{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:N6DJGALK7BV36LAX7FO7YO4DQB","short_pith_number":"pith:N6DJGALK","canonical_record":{"source":{"id":"1805.09984","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-25T05:40:09Z","cross_cats_sorted":[],"title_canon_sha256":"789c636bfe31b16ee6a4e528c42bbf0c7b6ff684e0c1a9c96f76bc2f77635f32","abstract_canon_sha256":"b61ea790cb31b22331173ea29cabedafed3c930a19ba6848c69175f8d762d7ae"},"schema_version":"1.0"},"canonical_sha256":"6f8693016af86bbf2c17f95dfc3b83806827f340b8ba413c325f3ef48ff748f0","source":{"kind":"arxiv","id":"1805.09984","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.09984","created_at":"2026-05-17T23:42:35Z"},{"alias_kind":"arxiv_version","alias_value":"1805.09984v1","created_at":"2026-05-17T23:42:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09984","created_at":"2026-05-17T23:42:35Z"},{"alias_kind":"pith_short_12","alias_value":"N6DJGALK7BV3","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"N6DJGALK7BV36LAX","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"N6DJGALK","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:N6DJGALK7BV36LAX7FO7YO4DQB","target":"record","payload":{"canonical_record":{"source":{"id":"1805.09984","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-25T05:40:09Z","cross_cats_sorted":[],"title_canon_sha256":"789c636bfe31b16ee6a4e528c42bbf0c7b6ff684e0c1a9c96f76bc2f77635f32","abstract_canon_sha256":"b61ea790cb31b22331173ea29cabedafed3c930a19ba6848c69175f8d762d7ae"},"schema_version":"1.0"},"canonical_sha256":"6f8693016af86bbf2c17f95dfc3b83806827f340b8ba413c325f3ef48ff748f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:35.105472Z","signature_b64":"fN6EXHm8J3u39Uo6TiJTGi2e3Exp2hmibNytv2bhnqPAbnq8+2s0MHT+pKuFfMHAXUXMdnCARBxvrByG6LXJBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f8693016af86bbf2c17f95dfc3b83806827f340b8ba413c325f3ef48ff748f0","last_reissued_at":"2026-05-17T23:42:35.104733Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:35.104733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.09984","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":"2026-05-17T23:42:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SIfwVgkYnDPg6zzf0WJp7ZgPdkf/IzXukj++SnFq2e+NIIiwI8Rfb2NHeTX98BVwfz7jnmso97DDhWhPhd2JDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:01:29.231740Z"},"content_sha256":"49764bc58079134bc7cb73e9209d0bb879536b568ff1a83e7702d5ffe54a43cd","schema_version":"1.0","event_id":"sha256:49764bc58079134bc7cb73e9209d0bb879536b568ff1a83e7702d5ffe54a43cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:N6DJGALK7BV36LAX7FO7YO4DQB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inherited conics in Hall planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aart Blokhuis, G\\'abor P. Nagy, Istv\\'an Kov\\'acs, Tam\\'as Sz\\H{o}nyi","submitted_at":"2018-05-25T05:40:09Z","abstract_excerpt":"The existence of ovals and hyperovals is an old question in the theory of non-Desarguesian planes. The aim of this paper is to describe when a conic of ${\\rm PG}(2,q)$ remains an arc in the Hall plane obtained by derivation. Some combinatorial properties of the inherited conics are obtained also in those cases when it is not an arc. The key ingredient of the proof is an old lemma by Segre-Korchm\\'aros on Desargues configurations with perspective triangles inscribed in a conic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09984","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":"2026-05-17T23:42:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yvgoBaGy+7pCZKYX9hkc6NO4xiQtPxqG0Za4/TZdoQYR+1NYP/v3IS8TCG7uKdpBFE7E9C1ojoLPCKze/Cj2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:01:29.232175Z"},"content_sha256":"66671b8efdef21c2630877d4d0573784cccb063ccf9a6e9d835d3c43cbf1d223","schema_version":"1.0","event_id":"sha256:66671b8efdef21c2630877d4d0573784cccb063ccf9a6e9d835d3c43cbf1d223"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N6DJGALK7BV36LAX7FO7YO4DQB/bundle.json","state_url":"https://pith.science