{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:OIEC4B3QNUDGTP4IM2JJL4ME5K","short_pith_number":"pith:OIEC4B3Q","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"},"canonical_sha256":"72082e07706d0669bf88669295f184ea867893d845133c27d69bd4923c49a5fb","source":{"kind":"arxiv","id":"1305.6674","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6674","created_at":"2026-05-18T03:22:18Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6674v1","created_at":"2026-05-18T03:22:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6674","created_at":"2026-05-18T03:22:18Z"},{"alias_kind":"pith_short_12","alias_value":"OIEC4B3QNUDG","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OIEC4B3QNUDGTP4I","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OIEC4B3Q","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:OIEC4B3QNUDGTP4IM2JJL4ME5K","target":"record","payload":{"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"},"canonical_sha256":"72082e07706d0669bf88669295f184ea867893d845133c27d69bd4923c49a5fb","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"},"source_kind":"arxiv","source_id":"1305.6674","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:22:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Uh+DBf2+FrxQ58A7yCFkL9+hH9r5j4EtNU4wgdczbhhi1l49i3ykTiiJKNlV5C7wFHxOuJTEwLZKVMQCAriBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T12:17:07.773575Z"},"content_sha256":"e770c19424f04d385b6bc2d056aa83377663a0228f87717870c1dc9fb444961a","schema_version":"1.0","event_id":"sha256:e770c19424f04d385b6bc2d056aa83377663a0228f87717870c1dc9fb444961a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:OIEC4B3QNUDGTP4IM2JJL4ME5K","target":"graph","payload":{"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. Barwick, Wen-Ai Jackson","submitted_at":"2013-05-29T02:13:21Z","abstract_excerpt":"Let B be a subplane of PG(2,q^3) of order q that is tangent to $\\ell_\\infty$. Then the tangent splash of B is defined to be the set of q^2+1 points of $\\ell_\\infty$ that lie on a line of B. 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6674","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:22:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uo9cP4ozD4GNIxaS+QN3M2fwN16Yc4pxcZ9saeY48fmG1GO77FTqYKBzi/9U04u6qG5vRHSF40Kqg7wMNHv7AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T12:17:07.773928Z"},"content_sha256":"73189eea3a76fba6ad910129e9d291525b8f6c76819eaf8d99859eac84b4e4ce","schema_version":"1.0","event_id":"sha256:73189eea3a76fba6ad910129e9d291525b8f6c76819eaf8d99859eac84b4e4ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OIEC4B3QNUDGTP4IM2JJL4ME5K/bundle.json","state_url":"https://pith.science/pith/OIEC4B3QNUDGTP4IM2JJL4ME5K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OIEC4B3QNUDGTP4IM2JJL4ME5K/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T12:17:07Z","links":{"resolver":"https://pith.science/pith/OIEC4B3QNUDGTP4IM2JJL4ME5K","bundle":"https://pith.science/pith/OIEC4B3QNUDGTP4IM2JJL4ME5K/bundle.json","state":"https://pith.science/pith/OIEC4B3QNUDGTP4IM2JJL4ME5K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OIEC4B3QNUDGTP4IM2JJL4ME5K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OIEC4B3QNUDGTP4IM2JJL4ME5K","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2c1d086b4dabf8e0b9dbe54d8d902d23a7af6b082af4d37dfc17dd61471fcb5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-29T02:13:21Z","title_canon_sha256":"ff57fcb62060c505fe40f725d390597b9b2380adf2d74b61664d8983cd0dbebc"},"schema_version":"1.0","source":{"id":"1305.6674","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6674","created_at":"2026-05-18T03:22:18Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6674v1","created_at":"2026-05-18T03:22:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6674","created_at":"2026-05-18T03:22:18Z"},{"alias_kind":"pith_short_12","alias_value":"OIEC4B3QNUDG","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OIEC4B3QNUDGTP4I","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OIEC4B3Q","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:73189eea3a76fba6ad910129e9d291525b8f6c76819eaf8d99859eac84b4e4ce","target":"graph","created_at":"2026-05-18T03:22:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let B be a subplane of PG(2,q^3) of order q that is tangent to $\\ell_\\infty$. Then the tangent splash of B is defined to be the set of q^2+1 points of $\\ell_\\infty$ that lie on a line of B. 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.","authors_text":"S.G. Barwick, Wen-Ai Jackson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-29T02:13:21Z","title":"The tangent splash in $\\PG(6,q)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6674","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e770c19424f04d385b6bc2d056aa83377663a0228f87717870c1dc9fb444961a","target":"record","created_at":"2026-05-18T03:22:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2c1d086b4dabf8e0b9dbe54d8d902d23a7af6b082af4d37dfc17dd61471fcb5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-29T02:13:21Z","title_canon_sha256":"ff57fcb62060c505fe40f725d390597b9b2380adf2d74b61664d8983cd0dbebc"},"schema_version":"1.0","source":{"id":"1305.6674","kind":"arxiv","version":1}},"canonical_sha256":"72082e07706d0669bf88669295f184ea867893d845133c27d69bd4923c49a5fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72082e07706d0669bf88669295f184ea867893d845133c27d69bd4923c49a5fb","first_computed_at":"2026-05-18T03:22:18.127613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:22:18.127613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mRNlob7bcputZWIlBchznXYXghrvN4MBSpjGNkg2oy1X5k0QJeHf/Iz+UEGc0RNdCqDPzT8oOe89MSHlMgyNCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:22:18.128072Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.6674","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e770c19424f04d385b6bc2d056aa83377663a0228f87717870c1dc9fb444961a","sha256:73189eea3a76fba6ad910129e9d291525b8f6c76819eaf8d99859eac84b4e4ce"],"state_sha256":"581d9f8168e3856635a463b59f4aaff1c75655f4500c60742eab73f2a6c6a3b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mhosObZJE2vBiUImG/A11tI1TSgTJy09LiBRWGNFNQE1m2ieCIYQA8Cu582OoTtvU3yGJNV5BYJ+eddzsaYbCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T12:17:07.775973Z","bundle_sha256":"8c1ac6ba4832dd0d64dac60c64aac57d35baddbcbd7f25e6883224169fb610ce"}}