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Pseudo-arcs of size $q^n+1$ are called pseudo-ovals, while pseudo-arcs of size $q^n+2$ are called pseudo-hyperovals. A pseudo-arc is called elementary if it arises from applying field reduction to an arc in $\\mathrm{PG}(2,q^n)$.\n  We explain the connection between dual pseudo-ovals and elation Laguerre planes and show that an elation Laguerre plane is ovoidal if and only if it arises from an elem"},"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":"1407.8415","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-31T13:55:54Z","cross_cats_sorted":[],"title_canon_sha256":"96e708070249ed1e216f61a0fac49f6d4ccb1b78d2b7216ac3c0d475929271f2","abstract_canon_sha256":"f011d31ee18d1d21846d270535504464374fd430d8f184c6ca4a9123bb55fa8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:05.164269Z","signature_b64":"mkLfB4vE1Kc4Qk4IOvVGL8ArkILnr/+INc2xpbfOYDwaDbKx6J9tNycX/Rfzh3cLVYquyk1u5EHGsdY3S+hXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46366c1a7b51a80e3e8460c8e7e1525877c621a5ce9475ebca2c57869f1aeb87","last_reissued_at":"2026-05-18T02:46:05.163704Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:05.163704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pseudo-ovals in even characteristic and ovoidal Laguerre planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Geertrui Van de Voorde, Sara Rottey","submitted_at":"2014-07-31T13:55:54Z","abstract_excerpt":"Pseudo-arcs are the higher dimensional analogues of arcs in a projective plane: a pseudo-arc is a set $\\mathcal{A}$ of $(n-1)$-spaces in $\\mathrm{PG}(3n-1,q)$ such that any three span the whole space. 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A pseudo-arc is called elementary if it arises from applying field reduction to an arc in $\\mathrm{PG}(2,q^n)$.\n  We explain the connection between dual pseudo-ovals and elation Laguerre planes and show that an elation Laguerre plane is ovoidal if and only if it arises from an elem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.8415","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":"1407.8415","created_at":"2026-05-18T02:46:05.163788+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.8415v1","created_at":"2026-05-18T02:46:05.163788+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.8415","created_at":"2026-05-18T02:46:05.163788+00:00"},{"alias_kind":"pith_short_12","alias_value":"IY3GYGT3KGUA","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"IY3GYGT3KGUA4PUE","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"IY3GYGT3","created_at":"2026-05-18T12:28:33.132498+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/IY3GYGT3KGUA4PUEMDEOPYKSLB","json":"https://pith.science/pith/IY3GYGT3KGUA4PUEMDEOPYKSLB.json","graph_json":"https://pith.science/api/pith-number/IY3GYGT3KGUA4PUEMDEOPYKSLB/graph.json","events_json":"https://pith.science/api/pith-number/IY3GYGT3KGUA4PUEMDEOPYKSLB/events.json","paper":"https://pith.science/paper/IY3GYGT3"},"agent_actions":{"view_html":"https://pith.science/pith/IY3GYGT3KGUA4PUEMDEOPYKSLB","download_json":"https://pith.science/pith/IY3GYGT3KGUA4PUEMDEOPYKSLB.json","view_paper":"https://pith.science/paper/IY3GYGT3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.8415&json=true","fetch_graph":"https://pith.science/api/pith-number/IY3GYGT3KGUA4PUEMDEOPYKSLB/graph.json","fetch_events":"https://pith.science/api/pith-number/IY3GYGT3KGUA4PUEMDEOPYKSLB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IY3GYGT3KGUA4PUEMDEOPYKSLB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IY3GYGT3KGUA4PUEMDEOPYKSLB/action/storage_attestation","attest_author":"https://pith.science/pith/IY3GYGT3KGUA4PUEMDEOPYKSLB/action/author_attestation","sign_citation":"https://pith.science/pith/IY3GYGT3KGUA4PUEMDEOPYKSLB/action/citation_signature","submit_replication":"https://pith.science/pith/IY3GYGT3KGUA4PUEMDEOPYKSLB/action/replication_record"}},"created_at":"2026-05-18T02:46:05.163788+00:00","updated_at":"2026-05-18T02:46:05.163788+00:00"}