{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:FBAOIJM3SQTRSVJA2WGCIPSEZV","short_pith_number":"pith:FBAOIJM3","schema_version":"1.0","canonical_sha256":"2840e4259b9427195520d58c243e44cd7544b598daffa45fdbca1e0523166b6d","source":{"kind":"arxiv","id":"2503.18262","version":1},"attestation_state":"computed","paper":{"title":"The partition of $PG(2,q^3)$ arising from an order 3 planar collineation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alice M.W. Hui, S.G. Barwick, Wen-Ai Jackson","submitted_at":"2025-03-24T01:12:03Z","abstract_excerpt":"Let $\\phi$ be a collineation of order 3 acting on $PG(2,q^3)$ whose fixed points are exactly an $\\mathbb F_q$-plane $\\pi_q$. Let $T$ be a point whose orbit under $\\phi$ is a triangle and let $S_G$ be the subgroup of $PGL(3,q^3)$ that fixes setwise the $\\mathbb F_q$-plane $\\pi_q$ and fixes setwise the line $T^\\phi T^{\\phi^2}$. The point orbits of $S_G$ form a partition of the points of $PG(2,q^3)$ and consist of: the singletons $T,T^\\phi, T^{\\phi^2}$; scattered linear sets on the sides of the triangle $T T^\\phi T^{\\phi^2}$; and $\\mathbb F_q$-planes.\n  This article studies the structure of this "},"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":"2503.18262","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-03-24T01:12:03Z","cross_cats_sorted":[],"title_canon_sha256":"02240ce767243b65d233e371b672a8db45bcb137d4992af413d6a3c6a3ddaa55","abstract_canon_sha256":"cd8f7882ab181e5534d8fa994163cc839fa1797f0e28f883e109f4e07e9ee029"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:38:06.267746Z","signature_b64":"6OwE3WcQSlNvk/Vs7VWSI5cx3FTJuZNkf7r7yoI4Typq5fH7v+e86iBUP4LAJ0XCdY+N4Qhnzb60iP+g90QICQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2840e4259b9427195520d58c243e44cd7544b598daffa45fdbca1e0523166b6d","last_reissued_at":"2026-07-05T10:38:06.266935Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:38:06.266935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The partition of $PG(2,q^3)$ arising from an order 3 planar collineation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alice M.W. Hui, S.G. Barwick, Wen-Ai Jackson","submitted_at":"2025-03-24T01:12:03Z","abstract_excerpt":"Let $\\phi$ be a collineation of order 3 acting on $PG(2,q^3)$ whose fixed points are exactly an $\\mathbb F_q$-plane $\\pi_q$. Let $T$ be a point whose orbit under $\\phi$ is a triangle and let $S_G$ be the subgroup of $PGL(3,q^3)$ that fixes setwise the $\\mathbb F_q$-plane $\\pi_q$ and fixes setwise the line $T^\\phi T^{\\phi^2}$. The point orbits of $S_G$ form a partition of the points of $PG(2,q^3)$ and consist of: the singletons $T,T^\\phi, T^{\\phi^2}$; scattered linear sets on the sides of the triangle $T T^\\phi T^{\\phi^2}$; and $\\mathbb F_q$-planes.\n  This article studies the structure of this "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.18262","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/2503.18262/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":"2503.18262","created_at":"2026-07-05T10:38:06.267061+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.18262v1","created_at":"2026-07-05T10:38:06.267061+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.18262","created_at":"2026-07-05T10:38:06.267061+00:00"},{"alias_kind":"pith_short_12","alias_value":"FBAOIJM3SQTR","created_at":"2026-07-05T10:38:06.267061+00:00"},{"alias_kind":"pith_short_16","alias_value":"FBAOIJM3SQTRSVJA","created_at":"2026-07-05T10:38:06.267061+00:00"},{"alias_kind":"pith_short_8","alias_value":"FBAOIJM3","created_at":"2026-07-05T10:38:06.267061+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/FBAOIJM3SQTRSVJA2WGCIPSEZV","json":"https://pith.science/pith/FBAOIJM3SQTRSVJA2WGCIPSEZV.json","graph_json":"https://pith.science/api/pith-number/FBAOIJM3SQTRSVJA2WGCIPSEZV/graph.json","events_json":"https://pith.science/api/pith-number/FBAOIJM3SQTRSVJA2WGCIPSEZV/events.json","paper":"https://pith.science/paper/FBAOIJM3"},"agent_actions":{"view_html":"https://pith.science/pith/FBAOIJM3SQTRSVJA2WGCIPSEZV","download_json":"https://pith.science/pith/FBAOIJM3SQTRSVJA2WGCIPSEZV.json","view_paper":"https://pith.science/paper/FBAOIJM3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.18262&json=true","fetch_graph":"https://pith.science/api/pith-number/FBAOIJM3SQTRSVJA2WGCIPSEZV/graph.json","fetch_events":"https://pith.science/api/pith-number/FBAOIJM3SQTRSVJA2WGCIPSEZV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FBAOIJM3SQTRSVJA2WGCIPSEZV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FBAOIJM3SQTRSVJA2WGCIPSEZV/action/storage_attestation","attest_author":"https://pith.science/pith/FBAOIJM3SQTRSVJA2WGCIPSEZV/action/author_attestation","sign_citation":"https://pith.science/pith/FBAOIJM3SQTRSVJA2WGCIPSEZV/action/citation_signature","submit_replication":"https://pith.science/pith/FBAOIJM3SQTRSVJA2WGCIPSEZV/action/replication_record"}},"created_at":"2026-07-05T10:38:06.267061+00:00","updated_at":"2026-07-05T10:38:06.267061+00:00"}