{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:K5K7FCVV7VFT7UN4CHGJXDEGHU","short_pith_number":"pith:K5K7FCVV","schema_version":"1.0","canonical_sha256":"5755f28ab5fd4b3fd1bc11cc9b8c863d22b76bec81b5537cc0aef484a8710bd5","source":{"kind":"arxiv","id":"1906.10280","version":1},"attestation_state":"computed","paper":{"title":"The Bose representation of PG(2,q^3) in PG(8,q)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Peter Wild, S.G. Barwick, Wen-Ai Jackson","submitted_at":"2019-06-25T00:37:19Z","abstract_excerpt":"This article looks at the Bose representation of $PG(2,q^3)$ as a 2-spread of $PG(8,q)$. It is shown that an $\\mathbb F_q$-subline of $PG(2,q^3)$ corresponds to a 2-regulus, and an $\\mathbb F_q$-subplane corresponds to a Segre variety $S_{2;2}$. Moreover, the extension of these varieties to $PG(8,q^3)$ and $PG(8,q^6)$ is determined. These are used to determine the structure of an $\\mathbb F_q$-conic of $PG(2,q^3)$ in the Bose representation in $PG(8,q)$."},"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":"1906.10280","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-25T00:37:19Z","cross_cats_sorted":[],"title_canon_sha256":"4fa4de7b0117665f8ecc8936b4e016bf18745651f3422458bc1c477589b232d2","abstract_canon_sha256":"e2a2b0e245c5fc85fc090e29bc6b45abd3aa71fe56b6351b42d162111c263e78"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:31.733548Z","signature_b64":"um9EMydPQshEn5lvxw4r2jmhus1iW7T0zzeGyUyvf3NTtKK1rPmenj+K178UsJjt8d5cMNXiewiyJzgpKWGqCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5755f28ab5fd4b3fd1bc11cc9b8c863d22b76bec81b5537cc0aef484a8710bd5","last_reissued_at":"2026-05-17T23:42:31.732826Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:31.732826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Bose representation of PG(2,q^3) in PG(8,q)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Peter Wild, S.G. Barwick, Wen-Ai Jackson","submitted_at":"2019-06-25T00:37:19Z","abstract_excerpt":"This article looks at the Bose representation of $PG(2,q^3)$ as a 2-spread of $PG(8,q)$. It is shown that an $\\mathbb F_q$-subline of $PG(2,q^3)$ corresponds to a 2-regulus, and an $\\mathbb F_q$-subplane corresponds to a Segre variety $S_{2;2}$. Moreover, the extension of these varieties to $PG(8,q^3)$ and $PG(8,q^6)$ is determined. These are used to determine the structure of an $\\mathbb F_q$-conic of $PG(2,q^3)$ in the Bose representation in $PG(8,q)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10280","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":"1906.10280","created_at":"2026-05-17T23:42:31.732943+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.10280v1","created_at":"2026-05-17T23:42:31.732943+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.10280","created_at":"2026-05-17T23:42:31.732943+00:00"},{"alias_kind":"pith_short_12","alias_value":"K5K7FCVV7VFT","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"K5K7FCVV7VFT7UN4","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"K5K7FCVV","created_at":"2026-05-18T12:33:21.387695+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/K5K7FCVV7VFT7UN4CHGJXDEGHU","json":"https://pith.science/pith/K5K7FCVV7VFT7UN4CHGJXDEGHU.json","graph_json":"https://pith.science/api/pith-number/K5K7FCVV7VFT7UN4CHGJXDEGHU/graph.json","events_json":"https://pith.science/api/pith-number/K5K7FCVV7VFT7UN4CHGJXDEGHU/events.json","paper":"https://pith.science/paper/K5K7FCVV"},"agent_actions":{"view_html":"https://pith.science/pith/K5K7FCVV7VFT7UN4CHGJXDEGHU","download_json":"https://pith.science/pith/K5K7FCVV7VFT7UN4CHGJXDEGHU.json","view_paper":"https://pith.science/paper/K5K7FCVV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.10280&json=true","fetch_graph":"https://pith.science/api/pith-number/K5K7FCVV7VFT7UN4CHGJXDEGHU/graph.json","fetch_events":"https://pith.science/api/pith-number/K5K7FCVV7VFT7UN4CHGJXDEGHU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K5K7FCVV7VFT7UN4CHGJXDEGHU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K5K7FCVV7VFT7UN4CHGJXDEGHU/action/storage_attestation","attest_author":"https://pith.science/pith/K5K7FCVV7VFT7UN4CHGJXDEGHU/action/author_attestation","sign_citation":"https://pith.science/pith/K5K7FCVV7VFT7UN4CHGJXDEGHU/action/citation_signature","submit_replication":"https://pith.science/pith/K5K7FCVV7VFT7UN4CHGJXDEGHU/action/replication_record"}},"created_at":"2026-05-17T23:42:31.732943+00:00","updated_at":"2026-05-17T23:42:31.732943+00:00"}