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In the Bruck-Bose representation of PG(2,q^3) in PG(6,q), we investigate the interaction between the ruled surface corresponding to B and the planes corresponding to the tangent splash of B. We then give a geometric construction of the unique order-$q$-subplane determined by a given tangent splash and a fixed order-$q$-subline."},"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":"1305.6674","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-29T02:13:21Z","cross_cats_sorted":[],"title_canon_sha256":"ff57fcb62060c505fe40f725d390597b9b2380adf2d74b61664d8983cd0dbebc","abstract_canon_sha256":"2c1d086b4dabf8e0b9dbe54d8d902d23a7af6b082af4d37dfc17dd61471fcb5e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:22:18.128072Z","signature_b64":"mRNlob7bcputZWIlBchznXYXghrvN4MBSpjGNkg2oy1X5k0QJeHf/Iz+UEGc0RNdCqDPzT8oOe89MSHlMgyNCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72082e07706d0669bf88669295f184ea867893d845133c27d69bd4923c49a5fb","last_reissued_at":"2026-05-18T03:22:18.127613Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:22:18.127613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The tangent splash in $\\PG(6,q)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"S.G. 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