/pith/N6DJGALK7BV36LAX7FO7YO4DQB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N6DJGALK7BV36LAX7FO7YO4DQB/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":"2026-05-25T19:01:29Z","links":{"resolver":"https://pith.science/pith/N6DJGALK7BV36LAX7FO7YO4DQB","bundle":"https://pith.science/pith/N6DJGALK7BV36LAX7FO7YO4DQB/bundle.json","state":"https://pith.science/pith/N6DJGALK7BV36LAX7FO7YO4DQB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N6DJGALK7BV36LAX7FO7YO4DQB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:N6DJGALK7BV36LAX7FO7YO4DQB","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":"b61ea790cb31b22331173ea29cabedafed3c930a19ba6848c69175f8d762d7ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-25T05:40:09Z","title_canon_sha256":"789c636bfe31b16ee6a4e528c42bbf0c7b6ff684e0c1a9c96f76bc2f77635f32"},"schema_version":"1.0","source":{"id":"1805.09984","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.09984","created_at":"2026-05-17T23:42:35Z"},{"alias_kind":"arxiv_version","alias_value":"1805.09984v1","created_at":"2026-05-17T23:42:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09984","created_at":"2026-05-17T23:42:35Z"},{"alias_kind":"pith_short_12","alias_value":"N6DJGALK7BV3","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"N6DJGALK7BV36LAX","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"N6DJGALK","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:66671b8efdef21c2630877d4d0573784cccb063ccf9a6e9d835d3c43cbf1d223","target":"graph","created_at":"2026-05-17T23:42:35Z","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":"The existence of ovals and hyperovals is an old question in the theory of non-Desarguesian planes. The aim of this paper is to describe when a conic of ${\\rm PG}(2,q)$ remains an arc in the Hall plane obtained by derivation. Some combinatorial properties of the inherited conics are obtained also in those cases when it is not an arc. The key ingredient of the proof is an old lemma by Segre-Korchm\\'aros on Desargues configurations with perspective triangles inscribed in a conic.","authors_text":"Aart Blokhuis, G\\'abor P. Nagy, Istv\\'an Kov\\'acs, Tam\\'as Sz\\H{o}nyi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-25T05:40:09Z","title":"Inherited conics in Hall planes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09984","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":"sha256:49764bc58079134bc7cb73e9209d0bb879536b568ff1a83e7702d5ffe54a43cd","target":"record","created_at":"2026-05-17T23:42:35Z","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":"b61ea790cb31b22331173ea29cabedafed3c930a19ba6848c69175f8d762d7ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-25T05:40:09Z","title_canon_sha256":"789c636bfe31b16ee6a4e528c42bbf0c7b6ff684e0c1a9c96f76bc2f77635f32"},"schema_version":"1.0","source":{"id":"1805.09984","kind":"arxiv","version":1}},"canonical_sha256":"6f8693016af86bbf2c17f95dfc3b83806827f340b8ba413c325f3ef48ff748f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f8693016af86bbf2c17f95dfc3b83806827f340b8ba413c325f3ef48ff748f0","first_computed_at":"2026-05-17T23:42:35.104733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:35.104733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fN6EXHm8J3u39Uo6TiJTGi2e3Exp2hmibNytv2bhnqPAbnq8+2s0MHT+pKuFfMHAXUXMdnCARBxvrByG6LXJBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:35.105472Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.09984","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49764bc58079134bc7cb73e9209d0bb879536b568ff1a83e7702d5ffe54a43cd","sha256:66671b8efdef21c2630877d4d0573784cccb063ccf9a6e9d835d3c43cbf1d223"],"state_sha256":"add372fe5f414f2aadbec22a97c12b063db131b090d1d824c6bb89ba57601a68"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZELro7NqPOuxJHz+4MtpJH198OQIY+c0TYu6AOSFD/U3t97JFCjTO0eSkDzYGyPLRAFdfXL9hDsgsCGMAlVgDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:01:29.235135Z","bundle_sha256":"c44fb42286e32bf4274a8e403a799927a200ef0501781e8f469f0a767e764781"}}