$. Moreover, using polynomial techniques we sh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.14213","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/2409.14213/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":"2409.14213","created_at":"2026-07-05T09:10:13.395857+00:00"},{"alias_kind":"arxiv_version","alias_value":"2409.14213v1","created_at":"2026-07-05T09:10:13.395857+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.14213","created_at":"2026-07-05T09:10:13.395857+00:00"},{"alias_kind":"pith_short_12","alias_value":"I4TKF453YZ7R","created_at":"2026-07-05T09:10:13.395857+00:00"},{"alias_kind":"pith_short_16","alias_value":"I4TKF453YZ7R3BWW","created_at":"2026-07-05T09:10:13.395857+00:00"},{"alias_kind":"pith_short_8","alias_value":"I4TKF453","created_at":"2026-07-05T09:10:13.395857+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2412.14615","citing_title":"Additive codes attaining the Griesmer bound","ref_index":58,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/I4TKF453YZ7R3BWW6XMGAT324X","json":"https://pith.science/pith/I4TKF453YZ7R3BWW6XMGAT324X.json","graph_json":"https://pith.science/api/pith-number/I4TKF453YZ7R3BWW6XMGAT324X/graph.json","events_json":"https://pith.science/api/pith-number/I4TKF453YZ7R3BWW6XMGAT324X/events.json","paper":"https://pith.science/paper/I4TKF453"},"agent_actions":{"view_html":"https://pith.science/pith/I4TKF453YZ7R3BWW6XMGAT324X","download_json":"https://pith.science/pith/I4TKF453YZ7R3BWW6XMGAT324X.json","view_paper":"https://pith.science/paper/I4TKF453","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2409.14213&json=true","fetch_graph":"https://pith.science/api/pith-number/I4TKF453YZ7R3BWW6XMGAT324X/graph.json","fetch_events":"https://pith.science/api/pith-number/I4TKF453YZ7R3BWW6XMGAT324X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I4TKF453YZ7R3BWW6XMGAT324X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I4TKF453YZ7R3BWW6XMGAT324X/action/storage_attestation","attest_author":"https://pith.science/pith/I4TKF453YZ7R3BWW6XMGAT324X/action/author_attestation","sign_citation":"https://pith.science/pith/I4TKF453YZ7R3BWW6XMGAT324X/action/citation_signature","submit_replication":"https://pith.science/pith/I4TKF453YZ7R3BWW6XMGAT324X/action/replication_record"}},"created_at":"2026-07-05T09:10:13.395857+00:00","updated_at":"2026-07-05T09:10:13.395857+00:00"}