{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:LRORYNJNMJIIYH3EA4BRHYYXHZ","short_pith_number":"pith:LRORYNJN","schema_version":"1.0","canonical_sha256":"5c5d1c352d62508c1f64070313e3173e5b730ae1e303a06a53ebaaf5a77f45ba","source":{"kind":"arxiv","id":"1512.04818","version":1},"attestation_state":"computed","paper":{"title":"A linear set view on KM-arcs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Geertrui Van de Voorde, Maarten De Boeck","submitted_at":"2015-12-15T15:32:33Z","abstract_excerpt":"In this paper, we study KM-arcs of type t, i.e. point sets of size q + t in PG(2, q) such that every line contains 0, 2 or t of its points. We use field reduction to give a different point of view on the class of translation arcs. Starting from a particular F2-linear set, called an i-club, we reconstruct the projective triads, the translation hyperovals as well as the translation arcs constructed by Korchmaros-Mazzocca, Gacs-Weiner and Limbupasiriporn. We show the KM-arcs of type q/4 recently constructed by Vandendriessche are translation arcs and fit in this family. Finally, we construct a fa"},"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":"1512.04818","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-15T15:32:33Z","cross_cats_sorted":[],"title_canon_sha256":"d48355450cf9d39614cf40f488989f2bfd1acc03cf6ad65e19f93b167cb9e746","abstract_canon_sha256":"963faf696cc0f8fe1678185dbb4815cd4751a3ef2e9affb2f765c0d645205f77"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:53.698129Z","signature_b64":"U4F+0/7peUYZVh1WpFDyJ8Ml4C+RjOwKT5nMCEZMUrUVETKr5mfZa+tWdonkZawF69J1vSKk5puHL2O9ucWsDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c5d1c352d62508c1f64070313e3173e5b730ae1e303a06a53ebaaf5a77f45ba","last_reissued_at":"2026-05-18T01:22:53.697538Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:53.697538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A linear set view on KM-arcs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Geertrui Van de Voorde, Maarten De Boeck","submitted_at":"2015-12-15T15:32:33Z","abstract_excerpt":"In this paper, we study KM-arcs of type t, i.e. point sets of size q + t in PG(2, q) such that every line contains 0, 2 or t of its points. We use field reduction to give a different point of view on the class of translation arcs. Starting from a particular F2-linear set, called an i-club, we reconstruct the projective triads, the translation hyperovals as well as the translation arcs constructed by Korchmaros-Mazzocca, Gacs-Weiner and Limbupasiriporn. We show the KM-arcs of type q/4 recently constructed by Vandendriessche are translation arcs and fit in this family. Finally, we construct a fa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04818","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":""},"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":"1512.04818","created_at":"2026-05-18T01:22:53.697626+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.04818v1","created_at":"2026-05-18T01:22:53.697626+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04818","created_at":"2026-05-18T01:22:53.697626+00:00"},{"alias_kind":"pith_short_12","alias_value":"LRORYNJNMJII","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"LRORYNJNMJIIYH3E","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"LRORYNJN","created_at":"2026-05-18T12:29:29.992203+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/LRORYNJNMJIIYH3EA4BRHYYXHZ","json":"https://pith.science/pith/LRORYNJNMJIIYH3EA4BRHYYXHZ.json","graph_json":"https://pith.science/api/pith-number/LRORYNJNMJIIYH3EA4BRHYYXHZ/graph.json","events_json":"https://pith.science/api/pith-number/LRORYNJNMJIIYH3EA4BRHYYXHZ/events.json","paper":"https://pith.science/paper/LRORYNJN"},"agent_actions":{"view_html":"https://pith.science/pith/LRORYNJNMJIIYH3EA4BRHYYXHZ","download_json":"https://pith.science/pith/LRORYNJNMJIIYH3EA4BRHYYXHZ.json","view_paper":"https://pith.science/paper/LRORYNJN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.04818&json=true","fetch_graph":"https://pith.science/api/pith-number/LRORYNJNMJIIYH3EA4BRHYYXHZ/graph.json","fetch_events":"https://pith.science/api/pith-number/LRORYNJNMJIIYH3EA4BRHYYXHZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LRORYNJNMJIIYH3EA4BRHYYXHZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LRORYNJNMJIIYH3EA4BRHYYXHZ/action/storage_attestation","attest_author":"https://pith.science/pith/LRORYNJNMJIIYH3EA4BRHYYXHZ/action/author_attestation","sign_citation":"https://pith.science/pith/LRORYNJNMJIIYH3EA4BRHYYXHZ/action/citation_signature","submit_replication":"https://pith.science/pith/LRORYNJNMJIIYH3EA4BRHYYXHZ/action/replication_record"}},"created_at":"2026-05-18T01:22:53.697626+00:00","updated_at":"2026-05-18T01:22:53.697626+00:00"}