{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:KNAFRPKMXPJXJ6SQL7KEXNS6YZ","short_pith_number":"pith:KNAFRPKM","schema_version":"1.0","canonical_sha256":"534058bd4cbbd374fa505fd44bb65ec64fd8c243e6a22590bfac5dc0a41ea429","source":{"kind":"arxiv","id":"1410.4269","version":1},"attestation_state":"computed","paper":{"title":"The exterior splash in $PG(6,q)$: Special conics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"S.G. Barwick, Wen-Ai Jackson","submitted_at":"2014-10-16T01:42:34Z","abstract_excerpt":"Let $\\pi$ be an order-$q$-subplane of $PG(2,q^3)$ that is exterior to $\\ell_\\infty$. The exterior splash of $\\pi$ is the set of $q^2+q+1$ points on $\\ell_\\infty$ that lie on an extended line of $\\pi$. Exterior splashes are projectively equivalent to scattered linear sets of rank 3, covers of the circle geometry $CG(3,q)$, and hyper-reguli of $PG(5,q)$. In this article we use the Bruck-Bose representation in $PG(6,q)$ to give a geometric characterisation of special conics of $\\pi$ in terms of the covers of the exterior splash of $\\pi$. We also investigate properties of order-$q$-subplanes\\ with"},"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":"1410.4269","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-16T01:42:34Z","cross_cats_sorted":[],"title_canon_sha256":"70672a9343479bf327cf2a7f3362ffb68302ade405ef3b9ebacd1e3207f9c46d","abstract_canon_sha256":"0bc3654dad235f302e91e2805130f1851914e38133a2cc38bed886ae052f40e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:56.545510Z","signature_b64":"eihKJEsBXSildrabH6Fj8q/jHV3omFzqr0ROOcoTNDLVDnRMYYf7m48PPzmTTDlb3O+tfhJR5hq20OJNvGL5CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"534058bd4cbbd374fa505fd44bb65ec64fd8c243e6a22590bfac5dc0a41ea429","last_reissued_at":"2026-05-18T02:39:56.545059Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:56.545059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The exterior splash in $PG(6,q)$: Special conics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"S.G. Barwick, Wen-Ai Jackson","submitted_at":"2014-10-16T01:42:34Z","abstract_excerpt":"Let $\\pi$ be an order-$q$-subplane of $PG(2,q^3)$ that is exterior to $\\ell_\\infty$. The exterior splash of $\\pi$ is the set of $q^2+q+1$ points on $\\ell_\\infty$ that lie on an extended line of $\\pi$. Exterior splashes are projectively equivalent to scattered linear sets of rank 3, covers of the circle geometry $CG(3,q)$, and hyper-reguli of $PG(5,q)$. In this article we use the Bruck-Bose representation in $PG(6,q)$ to give a geometric characterisation of special conics of $\\pi$ in terms of the covers of the exterior splash of $\\pi$. We also investigate properties of order-$q$-subplanes\\ with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4269","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":"1410.4269","created_at":"2026-05-18T02:39:56.545125+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.4269v1","created_at":"2026-05-18T02:39:56.545125+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.4269","created_at":"2026-05-18T02:39:56.545125+00:00"},{"alias_kind":"pith_short_12","alias_value":"KNAFRPKMXPJX","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"KNAFRPKMXPJXJ6SQ","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"KNAFRPKM","created_at":"2026-05-18T12:28:35.611951+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/KNAFRPKMXPJXJ6SQL7KEXNS6YZ","json":"https://pith.science/pith/KNAFRPKMXPJXJ6SQL7KEXNS6YZ.json","graph_json":"https://pith.science/api/pith-number/KNAFRPKMXPJXJ6SQL7KEXNS6YZ/graph.json","events_json":"https://pith.science/api/pith-number/KNAFRPKMXPJXJ6SQL7KEXNS6YZ/events.json","paper":"https://pith.science/paper/KNAFRPKM"},"agent_actions":{"view_html":"https://pith.science/pith/KNAFRPKMXPJXJ6SQL7KEXNS6YZ","download_json":"https://pith.science/pith/KNAFRPKMXPJXJ6SQL7KEXNS6YZ.json","view_paper":"https://pith.science/paper/KNAFRPKM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.4269&json=true","fetch_graph":"https://pith.science/api/pith-number/KNAFRPKMXPJXJ6SQL7KEXNS6YZ/graph.json","fetch_events":"https://pith.science/api/pith-number/KNAFRPKMXPJXJ6SQL7KEXNS6YZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KNAFRPKMXPJXJ6SQL7KEXNS6YZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KNAFRPKMXPJXJ6SQL7KEXNS6YZ/action/storage_attestation","attest_author":"https://pith.science/pith/KNAFRPKMXPJXJ6SQL7KEXNS6YZ/action/author_attestation","sign_citation":"https://pith.science/pith/KNAFRPKMXPJXJ6SQL7KEXNS6YZ/action/citation_signature","submit_replication":"https://pith.science/pith/KNAFRPKMXPJXJ6SQL7KEXNS6YZ/action/replication_record"}},"created_at":"2026-05-18T02:39:56.545125+00:00","updated_at":"2026-05-18T02:39:56.545125+00:00"}